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followed by an FFT along time. Subsequently, the Hanning filter (
= 0.66) was applied and gridding onto

Cartesian coordinate and applying a 2D spatial inverse FFT were performed. Metabolite maps of pyruvate,

pyruvate-hydrate, lactate, and bicarbonate were generated by integrating the corresponding metabolite

peaks in the absorption mode spectra, and normalized to the total 3

C map, which is sum of pyruvate,

pyruvate-hydrate, lactate, and bicarbonate maps to compensate the spatial heterogeneity in HP pyruvate

delivery and 13C receive profile. The final axial metabolite maps were overlaid on the corresponding 1

H

MRI for anatomical reference.

For quantitative assessment of each brain metabolite, spectra were averaged over selected regions

of interest (ROIs) before integrating individual peaks. Two regions of interest (ROIs) were selected; one in

injured brain region (ROI) and another brain ROI in the contralateral hemisphere (ROI ). Each

metabolite was separately reconstructed and phase was corrected up to 1st order for display of the

reconstructed spectra. Each metabolite was normalized to the sum of total 13C-labeled metabolite (TC)

signal.

ppe

enta e

erenes

Ma, ., Hashoian, R.S., Sun, C., *right, S.M., Ivanishev, A., Lenkinski, R.E., Malloy, C.R., Chen, A.P.,

Park, .M., 2019. Development of 1H/13C RF head coil for hyperpolarized 13C imaging of human

brain, Presented at the International Society of Magnetic Resonance in Medicine, Montreal, Canada,

568.

Park, .M., osan, S., ang, T., Merchant, M., +en, +.-F., Hurd, R.E., Recht, L., Spielman, D.M., Mayer,

D., 2012. Metabolite kinetics in C6 rat glioma model using magnetic resonance spectroscopic imaging

of hyperpolarized [1-(13)C]pyruvate. Magn Reson Med 68, 1886H1893. doi:10.1002/mrm.24181

Park, .M., Liticker, ., Harrison, C.E., Reed, G.D., Hever, T., Ma, ., Martin, R., Mayer, D., Hashoian,

R.S., Madden, C.., Pinho, M., Malloy, C.R., 2019. Feasibility and reproducibility of imaging brain

metabolism using hyperpolarized 13C pyruvate in humans, Presented at the International Society of

Magnetic Resonance in Medicine, Montreal, Canada, 4311.

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技術(shù)方法篇

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Spatio-Temporally Constrained Reconstruction for Hyperpolarized Carbon-13 MRI Using

Kinetic Models

研究背景

研究過程簡介

研究對象

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研究結(jié)論

應用方向

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????????????????????? ??研??????????????????????????

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EPI (A) ? EPSI (B) 研????? 1H MRI ? 13C kPL ????????? ??????? kPL ????????????

?????? ?????? MRI ????????? T2 ???????? ADC ???????? ???????

???? kPL ??????????????????????????????

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IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 37, NO. 12, DECEMBER 2018 2603

Spatio-Temporally Constrained Reconstruction

for Hyperpolarized Carbon-13 MRI

Using Kinetic Models

John Maidens , Jeremy W. Gordon, Hsin-Yu Chen, Ilwoo Park, Mark Van Criekinge, Eugene Milshteyn,

Robert Bok, Rahul Aggarwal, Marcus Ferrone, James B. Slater, John Kurhanewicz,

Daniel B. Vigneron, Murat Arcak , and Peder E. Z. Larson

Abstract—We present a method of generating spatial

maps of kinetic parameters from dynamic sequences of

images collected in hyperpolarized carbon-13 magnetic resonance imaging (MRI) experiments. The technique exploits

spatial correlations in the dynamic traces via regularization

in the space of parameter maps. Similar techniques have

proven successfulin other dynamic imaging problems, such

as dynamic contrast enhanced MRI. In this paper, we apply

these techniques for the first time to hyperpolarized MRI

problems, which are particularly challenging due to limited

signal-to-noise ratio (SNR). We formulate the reconstruction

as an optimization problem and present an efficient iterative

algorithm for solving it based on the alternation direction

method of multipliers. We demonstrate that this technique

improves the qualitative appearance of parameter maps

estimated from low SNR dynamic image sequences, first

in simulation then on a number of data sets collected in

vivo. The improvement this method provides is particularly

pronounced at low SNR levels.

Index Terms—Parameter estimation, linear systems,

inverse problems, optimization, magnetic resonance

imaging (MRI), carbon, molecular imaging.

Manuscript received March 18, 2018; revised May 25, 2018;

accepted May 30, 2018. Date of publication June 5, 2018; date of

current version November 29, 2018. This work was supported in part

by NSF under Grant ECCS-1405413 and in part by NIH under Grants

R01EB017449, R01CA166655, and P41EB013598. (Corresponding

author: John Maidens.)

J. Maidens is with the Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, ON M5B 2K3, Canada (e-mail:

johnmaidens@gmail.com).

J. W. Gordon, H.-Y. Chen, M. Van Criekinge, E. Milshteyn, R. Bok,

J. B. Slater, J. Kurhanewicz, D. B. Vigneron, and P. E. Z. Larson are

with the Department of Radiology and Biomedical Imaging, University of

California at San Francisco, San Francisco, CA 94158 USA.

I. Park is with the Department of Radiology, Chonnam National University Medical School, Gwangju 61469, South Korea.

R. Aggarwal is with the Department of Medicine, University of California

at San Francisco, San Francisco, CA 94115 USA.

M. Ferrone is with the Department of Clinical Pharmacy, University of

California at San Francisco, San Francisco, CA 94158 USA.

M. Arcak is with the Department of Electrical Engineering and

Computer Sciences, University of California at Berkeley, Berkeley,

CA 94720 USA.

Color versions of one or more of the figures in this paper are available

online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMI.2018.2844246

I. INTRODUCTION

MAGNETIC resonance imaging (MRI) using hyperpolarized carbon-13 labeled substrates has made it possible

to probe metabolism in vivo with chemical specificity [1], [2].

This technique is increasingly being applied in the clinic,

allowing researchers to investigate metabolic conditions ranging from prostate cancer [3] to heart disease [4]. In particular, experiments studying the conversion of hyperpolarized

[1-13C]pyruvate to [1-13C]lactate are common, as the rate of

conversion is upregulated in many cancers, a phenomenon

known as the Warburg effect.

MRI using hyperpolarized carbon-13 is challenging due

to the dynamic nature of the data collected, the low signalto-noise ratio (SNR), and the difficulty of presenting large

data sets consisting of dynamic spectroscopic images in an

interpretable manner. Metabolism mapping by estimating parameters in a kinetic model from hyperpolarized MRI data

has been shown to be useful for overcoming a number

of these challenges [5]. Constraining the time evolution of

signal in a given voxel to follow a kinetic model has been

shown to allow map reconstruction from noisy, undersampled

dynamic images, and to reduce the number of signal-depleting

excitations required to generate images. Parameter mapping

also facilitates interpretation of dynamic image data by summarizing spatial, temporal and chemical (i.e. chemical shift

spectrum) information in a single spatial map.

Parameter maps are naturally a form of constrained reconstruction, as they constrain the data to lie on a manifold

of trajectories of the dynamical system parametrized by the

system’s parameters. This constrained reconstruction reduces

the sequence of dynamic images to a single map by exploiting

temporal correlations within the dynamic imaging data. In this

paper, we demonstrate that we can exploit spatial correlations in addition to temporal correlations by integrating prior

information about the parameter map through regularization.

Similar approaches have proven useful recently in the context

of pharmacokinetic parameter mapping in dynamic contrast

enhanced and cardiac perfusion MRI [6]–[12]. To our knowledge, this is the first time this family of spatial regularization

techniques have been used in hyperpolarized MRI, where they

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See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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2604 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 37, NO. 12, DECEMBER 2018

are particularly beneficial due to the challenges of working

with low SNR images.

This paper is organized as follows. In Section II we introduce background on modelling hyperpolarized 13C MRI data

and existing approaches to parameter mapping. In Section III

we introduce a framework for spatially-constrained parameter mapping to exploit spatial correlations in the data.

In Section IV we present an algorithm for efficient inference

in this framework. In Section V we present the results of simulation experiments where we demonstrate the effectiveness

of the method. In Section VI we then apply the method to a

collection of clinically-relevant data sets. Finally, Section VII

concludes the paper and briefly discusses potential extensions

of this work.

Preliminary results from this paper were presented at

the 2017 Annual Meeting of the International Society of

Magnetic Resonance in Medicine [13].

II. BACKGROUND

A. Data Model

We model the dynamic evolution of the data Yi collected from a single voxel i using a dynamic model for a

two-dimensional state x(t) = [x1(t) x2(t)]

T :

dx

dt (t) =

!

?kP L ? R1P 0

kP L ?R1L

"

x(t) +

!

kT RANS

0

"

u(t).

(1)

This system of ordinary differential equations (ODEs) has

been widely used to model the uni-directional conversion of

an injected substrate (pyruvate, in this case) to a metabolic

product (lactate, in this case) [14]. The state x1(t) models

the longitudinal magnetization in the substrate pool, and

the state x2(t) models the longitudinal magnetization in the

product pool. The parameter kP L describes the rate at which

the substrate is metabolized, the parameter kT RANS describes

the rate at which the substrate is taken up by the tissue, and the

parameters R1P and R1L are lumped parameters that account

for T1 magnetization decay, metabolism of the substrate into

unmeasured products and flow of substrate out of the voxel.

Measurements are collected at a sequence of times

{t1,...,tN }. Neglecting the effect of the input between tk

and tk+1, integrating this continuous-time dynamic model

and incorporating the effect of repeated radio-frequency (RF)

excitation leads to a discrete-time model for the magnetization

at acquisition times tk of the form

L?(k + 1) = e?R1L!t cos(αL (k))L?(k)

? kP L

e?(R1P+kP L )!t ? e?R1L!t

R1P ? R1L + kP L

cos(αP(k))P(k).

(2)

This gives a statistical model that describes the evolution of

the predicted lactate signal L?(k) = x2(tk ) as a function of the

measured pyruvate signal P(k) = x1(tk ) and the flip angles

αP and αL applied to the pyruvate and lactate compartments.

The predicted lactate is assumed to be L?(0) = 0 at the

beginning of the experiment.

For the purpose of generating simulated data, the data

measured at each time tk are assumed to be independent and

follow a bivariate normal distribution with mean δx δyδzx(tk )

and covariance σ2 I where I denotes the 2 × 2 identity

matrix and δx , δy and δz describe the image resolution and

slice thickness. We collect the time series data collected from

voxel i into a matrix Yi =

!

P(1) ··· P(N)

L(1) ··· L(N)

"

and denote the

unknown parameters to be estimated from the data θi = kP L.

B. Voxel-Wise Parameter Estimation

Given a collection of data Yi from a voxel i we wish to

generate an estimate of the parameter θi that describes the

tissue in that voxel. We assume that θi lies in a parameter

space &. We consider the class of “M-estimators” [15] that

minimize a loss function

θ?

i ∈ argmin

θ∈&

'(θi|Yi).

In the present paper, we consider the nonlinear least squares

loss function

'(θi|Yi) = $Yi ? Y?

i(θi)$F (3)

where Y? =

!

P(1) ... P(N)

L?(1) ... L?(N)ξ

"

denotes the predicted signal

given the pyruvate time series and $·$F denotes the Frobenius

norm (i.e. the '2 norm of the vectorized matrix). Under the

assumption that the data collected are normally-distributed

with mean proportional to x(tk ), independent with identical

variance, the minimum of this nonlinear least squares loss

is also the maximum likelihood estimate of the parameter

vector. While we consider only this loss in the present paper,

the results are applicable generally to any computationally

tractable loss function.

III. CONSTRAINED PARAMETER MAPPING

In order to incorporate prior information about the spatial

distribution of metabolic rates and exploit spatial correlations

within the data, we constrain the maps to have a desired

structure through regularization. This results in an optimization

problem in Lagrangian form

minimize#

i∈V

'(θi|Yi) + λr(θ) (4)

where θ = (θi)i∈V denotes the map of parameters across all

voxels, r is a regularization term, and λ denotes a Lagrange

multiplier that can be tuned in order to achieve the desired

regularization strength. The choice of an appropriate regularizer depends on the desired features of the parameter

map. Common choices include Tikhonov ('2) regularization,

'1 regularization, and total variation regularization. We briefly

summarize these three methods below.

Tikhonov regularization, or '2 regularization penalizes the

size of the parameters θi . It involves adding a quadratic penalty

term

r(θ) = $θ$2

2

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MAIDENS et al.: SPATIO-TEMPORALLY CONSTRAINED RECONSTRUCTION FOR HYPERPOLARIZED CARBON-13 MRI 2605

where ! · !2 denotes the ordinary Euclidean norm. For linear

regression problems with orthogonal covariates, this regularization leads to uniform shrinkage of the estimates [16].

For the nonlinear parameter mapping problems we consider

here, using Tikhonov regularization helps to suppress large

parameter values in the unperfused “background” region.

!1 regularization is another shrinkage method that penalizes

parameters based on their !1 norm

r(θ) = !θ!1.

This method induces sparsity in the resulting parameter maps,

and hence also helps to suppress parameter values in the

background region. It is closely-related to basis pursuit denoising [17] and lasso regression [18].

Total variation (TV) regularization is another method commonly used for image denoising [19]. In this paper, we use an

anisotropic total variation regularization term given by

r(θ) = !?θ!1 := !

(i,j)∈N

|θi ? θ j|

where ? denotes a discrete differencing operator and N

denotes the set of all neighbouring voxels. As all applications

we consider in this paper we consider three-dimensional

images, the neighbourhood N consists of the six voxels j

immediately adjacent to the voxel i. Anisotropic total variation

is chosen due to the availability of numerical packages for

extremely fast computation of proximity operators via the

proxTV package [20], [21]. TV regularization is known to

preserve edges and large-scale structure in images while

rejecting noise [22], resulting in natural-looking reconstructed

images.

IV. ITERATIVE ALGORITHMS FOR CONSTRAINED

PARAMETER MAPPING

A naive algorithm for solving this optimization problem

by directly optimizing the objective function (4) would be

inefficient because it involves solving a joint optimization over

all {θi : i ∈ V}. Thus the computation time required to directly

solve the optimization problem increases dramatically with

matrix size, making naive approaches inefficient even for the

images of moderate resolution considered here. To solve the

optimization problem more efficiently, we can take advantage

of the particular structure of the problem using the ADMM

algorithm.

The alternating direction method of multipliers (ADMM)

is an iterative optimization algorithm that is well-suited to

efficiently solving such problems that can be decomposed into

a sum of two terms [23]. In contrast with other distributed

optimization algorithms, the ADMM algorithm is particularly

well-suited to the problem formulated in this paper as it

splits the required optimization into the sum of a set of

loss functions ! that are complex to optimize, but can be

optimized independently for each voxel, and a regularization r

that is relatively simple but high-dimensional as it couples

a large number of neighboring voxels. By exploiting this

decomposition, ADMM allows the optimization problem to be

solved efficiently. The general problem that ADMM attempts

to solve is an optimization problem of the form

minimize f (x) + g(z)

subject to Ax + Bz = c. (5)

The algorithm does so by iteratively applying the updates

xk+1 = argmin x

"

f (x) + ρ

2

!Ax ? Bzk ? c + uk!2

2

#

zk+1 = argmin z

"

g(z) + ρ

2

!Axk+1 ? Bz ? c + uk!2

2

#

uk+1 = uk + Axk+1 + Bzk+1 ? c.

Under the assumption that f and g are closed, proper, convex

functions and that the Lagrangian

L(x,z, λ) = f (x) + g(z) + λT (Ax + Bz ? c)

has a saddle point, it can be shown [23] that the residuals r k =

Axk + Bzk ? c converge to zero and the values f (xk ) + g(zk)

converge to the optimal value of the problem (5).

A. ADMM for Iterative Parameter Mapping

To solve (4) we transform the problem to a form amenable

to the ADMM algorithm by introducing a new variable z = θ

and solving

minimize !

i∈V

!(θi|Yi) + λr(z)

subject to θ ? z = 0. (6)

The ADMM iteration is then given as

θ k+1 = argmin

θ

!

i∈V

!(θi|Yi) + ρ

2

!θ ? zk + uk!2

2

zk+1 = argmin zλr(z) + ρ

2

!θ k+1 ? z + uk!2

2

uk+1 = uk + θ k+1 ? zk+1.

This method is sometimes known as Douglas-Rachford splitting [24]. Note that the θ update is additively separable.

Introducing the proximity operator

prox f (x) = argmin u

f (u) +

1

2

!u ? x!2

2

we can re-write this iteration as

θ k+1

i = prox 1

ρ !(·|Yi)

(zk

i ? uki ) i ∈ V

zk+1 = prox λ

ρ r(θ k+1 + uk )

uk+1 = uk + θ k+1 ? zk+1.

Here, the θi updates can be performed independently for each

i ∈ V, significantly decreasing time and memory required for

computation and allowing the parallelization of this step.

Note that for the particular choice of loss function given

in Section III, !(·|Yi) are nonconvex functions and thus the

formal convergence guarantees do not apply. Despite this

fact, we have seen in all the experimental instances of the

problem we have considered that the algorithm converges to

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2606 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 37, NO. 12, DECEMBER 2018

Fig. 1. Slice through z = 0 of a 16 × 16 × 16 voxel 3D dynamic

phantom. (a) kTRANS map. (b) kPL map

a sensible optimum robustly for a variety of initializations.

In what follows, we use the modified Levenberg-Marquardt

algorithm [25] implemented in MINPACK [26] to solve

the nonlinear least squares problem corresponding to the θ

update step in the ADMM iteration, and for the unregularized

estimation.

V. SIMULATED RESULTS AND DISCUSSION

To demonstrate the effectiveness of this method, we perform

a sequence of experiments on simulated data. We begin with

an experiment using a simple numerical phantom designed to

test the robustness of metabolic parameter mapping methods

to differences in perfusion, as well as their ability to reliably

resolve large and small features.

A. Reconstruction at a Variety of Noise Levels

To generate simulated data for validating our algorithm,

we simulate trajectories for each voxel of the 16 × 16 × 16

dynamic phantom described shown in Figure 1. This phantom

describes maps of the kT RANS and kP L parameters and is

designed to test an algorithm’s ability to resolve both large and

small features under high and low perfusion conditions. More

details about the phantom can be found in [27, Sect. 5.5]. The

data are generated according to the model (1) with arterial

input u(t) = kT RANS A0(t ? t0)γ e(?(t?t0)/β) added to the

pyruvate compartment, and states scaled by cos(αP/L (k)) and

measured outputs scaled by sin(αP/L(k)) each time that simulated data are collected, where αP/L(k) is a spectrally-selective

flip angle applied to spins in the P or L compartment during

acquisition k. An optimized dynamic flip angle sequence based

on the method of [28] is used for the simulation, and shown

in Figure 2. This same flip angle sequence is also used for a

majority of the in vivo experiments.

We then add independent, identically-distributed (iid)

Gaussian noise at a variety of SNR levels, measured based

on the SNR in the lactate channel corresponding to the peak

lactate level. Simulated time series and image data are shown

in Figure 3.

For SNR levels of 8, 4, 2, and 1, we fit the model (2)

to the data using the loss function (3) and the regularization

r(θ) = λ1#?θ#1 + λ2#θ#2

2 with λ1 =1e06 and λ2 =1e08.

A combination of &2 and TV regularization was chosen

because the &2 penalty prevents estimation bias in the unperfused region while the TV penalty encourages smooth maps

Fig. 2. Dynamic flip angle sequence used for experimental validation

Fig. 3. Simulated data generated at a maximum lactate SNR level of 2.

(a) Sample time series data from a high kTRANS, high kPL voxel.

(b) Pyruvate image slice through z = 0. (c) Lactate image slice

through z = 0.

with well-defined tissue boundaries. The values of λ1 and λ2

are selected such that the total absolute error is minimized

(see Section V-B). Before fitting, the simulated data are scaled

by 1/ sin(αP/L(k)) to counteract the effect of the time-varying

flip angle sequence. In Figure 4 we compare the results of this

constrained fit against two competing methods: independent

voxel-wise fit (equivalent to our method with λ1 = λ2 = 0)

and independent voxel-wise fit followed by anisotropic total

variation denoising of the resulting parameter map. We see that

the constrained reconstruction allows accurate parameter maps

to be generated in high noise regimes where the competing

methods have difficulty. In particular, the baseline method of

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Fig. 4. Results of simulated kPL mapping experiment for various values

of the maximum lactate image SNR

Fig. 5. Total absolute estimation error for kPL for various values of the

regularization parameters λ1 and λ2.

unconstrained mapping followed by denoising performs poorly

in unperfused areas where it is attempting to fit parameter

values to pure noise. In contrast, the constrained fit is able to

suppress noise in the unperfused region via !2 regularization.

B. Quantitative Improvements

In addition to the qualitative benefits of spatial regularization demonstrated in the previous section, regularization

can also lead to quantitative improvements in the estimates

of dynamic parameters. In simulation experiments where we

have access to the ground truth values of the model parameters,

we can quantify the improvement in estimates θ? of θ via the

total absolute error

!θ? ? θ!1 = !

i∈V

|k?P Li ? kP Li |.

In Figure 5 we plot the total absolute error for various values

of the regularization parameters λ1 and λ2. This experiment

was performed using the 16×16×16 phantom from Figure 1

with a maximum lactate SNR value of 2.0. We see that small

values of λ1 and λ2 lead to larger quantitative errors in the

parameter maps than the optimized values λ1 =1e06 and

λ2 =1e08 used in the previous section. Note that the optimal

values will depend on a number of factors potentially including

the geometry and sparsity of the phantom, and the noise

distribution, SNR and signal amplitude in the dynamic images.

Thus by appropriately choosing λ1 and λ2, we can achieve

quantitative improvements in the parameter map in addition to

the qualitative improvements we have already demonstrated.

VI. IN VIVO RESULTS AND DISCUSSION

We now move on to experiments on a number of datasets

collected in vivo. In contrast to the simulation experiments,

we no longer have access to ground truth values of the

model parameters to make quantitative comparisons. However,

we will use the in vivo experiments to demonstrate that the

spatially-constrained parameter mapping technique leads to

qualitative improvements in the parameter maps.

We begin with an experiment in healthy rats where we

can collect high SNR data. For these data, we add artificial

noise to demonstrate how the spatially-constrained parameter

mapping technique can be used to allow reconstruction in

low SNR regimes, for realistic anatomies. We then apply

this technique to the analysis of a number of low SNR

clinical datasets collected in prostate cancer patients. These

experiments demonstrate that spatio-temporally constrained

kinetic modelling can be used to generate improved metabolic

parameter maps from low SNR experimental data.

A. High SNR Rat Kidney Data Analysis

We begin by analyzing a metabolic dataset acquired

in healthy Sprague-Dawley rats on a 3T MRI scanner

(MR750, GE Healthcare). 2.5mL of 80mM hyperpolarized [1-

13C]pyruvate was injected over 15s, and data acquisition coincided with the start of injection. Metabolites from a single slice

were individually excited with a singleband spectral-spatial RF

pulse and encoded with a single-shot EPI readout [29], an

in-plane resolution of 3 x 3mm, a 15mm slice thickness

centered on the kidneys, and a 2s sampling interval. The

resulting dynamic image sequences are relatively high SNR

with Rician noise resulting from magnitude images, are shown

in Figure 6.

In Figure 7 we compare a spatially constrained fit of the

data against an independent voxel-wise fit. The voxel-wise

fit is masked to only show kP L fit in the highly perfused

regions where the total area under the pyruvate curve (AUC)

is greater than 2e04. We see that the constrained fit leads

to more smoothly-varying maps. Additionally, the Tikhonov

regularization helps alleviate problems with artificially high

kP L estimates in the background region and tissues with low

perfusion, a common problem with kP L mapping from Riciandistributed data. This leads to more realistic kP L values in the

intestinal tissue proximal to the kidneys without significantly

affecting the kP L estimates in the kidney voxels, and also

removes the need to mask the images to the high perfusion

region.

To investigate the robustness of this technique to noise,

we perform a sequence of experiments in which artificial

iid Gaussian noise of varying strengths is added to the

in vivo data using Python’s numpy.randn random number

generator before fitting kP L . The random number generator is

seeded explicitly using numpy.random.seed(0) to ensure

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2608 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 37, NO. 12, DECEMBER 2018

Fig. 6. Dynamic metabolite images collected in the healthy rat experiment. Maximum lactate SNR in these images is 21.1. (a) Sample time

series data from high lactate SNR voxel. (b) Pyruvate image at time

t = 50 s. (c) Lactate image at time t = 50 s.

Fig. 7. Comparison of unconstrained and constrained kPL maps fit

to the healthy rat dataset. (a) Independent voxel-wise fit masked to

region with pyruvate AUC > 2e04. (b) Independent voxel-wise fit without

masking exhibits high kPL values in the background region. (c) Spatiallyconstrained fit with λ1 = 1e07 and λ2 = 1e10. (d) Scatterplot of

constrained and unconstrained kPL fits.

reproducibility. This allows us to replicate the results of

Figure 4 with more realistic anatomy. We see in Figure 8

that qualitatively, the spatially-constrained fit is more robust

Fig. 8. Comparison of kPL maps at various artificial noise levels. Noise

level is measured based on maximum lactate SNR over the time and

space dimensions in the dynamic images. Regularization parameters

used for the constrained fits are chosen to be the same as in Figure 7.

(a) Raw maps. (b) Difference maps using reconstruction without added

noise as baseline.

Fig. 9. Comparison of kPL maps for varying spatial resolutions. Raw data

is downsampled to the appropriate matrix size prior to fitting parameter

maps for the independent voxel-wise and spatially-constrained fits.

to strong noise than the independent fit. Further, we see

in Figure 9 that spatially-constrained parameter mapping

outperforms a baseline of simply downsampling the raw image

sequence.

B. Human Prostate Cancer Data Analysis

To demonstrate feasibility of this technique on clinicallyrelevant data, we have analyzed two prostate cancer datasets

collected during clinical experiments at UCSF. These datasets

were chosen because they had relatively low SNR compared to

our typical prostate cancer studies, and thus would potentially

benefit the most from this approach.

Imaging was performed using a 3T GE scanner using a

abdominal clamshell 13C transmission coil and an endo-rectal

receive coil. The injected solution consisted of 220-260 mM

[1-13C]-pyruvate at a dose of 0.43 mL/kg. Dissolution DNP

was performed using a 5T SpinLab polarizer (GE Healthcare).

Before injection the electron paramagnetic agent is filtered out,

and automated pH, temperature, polarization, volume and EPA

concentration tests were performed.

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Fig. 10. Sample of raw EPI data collected in a prostate cancer patient.

(a) Time series data at pyruvate and lactate frequencies corresponding

to the voxel indicated in red. (b) Lactate data from 8 of the 16 slices at

the time of the final acquisition t = 42 seconds from the start of injection.

Images were encoded using two techniques. One set of

images labeled “EPI” were collected using a spectrallyselective excitation with an echo-planar (EPI) readout [29].

The other set of images labelled “EPSI” was collected using

a blipped EPSI acquisition with a compressed sensing reconstruction [30].

Raw space/time/chemical data reconstructed from the EPI

acquisition are shown in Figure 10. The raw data are rather

noisy and also difficult to interpret for metabolic activity due

to 3D spatial, temporal and chemical dimensions.

We fit 3D kP L parameter maps to the data using the

constrained reconstruction method. Regularization strengths λ1

and λ2 are selected manually based on the qualitative appearance of the parameter maps. Due to the quick parameter map

estimation enabled by the parallelized ADMM iteration, it is

possible to perform this hyperparameter exploration relatively

efficiently. In Figure 11 we compare the resulting parameter

maps for a variety of values for the regularization parameters

λ1 and λ2. The results suggest that we should choose λ1

large enough that the images do not appear noisy, but small

enough that the signal does not disappear, and choose λ2

large enough to suppress the bias in the unperfused region

Fig. 11. Constrained estimates of the kPL paramater with different

regularization strengths compared on a single slice from the 3D EPI

human prostate cancer dataset.

Fig. 12. L-curve analysis for the 3D EPI human prostate cancer dataset.

The residual !!(θi

|Yi) is plotted against the regularizer r(θ) for various

values of λ1 and λ2. (a) L-curve for λ1 for fixed λ2 = 1e09. (b) L-curve

for λ2 for fixed λ1 = 2e05.

but small enough that it does not cause too much shrinkage in

the perfused region. Figure 12 shows L-curves for the choice

of λ1 and λ2, providing an alternative quantitative method

of choosing parameters. We see that for very low or very

high values of the regularization parameters, the regularization

and residual terms cluster at the top left and bottom right

of the figures respectively. Regularization parameter values

approximately midway between the two clusters correspond to

the qualitatively good parameter choices found in Figure 11.

Additionally, in Figures 13 and 14 we compare unconstrained

and constrained fits on the dataset from the EPI and EPSI

acquisitions. The fits are overlaid on 1H images of the anatomy

using SIVIC [31]. The unconstrained fit is masked to voxels

with a minimum pyruvate SNR due to fitting instability with

low pyruvate signals, whereas this is not necessary for the

constrained fit. We see that with an appropriate choice of regularization, we can recover qualitatively satisfying parameter

maps for a variety of datasets. Note that the regularization

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2610 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 37, NO. 12, DECEMBER 2018

Fig. 13. Comparison of unconstrained and constrained kPL maps fit to the 3D EPI data set overlaid on proton images of the prostate anatomy.

Maps are plotted for four slices through the prostate with high lactate signal. This patient had biopsy proven cancer in the left base and midgland

(Gleason 3+3 and 3+4), which is consistent with the results seen in the spatially-constrained kPL fit. (a) Unconstrained fit (λ1 = λ2 = 0) masked to

the region of high SNR. (b) Spatially-constrained fit (λ1 = 5e04 and λ2 = 1e09).

Fig. 14. Comparison of unconstrained and constrained kPL maps fit to 3D EPSI data overlaid on prostate anatomy. Maps are plotted for five slices

through the prostate with high lactate signal. This patient had extensive bilateral biopsy-proven prostate cancer (Gleason 4+4 and 4+3) involving

the entire prostate. The spatially-constrained fit is consistent with significant bilateral disease, though the high kPL region does not extend all the

way to the prostate apex, likely due to its distance from the endo-rectal 13C RF coil. (a) Unconstrained fit (λ1 = λ2 = 0) masked to the region of

high SNR. (b) Spatially-constrained fit (λ1 = 2e17 and λ2 = 1e14).

parameters differ significantly between the EPI and EPSI

acquisitions due mainly to the different amplitudes of the

raw dynamic image data. Note that the strong regularization

leads to significant quantitative shrinkage of the kP L estimates.

However, it improves the qualitative indication of the highly

metabolically-active regions and removes noise-like characteristics of the fitting that is primarily due to low pyruvate SNR.

Figure 15 demonstrates how the constrained kPL maps

could be integrated with the multi-parametric 1H MRI into the

clinical workflow to improve tumor localization and visualize

treatment response. Elevated kP L in the prostate regions of

Figures 13, 14 and 15 were consistent with biopsy and

multiparametric (mp)-MRI [32] results. The patient studied

in Figures 13 and 15A had biopsy proven cancer in the left

base and midgland (Gleason 3+3 and 3+4). Their mp-MRI

exam had an associated clear-cut region of reduced T2 signal

and water apparent diffusion coefficient (ADC), and enhanced

uptake and washout on dynamic contrast enhanced (DCE)

MRI in the left posterior peripheral zone of the midgland

with extension across the midline. This is in strong agreement

with the region of high kP L shown with the constrained

mapping in Figures 13 and 15A, which is in the left base

and midgland with some extension across the midline. The

patient studied in Figures 14 and 15B had extensive bilateral

biopsy-proven prostate cancer (Gleason 4+4 and 4+3). mpMRI demonstrated a large volume of prostate cancer involving

the entire prostate, with right, posterior mid gland macroscopic

extracapsular extension and bilateral seminal vesicle invasion.

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MAIDENS et al.: SPATIO-TEMPORALLY CONSTRAINED RECONSTRUCTION FOR HYPERPOLARIZED CARBON-13 MRI 2611

Fig. 15. Multi-parametric 1H MRI and 13C kPL maps for the EPI (A) and EPSI (B) study showing the midgland prostate. Regions of high kPL on

the constrained reconstruction correlated well with biopsy proven aggressive cancer. It also agrees with lesions on multiparameteric MRI, including

T2-weighted, diffusion weighted, and ADC maps (red arrows). In contrast, the lesions are obfuscated by spurious noise on the unconstrained

kPL maps, or require an empirical hard threshold on the pyruvate signal to visualize.

The kP L fitting in Figures 14 and 15B also shows bilateral

regions of high kPL, including the right, posterior midgland

region identified by mp-MRI. The high kP L does not, however,

extend through the entire prostate, most likely due to low

SNR further away from the endo-rectal 13C RF coil sitting

just below the prostate in the images. While further studies

are required to fully evaluate the potential improvements

in assessing cancer metabolism, this work demonstrates the

feasibility and qualitative results of this approach on clinical

datasets.

VII. CONCLUSION

We have demonstrated that constrained reconstruction of

parameter maps via spatial regularization improves the qualitative performance of model-based parameter mapping. We have

shown this first in simulated experiments where we can

also demonstrate quantitative improvements in the parameter

estimates. The results of the in vivo studies echo the qualitative

benefits of constraining parameter maps through regularization, and validate that the ADMM-based algorithm we have

presented enables efficient reconstruction of parameter maps

for problems of practical interest by exploiting the objective

function’s structure.

Looking forward, the ability to exploit spatial and temporal correlations in the data for denoising could potentially

help to overcome problems with low SNR in hyperpolarized

13C MRI, enabling the reconstruction of higher resolution

kP L maps. Also, developing methods to choose the regularization strength hyperparameters systematically may help to

improve the quantitative bias seen in some of the in vivo experiments. In particular, methods based on Shure’s unbiased risk

estimate used for selecting hyperparameters in total variation

denoising applications [33] can likely be adapted to this context. We suspect that the results of this paper could be further

improved by replacing the ordinary least squares objective

used by a weighted least squares objective where weights are

chosen based on SNR, or based on an optimization problem

based on maximizing Fisher information about the metabolic

rate [34]. Finally, we would like to develop a better theoretical

understanding of the ADMM algorithm’s convergence on the

non-convex optimization problem presented.

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Hyperpolarized 13C MRI data acquisition and

analysis in prostate and brain at University of

California, San Francisco

研究背景

研究過程簡介

研究對象

????極?? 13 (HP-13C) MRI ???????研?????????????????????????????

?????????????代謝??研???研????????? HP-13C ?集???? / ????????研?

??????????????????????????????????????? HP-13C ????????

???集????????ǖ?????? 3D ????????????????? 2D ???????????

?????????????????????????研????????????????研??

?????極?) d-DNP) ????????????????? 13 ?????????磁共振?代謝??????

???????????????????????

UCSF ???????研?? (NIH) P41 ?????????????????????研????????極?

MRI ?????? (HMTRC) ? 2011 ?? Daniel Vigneron ????????????? HP-13C MRI ????????

??????????????研??????????

????????研????????????集?????????????????????????????

??????????????????????集 ?13C-HP ???????????????????????

?????????????????????? MRI 研?????

?????????

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研究結(jié)論

應用方向

研究結(jié)果

? d-DNP ????? 15 ???HP ???????代謝??????????????????????????

???????????????????共??????????????????????????????

???????共?????? HP-13C MR ???????????????????????????????

?????代??????????????????研??????????????????????????

????? NIH ??? HMTRC ???????????研????????????????????????

?????????集???????????????????????????????????????

SNR ???????集?????????????????????????????????????????

??????????????????????????????????? MRI ???? PACS ??集???

?????????????????

???????

1. EPSI/EPI ??? kPL ????????研???? kPL ?????????????????? HP [1-13C] ?????

??ǖEPSI kPL ?????????????? T2 ??????????????????代謝???? ??ǖEPI

kPL ??????????????????? T1 ??? 1H ????HP [1-13C] ??? ] 13C] ??????????

????????????????

2. SIVIC ?????? HP-13C ??集??????????????????????3D 代謝???????????

??? HP ?????共振??????????????

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SPECIAL ISSUE RESEARCH ARTICLE

Hyperpolarized 13C MRI data acquisition and analysis in

prostate and brain at University of California, San Francisco

Jason C. Crane1 | Jeremy W. Gordon1 | Hsin-Yu Chen1 | Adam W. Autry1 |

Yan Li1 | Marram P. Olson1 | John Kurhanewicz1,2 | Daniel B. Vigneron1,3 |

Peder E.Z. Larson1 | Duan Xu1

1

Department of Radiology and Biomedical

Imaging, University of California, San

Francisco, USA

2

Department of Pharmaceutical Chemistry,

University of California, San Francisco, USA

3

Department of Bioengineering and

Therapeutic Sciences, University of California,

San Francisco, USA

Correspondence

Jason C. Crane, Department of Radiology and

Biomedical Imaging, UCSF Radiology MC

2532, Byers Hall 301A, CA Institute for

Quantitative Biomedical Research, 1700 4th

Street, San Francisco, CA 94158-2330.

Email: jason.crane@ucsf.edu

Funding information

American Cancer Society, Grant/Award

Number: Research Scholar Grant

#131715-RSG-18-005-01-CCE; NIH, Grant/

Award Numbers: P41EB013598,

R01CA183071, U01CA232320,

U01EB026412

Abstract

Based on the expanding set of applications for hyperpolarized carbon-13 (HP-13C)

MRI, this work aims to communicate standardized methodology implemented at the

University of California, San Francisco, as a primer for conducting reproducible metabolic imaging studies of the prostate and brain. Current state-of-the-art HP-13C

acquisition, data processing/reconstruction and kinetic modeling approaches utilized

in patient studies are presented together with the rationale underpinning their usage.

Organized around spectroscopic and imaging-based methods, this guide provides an

extensible framework for handling a variety of HP-13C applications, which derives

from two examples with dynamic acquisitions: 3D echo-planar spectroscopic imaging

of the human prostate and frequency-specific 2D multislice echo-planar imaging of

the human brain. Details of sequence-specific parameters and processing techniques

contained in these examples should enable investigators to effectively tailor studies

around individual-use cases. Given the importance of clinical integration in improving

the utility of HP exams, practical aspects of standardizing data formats for reconstruction, analysis and visualization are also addressed alongside open-source software packages that enhance institutional interoperability and validation of

methodology. To facilitate the adoption and further development of this methodology, example datasets and analysis pipelines have been made available in the

supporting information.

KEYWORDS

Brain cancer, 13C, hyperpolarized MRI, metabolic imaging, prostate cancer

1 | INTRODUCTION

Following the emergence of dissolution dynamic nuclear polarization (d-DNP),1 which significantly enhances carbon-13 signal in labeled compounds, and the subsequent demonstration of rapid noninvasive imaging of metabolic conversion via magnetic resonance,2 there has been a substantial expansion of applications for this technology. In short order, the field has moved from animal studies into clinical trials investigating

human prostate,3 brain,4-6 kidney7 and liver8 cancer and metastasis, along with deviations in cardiac metabolism.9 Given the ongoing efforts

Abbreviations used: AUC, area under curve; CS, compressed sensing; CSI, chemical shift imaging; d-DNP, dissolution dynamic nuclear polarization; EPI, echo-planar imaging; EPSI, echo-planar

spectroscopic imaging; HP, hyperpolarized; MRSI, MR spectroscopic imaging; SNR, signal-to-noise ratio; SPSP, spectral-spatial.

Received: 13 July 2019 Revised: 24 January 2020 Accepted: 27 January 2020

DOI: 10.1002/nbm.4280

NMR in Biomedicine. 2020;e4280. wileyonlinelibrary.com/journal/nbm ? 2020 John Wiley & Sons, Ltd. 1 of 16

https://doi.org/10.1002/nbm.4280

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towards leveraging hyperpolarized carbon-13 (HP-13C) MRI at more than 15 institutions worldwide, the importance of robust acquisition,

processing and quantitation that provides reproducible findings is starting to be recognized. The current perspective aims to describe the

approaches taken at the University of California, San Francisco (UCSF) for standardizing HP-13C methodology to maintain consistency across

exams.

At UCSF, with the assistance of a National Institutes of Health (NIH) P41 center mechanism through the National Institute of Biomedical

Imaging and Bioengineering, a Hyperpolarized MRI Technology Resource Center (HMTRC) was established in 2011 under the leadership of

Dr. Daniel Vigneron with the goals of HP-13C MRI technology development, training of researchers from around the world, and disseminating

methods and information about the technology. Since then, the center has maintained a collection of resources for HP-13C probe preparation,

hardware documentation, and a repository of software packages for RF pulses, pulse sequences, processing and visualization. In keeping with the

collaborative spirit of the open-source community, a majority of the items discussed in this paper are readily available on the HMTRC website

(https://radiology.ucsf.edu/research/labs/hyperpolarized-mri-tech/), including example datasets and corresponding analysis software and

pipelines.

This paper focuses on our acquisition and processing approaches for investigating prostate and brain cancer in patients owing to the diverse

range of size and spatial resolution represented in these applications, which can easily be adjusted for other organs. The practical outlining of

methodological considerations for spectroscopic and imaging-based HP-13C acquisitions, together with step-wise detailing of associated

processing routines, is intended to serve as a primer for conducting MRI studies at local institutions and in the context of multicenter trials.

2 | ACQUISITION AND DATA FORMATS

Current acquisition strategies for HP-13C MRI can be classified into two categories with specific considerations and trade-offs in the type of data

they produce: (1) spectroscopic imaging methods (chemical shift imaging [CSI]/MR spectroscopic imaging [MRSI]) and (2) imaging-based methods

(eg, echo-planar imaging [EPI]). Below is a brief overview of these categories, followed by details of our specific implementations (Table 1) for a

spectroscopic imaging method used in the prostate and an imaging-based method used in the brain.

The other major design choice in the data acquisition is whether to acquire data dynamically or at a single time-point. We have chosen to

acquire dynamic time-resolved data because it ensures capturing of the bolus in-flow and is robust to variations in bolus delivery, which can vary

between patients due to the injection or physiology (eg, cardiac function, vascular delivery). Single time-point data can be very sensitive to measurement timing relative to the bolus delivery, which so far has been observed to be variable across human subjects in multiple studies.6,18-20

2.1 | Spectroscopic imaging methods

The CSI/MRSI-based strategies acquire data simultaneously from all metabolites and utilize spectrally encoded readouts to resolve the HP substrate from its metabolic products for image synthesis. Some examples currently in use throughout the community include 2D phase-encoded

CSI, 2D spiral CSI, 2D and 3D dynamic MRSI, and IDEAL CSI,22 many of which were employed in early phase clinical studies. The 2D phaseencoded CSI and 2D/3D dynamic MRSI have been applied in prostate3,9 and brain cancer studies, and spiral-IDEAL CSI has been utilized to investigate brain and breast cancer23,24 in patients.

TABLE 1 Key acquisition parameters for spectroscopic imaging of the prostate and metabolite-specific imaging of the brain at University of

California, San Francisco (UCSF)

Acquisition method Spectroscopic imaging Metabolite-specific imaging

UCSF application area Prostate Brain

k-space sampling Blipped EPSI Symmetric EPI10

RF pulses Metabolite-specific, variable flip angles with multiband

spectral-spatial pulses

Metabolite-specific flip angles with singleband

spectral-spatial pulses

Spatial resolution

(application-specific)

8 x 8 x 8 mm 15 x 15 x 15 mm

FOV (application-specific) 9.6 x 9.6 x 12.8 cm (12 x 12 x 16) 24 x 24 x 12 cm (16 x 16 x 8)

Temporal resolution 2 s 3 s

Reconstruction methods Compressed sensing11-14 Reference scan corrections10,15

Refpeak coil combination16,17

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The echo-planar spectroscopic imaging (EPSI)-based acquisition strategies are faster than in conventional phase-encoded CSI as a result of

the multi-echo readout gradient for spectral encoding. Design of an EPSI readout entails consideration of several key factors. While symmetric

EPSI is more SNR-efficient,25 flyback EPSI is compatible with random phase-encoding for 3D acceleration.12,26 Other considerations of importance to EPSI are spectral-spatial (SPSP) resolution and spectral bandwidth. Currently, our symmetric EPSI readout has a 543 Hz spectral bandwidth and a 10 Hz resolution, whereas flyback EPSI has a 581 Hz bandwidth and a 9.8 Hz resolution for 3 T studies.27 The ~ 10 Hz spectral

resolution provides more than sufficient spectral separation at 3 T, where the majority of human studies were conducted to date, as HP-13C resonances are discrete, and retain their line profile for phase-sensitive peak quantification. These parameters were designed around [1-13C]pyruvate

studies, where the EPSI bandwidth covers the range of frequencies from [1-13C]pyruvate to [1-13C]lactate (Figure 1), but allows aliasing of 13Curea (from built-in calibration phantom) and 13C-bicarbonate at 3 T. By carefully choosing the bandwidths, the aliased 13C-bicarbonate signal can

be placed between [1-13C]pyruvate-hydrate and [1-13C]alanine resonances. This aliasing leads to blurring artifacts in the image and spectral

domains, which can be removed by reconstructing after demodulating the raw data with a shifted frequency.28

2.2 | UCSF prostate spectroscopic imaging strategy

Imaging of patients with prostate cancer at UCSF utilizes a 3D compressed sensing (CS)-EPSI acquisition,11 which features highly undersampled

acceleration techniques that provide coverage of the entire gland from base to apex. Given the relatively small FOV of the prostate, which

exhibits good B0 and B1 homogeneity, this sequence can achieve suitable performance. Its full 3D encoding mitigates potential slice profile effects

arising from 2D multislice acquisitions, thus improving metabolite quantification. The reduction in TE owing to the relatively short multiband SPSP

excitation also enhances the SNR of metabolites with shorter T2* (eg, lactate),29-31 where SPSP minimized the chemical-shift slice offset and has

been designed to provide different flip angles for each metabolite, improving SNR over a constant flip angle scheme.32,33 Investigations into highversus low-grade human and preclinical prostate cancer using the 3D CS-EPSI acquisition were shown to well characterize differences in pyruvate

metabolism corresponding to upregulation of lactate dehydrogenase activity. The mean pyruvate SNR ~ 45 and lactate ~ 10 observed in prostate

(8 mm isotropic resolution) was adequate for kinetic modeling. As an example of the dynamic 3D CS-EPSI implementation at UCSF, Figure 2 presents HP-13C spectral data from a patient with suspected prostate cancer. Sample 3D CS-EPSI data and reconstruction code are also included in

the supporting information.

2.3 | Imaging-based methods

The nonrecoverable magnetization of metabolically active HP substrates, such as [1-13C]pyruvate, necessitates imaging sequences that are RFefficient, can rapidly encode both spectral and spatial dimensions, and have a high temporal resolution. As an alternative to spectroscopic imaging,

we have also employed a metabolite-specific imaging approach10,34 for many of our clinical imaging studies. While not discussed in detail here, it

is important to note that there are alternative imaging-based strategies for hyperpolarized 13C MRI, including bSSFP35-37 and model-based

approaches such as spiral-IDEAL38,39 or k-t spiral.40 The metabolite-specific imaging approach used here is based on a sequence consisting of a

single-band SPSP RF pulse that independently excites each metabolite, followed by a rapid, single-shot readout to encode the data within a single

TR per metabolite/slice. HP 13C MR imaging offers an appealing alternative to EPSI because it can provide higher temporal resolution, is more

robust to motion, and can be scaled to large, clinically relevant FOVs without an increase in scan time. The main limitations in this scheme are that

FIGURE 1 Representative time-resolved dynamic spectrum in

brain, showing the substrate [1-13C]pyruvate and downstream

products [1-13C]lactate and [13C]bicarbonate. Figure reproduced with

permission from Park et al4

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a minimum spectral separation is required between all metabolites to only excite a single metabolite with the SPSP RF pulse, and B0 inhomogeneity must be sufficiently small, such that the actual metabolite frequency resides within the spectral passband of the pulse.

2.4 | UCSF brain imaging strategy

HP imaging of patients with brain cancer at UCSF utilizes a frequency-selective imaging approach with a single-shot symmetric echo-planar readout. This approach is well-suited for the clinical imaging of [1-13C]pyruvate, where a small number of well-separated resonances are known a

priori. Compared with the 3D EPSI sequence used for prostate imaging, an EPI approach is more robust to motion and can easily be scaled to

larger FOVs without an increase in scan time by increasing the echo train length to maintain the desired spatial resolution. A broader point spread

function (PSF) in the blip dimension may arise due to T2* decay, which can be partially mitigated through the use of ramp sampling, partial-Fourier

acquisition, or acceleration with parallel imaging to reduce the echo-spacing and/or echo time. While the singleband SPSP RF pulses used for excitation are in principle sensitive to off-resonance, they were designed to maintain spectral selectivity and passband flip angle for B0 inhomogeneity

within ±1 ppm (±30 Hz for 13C at 3 T), which we have achieved in our prostate and brain cancer studies. (For B0 inhomogeneity just outside of

this range in the RF pulse transition region, the flip angles will be reduced, which should be accounted for [eg, with a B0 map and RF pulse profiles] for accurate quantification. If the B0 inhomogeneity goes into the RF pulse stopband region, then no signal will be seen.) The B0 inhomogeneity can also lead to spatial distortions with the EPI readout. In our studies, we chose to maintain a short echo spacing of 1.032 ms in the phaseencoding direction, meaning ±1 ppm inhomogeneity would result in a ± 0.5 voxel shift for our 16 x 16 matrix. For regions with larger B0 inhomogeneities, EPI distortion correction methods can be applied.15,41 Figure 3 depicts multiresonance metabolite images acquired from a patient with

brain cancer using dynamic HP-13C EPI with whole-brain coverage implemented at UCSF. Sample EPI data and reconstruction code are included

in the supporting information.

2.5 | RF excitation strategies

The choice of flip angles is crucial in an HP experiment due to the unrecoverable hyperpolarized magnetization, and depends on the temporal resolution and total imaging time. Both spectroscopic imaging and imaging-based methods (eg, EPI) can benefit from flip angle schemes that vary

between metabolites (“multiband” methods) and over time (“variable flip angles”).

Multiband methods use a lower flip angle on the substrate compared with the metabolic products, thereby preserving substrate magnetization for future conversion to metabolic products. For the MRSI/CSI-based methods, we achieve this by using multiband SPSP RF excitation

pulses. To design these pulses, the metabolite of interest needs to be identified. For instance, brain imaging using [1-13C]pyruvate targets [1-13C]

pyruvate, [1-13C]lactate and [13C]bicarbonate, whereas abdominal/liver imaging focuses on [1-13C]pyruvate, [1-13C]lactate and [1-13C]alanine.

FIGURE 2 Example 3D dynamic HP-13C CS-EPSI: Prostate data. Dynamic spectra from HP-13C CS-EPSI of a patient with prostate cancer are

shown with reference to a spectral grid overlaid on T2-weighted prostate images

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Assignment of “don't care” resonances relaxes design parameters to allow reduced effective time-bandwidth and therefore shorter pulse duration.

In imaging-based methods, multiband strategies are achieved by simply modulating the flip angles of the individual metabolite excitations.

Variable flip angle strategies can theoretically provide higher SNR and/or improved estimates of kPL.

42,43 However, these methods are more

sensitive to B1 miscalibration and inhomogeneity.44 For our prostate studies, where the FOV is small and B1 inhomogeneity is minimized, a variable flip angle scheme was designed to minimize kPL sensitivity to B1 error.45 In our brain studies, which required a larger FOV, a constantthrough-time flip angle scheme was employed. In all cases, the flip angle strategy must also be incorporated into the analysis, as this can substantially affect the apparent metabolite kinetics.

2.6 | Acquisition parameters required for reconstruction and analysis

Reconstruction of MRSI and MRI data requires knowledge of the k-space and time sampling, typically through characterization of the gradients.

For example, in our EPSI studies, essential information entails the FOV/resolution, number of EPSI lobes, timing of gradient plateau and ramp, and

timing offsets between gradients and data acquisition. For CS-EPSI, the pseudorandom undersampling pattern needs to be saved for k-space

reordering. The TE and any other timing parameters (ie, isodelay of RF pulses) are also important for phase correction in CSI/MRSI. For our EPI

studies, this includes FOV, resolution, timing of gradient plateaus and ramp, and also phase-correction factors from a reference scan.10

In analyzing the data, it is critical to know the acquisition timing (ie, temporal resolution) and the usage of magnetization by RF pulses. This

magnetization usage is determined by the expected flip angles for each HP resonance, the number of excitation pulses per frame, and, if available,

a B1+ map to correct for inhomogeneity in the transmit field.

Acquiring time-resolved data ensures capturing of the bolus in-flow, which can vary between patients due to the injection or vascular delivery. An alternative would be to acquire single time-point data, but the resulting measurements of lactate and pyruvate are very sensitive to the

timing of this single measurement. Time-resolved acquisitions are insensitive to timing differences so can provide more accurate assessments of

metabolism.

2.7 | HP data formats

Raw spectroscopic data from the research sequences described here are generally provided on the scanner in vendor-specific raw data formats.

As described in the previous section, the acquired data must include sufficient information about the acquisition to reconstruct the data for

FIGURE 3 Example dynamic HP-13C EPI: Brain data. HP [1-13C]pyruvate, [1-13C]lactate and [13C]bicarbonate area under the curve (AUC) EPI

images from eight slices covering the entire brain of a patient who has undergone treatment for brain cancer. Images are devoid of Nyquist ghost

artifacts or apparent geometric distortion. For anatomic reference, 1

H FLAIR images are provided in the bottom row

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analysis. This is complicated by the lack of standardization for how this information is encoded among various vendor formats. Customizing software to read these formats and data ordering from constantly evolving pulse sequences can represent a significant effort. Moreover, the file formats that are employed to encode HP data determine which software packages can be used for analysis, visualization and communication of the

data, and thereby impact software interoperability, methodology validation and integration of HP methods into clinical data delivery workflows.

At UCSF, the strategy to address these issues has been to (1) standardize the parameterization of acquisitions and to encode this information in a

consistent format called the data acquisition descriptor (DAD), and (2) to convert data encoded in vendor-specific formats to a standard DICOM

format to improve interoperability with different software packages and data flows.

To standardize the encoding of HP acquisition parameters, we followed the approach taken by the ISMRMRD,46 which provides a vendorneutral raw imaging data format. We extended this approach to support spectroscopy-specific parameterization for common MRSI acquisition

strategies including EPSI encoding, CS and phase encoding. While the ISMRMRD format stores the entire dataset, the current approach only

addresses the metadata parameters that would accompany vendor-specific raw data. These parameters are written into a DAD file47 developed

at UCSF, which encodes information in XML format and enables cross-vendor utilization for data analysis, as depicted by the schematic workflow

in Figure 4. Custom UCSF pulse sequences were modified to write DAD files with their acquisition parameters, and each raw file produced has an

associated DAD file containing every parameter relevant for processing. Figure 5 illustrates such intricate parameterization of an EPSI readout trajectory for analysis using a DAD file. The DAD xml format can be extended to support other acquisition schemes and supports parametrization of

other complex k-space trajectories such as CS.48 By using standardized parameterization of the data, we are able to develop vendor-agnostic software modules capable of processing different classes of acquired data, thus greatly reducing the software development burden for supporting HP

data analysis across institutional platforms. For example, an EPSI sequence on a preclinical Bruker and a human GE scanner can use the same data

FIGURE 4 Vender neutral

data acquisition descriptor (DAD)

file utilization. DAD files contain

a standard parameterization of an

acquisition including the readout

trajectory. This enables a single

set of data reordering software

modules to be used to construct a

vendor-neutral analysis pipeline

shown here for an EPSI CS

acquisition

FIGURE 5 Data acquisition descriptor (DAD) file parameterization of EPSI readout trajectory. DAD files contain standard parameterization of

acquisitions. Here, the parameters required to define an EPSI readout trajectory are defined graphically on the left and the corresponding DAD

XML elements are represented on the right

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reordering module to convert the raw data into a regular Cartesian grid of k-space spectra suitable for FFT reconstruction. The usage of the DAD

file is also extensible in the sense that it can be tailored to define parameters for acquiring data in a consistent fashion across sites and time, and

may accordingly serve as an explicit record of the acquisition. Open-source libraries for writing acquisition parameters to DAD files are available

in C and C++ and could be leveraged on other vendor platforms to generate datasets compatible with the open-source analysis tools described

here. The parameter sets will be presented to the ISMRMRD as possible extensions to support the present methods.

Reconstructed MRSI data are written in DICOM MRS formats using UCSF software49 (see tutorials referenced in the supporting information).

Metabolite maps from single time-point or dynamic acquisitions are written as standard DICOM MR Images, or Enhanced MR Image storage

objects, which enables interoperability with other DICOM-compliant software and integration into clinical information systems.

Reconstructed MRI data from EPI sequences are encoded in standard DICOM MR Image or Enhanced MR Image format for single timepoints. Dynamic acquisitions comprising multiple 3D volumes for each frequency band are encoded as DICOM Enhanced MR Image Storage

objects, which have explicit fields that represent time-point indexing of each 3D volume in the series.

3 | RECONSTRUCTION METHODS

3.1 | EPSI reconstruction

Our 3D CS-EPSI sequence uses a pseudorandom undersampling encode pattern that travels in (kx,ky) to allow random sampling of data in (kx,ky,kf,

dynamic) dimensions. The conditions of CS reconstruction are fulfilled by the intrinsic sparsity in human and preclinical HP-13C data, and the current pharmacy and hardware setups provide sufficient SNR for the L1 + TV-enforcing reconstruction algorithm. In the case of multichannel data, a

singular value decomposition (SVD) algorithm is applied to simultaneously benefit from parallel imaging and CS. The L1, TV penalties in CS, and

the singular value threshold in SVD, can be chosen either empirically or by simulations based on the underlying SPSP correlation and complexity

of the HP dataset for each imaging target.12,13 Briefly, the full reconstruction workflow entails k-space reordering and CS reconstruction, followed

by phase-sensitive peak quantification (Figure 6). These steps are facilitated in a flexible way by using the acquisition parameters from the specific

FIGURE 6 HP-13C EPSI data processing. This schematic summarizes the dynamic HP-13C MRSI processing framework for the 3D CS-EPSI

sequence, which is currently used in human prostate cancer studies

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dataset, as recorded in the DAD file accompanying the raw data. To tackle multichannel data, noise decorrelation is applied to the raw data in the

first step,50 and whitened singular-value decomposition (WSVD) is later utilized to estimate a complex coil sensitivity map and combine channels.51 Example EPSI data and reconstruction code are provided in the supporting information.

3.2 | EPI reconstruction

Our metabolite-specific imaging sequence uses a symmetric echo-planar readout. A symmetric readout is used instead of a flyback readout

because of its higher SNR efficiency, reduced echo-spacing and shorter TE. However, despite these advantages, the symmetric readout results in

Nyquist ghost artifacts, which appear at ±FOV/2. Such artifacts can be readily corrected for by performing a reference scan using the 13C trajectory on the 1

H channel10 or in postprocessing through an exhaustive search of the phase coefficients.15 For multichannel data, prewhitening is

also applied to the raw data to account for noise correlation between elements. The noise covariance matrix can be calculated from a separate,

noise-only scan or from the final time-point in the dynamic HP acquisition where no signal is present. An overview of the dynamic HP-13C EPI

processing pipeline utilized for brain patient studies at UCSF is shown in Figure 7. Here, we found that independently phasing [13C]bicarbonate

data was superior to using [1-13C]pyruvate as a phase reference, given the associated flow effects of blood. Example EPI data and reconstruction

code are provided in the supporting information. Misalignment from a bulk shift is accounted for by using the measured pyruvate frequency from

the 1D spectra acquired immediately after the acquisition. The echo spacing and readout duration are kept short as a tradeoff between SNR

FIGURE 7 HP-13C EPI data processing. An overview of the processing of dynamic HP-13C EPI data acquired from patients with brain cancer

is presented in this schematic. Both the HP patient data and noise-only data, which is captured in the same fashion prior to [1-13C]pyruvate

injection, are utilized in processing, with the latter enabling robust SNR thresholding. Metabolite AUC maps and modeled rate constant (kpl, kpb)

maps are the final output

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efficiency and sensitivity to distortion. For the brain studies, the total readout duration is 16 ms, equivalent to a 4 ms readout on the 1H channel,

where we have not observed misregistration between 1

H and 13C images (Figure 5).52

3.3 | Coil combination

Multichannel arrays are used in 13C studies to improve SNR, increase volumetric coverage and enable acceleration. However, many coil combination methods cannot be directly applied to HP-13C data. Sensitivity maps are difficult to acquire directly, as they would waste nonrecoverable HP

magnetization, and there is insufficient 13C in the body for direct acquisition on the basis of natural abundance. While a sum-of-squares approach

can be used to combine the multichannel data, it cannot preserve the phase and equally weights each channel, resulting in magnitude images that

are combined suboptimally.

Alternatively, multichannel data can be combined using sensitivity maps generated from the fully sampled data itself16,17,53 and then combined in an SNR-optimal way. This has the advantage of preserving the HP magnetization for metabolic studies and has inherently coregistered

sensitivity maps and image data, thus removing the potential for misregistration between the sensitivity calibration scan and the imaging experiment. For imaging experiments, data are combined using complex sensitivity maps derived from the fully sampled pyruvate data (RefPeak

method):

S xi,yj,ck

! " = I xi,yj, fRef,ck

! "

ISOS xi,yj, fRef ! "

IRefPeak xi,yj,f ! " =

XKCoil

k

S* xi,yj,ck

! "I xi,yj,f,ck! "

In this nomenclature, fRef refers to the metabolite used to estimate the sensitivity map S for each coil ck. In principle, this can be estimated

from any metabolite, but pyruvate is most commonly used because of its high SNR. Combining the data in this manner greatly improves image

quality compared with sum-of-squares in low-SNR metabolites such as bicarbonate. Employing this strategy also assures zero-mean data noise,

which increases the reliability of subsequent kinetic modeling. Coil combination code is available in the “hyperpolarized-mri-toolbox” (see the

supporting information). In the context of this communication, coil combination was performed in multichannel arrays for brain, whereas prostate

imaging used a single-element receiver.

4 | DATA POSTPROCESSING AND QUANTIFICATION

4.1 | SNR thresholding

Prior to performing quantifications, we perform thresholding based on the [1-13C]pyruvate SNR. The noise itself can readily be estimated from

noise-only dynamic datasets acquired with the same parameters as the patient data, but without HP-13C compounds onboard. The rationale for

SNR thresholding is that ratiometric and kinetic modeling methods rely on the measurement of pyruvate to quantify metabolic conversion, and

become unstable with low [1-13C]pyruvate signal.19

4.2 | Noise considerations

The noise characteristics of metabolite data must also be considered in all quantification. Whenever possible we avoid the use of magnitude data,

as this can lead to bias at low SNR. In MRSI processing, we use phase-sensitive peak detection and integration, resulting in real-valued (ie, can be

negative) peak data. This provides Gaussian noise characteristics that allow for optimal fitting with least-squares minimization. For magnitude

data, a Rician noise model should be employed to avoid bias arising from the Rician floor at low SNR values.54

4.3 | Metabolite extraction

Following data reconstruction, we perform several postprocessing steps prior to quantification. For MRSI data, phasing the spectra allows for

improved detection of low SNR peaks.51 Because these data are contaminated by first-order phase due to the gradient-echo acquisition, we

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independently phase the spectra from each metabolite on a voxel-wise basis, and assume that the phase remains constant through time. This is

done by finding the phase offset that maximizes the real component of the complex spectra for the region around each metabolite, which are

concatenated in time. Following phasing, the metabolite amplitudes are extracted as integrated peak areas. In the prostate MRSI paradigm, a pyruvate SNR threshold of 210 was applied to quantify pyruvate-lactate data. Admittedly, the phasing error translates to a small positive bias,

ΔkPL < 0.001 s?1

, but it does not increase the standard error of kPL estimates.5 Also, phase-mode error should be relatively benign compared with

magnitude-mode peak quantification, as phasing error cancels out through time as opposed to constructive addition in magnitude in terms of

kinetic modeling.

4.4 | Quantification of metabolic conversion

There exist many promising approaches for quantification of metabolic conversion.55 We primarily use area-under-(time)-curve ratiometric

methods as well as an input-less kinetic modeling approach for human studies. The rationale for using these methods is that they have been

shown to be robust to variations in polarization, SNR and pyruvate delivery, which can be considerable among human subjects. These approaches

and considerations for their implementation are presented in the following sections.

Ratiometric methods for quantifying metabolic conversion rates, based on the metabolite-to-pyruvate ratios, are simple and robust when certain assumptions are met. It has been shown that the ratio of the area under curve (AUC) between product (ie, [1-13C]lactate) and substrate (ie,

[1-13C]pyruvate) is proportional to the conversion rate (ie, kPL) when the following assumptions are fulfilled: product relaxation rate (ie, T1L) does

not change; dynamic measurements begin before metabolite signals appear; and, when variable flip angles are used, the substrate bolus characteristics (arrival time, bolus duration and shape) are fixed.56

Kinetic modeling is used to estimate apparent rate constants for conversion of pyruvate-to-lactate (kPL) and pyruvate-to-bicarbonate (kPB). It

is important to note that these apparent rate constants are not conventional rate constants of chemical kinetics. They are based on a simplified

first-order kinetic model of label exchange, and also may include contributions from other factors in vivo, such as perfusion and cellular transport.

Our current approach for kinetic modeling is to use an “input-less” strategy that shares many of the same assumptions as the AUC ratio

method. This makes it robust to low SNR data and insensitive to variability in the bolus characteristics, while accounting for arbitrary flip angle

strategies. We observed, through Monte Carlo simulations, that an input-less model provides more robust performance than ratiometric methods.

Also, this strategy does not require fitting or knowledge of the pyruvate input function, which are required by other popular modeling strategies

and can introduce additional error or uncertainty.

The input-less strategy assumes unidirectional 13C label exchange from pyruvate to the metabolic products (ie, kLP = kBP = 0), and uses fixed

relaxation rates (T1P, T1L, T1B), which are estimated from prior studies.18,57 The inputs are the metabolite amplitudes, acquisition timings and RF

flip angles. As shown in Figure 8, the input-less model can readily be applied to fit dynamic data acquired by means of EPSI or EPI in human studies of prostate and brain cancer, to generate maps of kPL within regions of interest.

There are also more detailed kinetic models, including additional factors of vascular components within a voxel as well as intra- and extracellular compartments. One promising approach we are investigating includes a vascular component within each voxel,58 which may be important since there are likely substantial vascular metabolite fractions resulting from the short time between injection and acquisition. This

approach was shown to be more appropriate in a variety of animal models.58 For these models, a vascular input function was estimated from a

vascular voxel that was identified on the 1H anatomical images. The assumptions of unidirectional conversion and fixed relaxation rates remain

the same.

The input-less kinetic model, AUC ratio methods and kinetic models with input functions are available within the “hyperpolarized-mri-toolbox”

21 under the “kinetic_modeling/” directory.

5 | VISUALIZATION AND CLINICAL INTEGRATION

5.1 | Visualization

Visualization software for HP experiments must support the display of dimensions representing space, frequency, time and receiver channel. The

software must be capable of rendering 3D arrays of spectral voxels at the correct spatial location on standard anatomical images and for comparison with 1

H spectra. It must also be able to display frequency-resolved temporal changes (Figure 9, top) as well as the temporal evolution of individual metabolites (Figure 9, middle and bottom) for kinetic modeling. A receiver channel dimension is required for QC of analysis pipelines to

visualize individual raw and processed data channels prior to combination. At UCSF, we developed a custom software package49,59 (SIVIC) to support these requirements. SIVIC reads MRI and MRSI DICOM images as well as multiple vendor-specific raw data formats. The package runs on

Windows, Linux and Mac and can be used for offline analyses, or run on a variety of scanner consoles (GE, Bruker, Agilent).

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5.2 | Integration with other molecular imaging modalities

The initial application of HP [1-13C]pyruvate in cohorts of patients with primary or metastatic brain tumors demonstrated varied (similar, lower or

increased) conversions to lactate and bicarbonate in the lesions compared with those in the normal brain.4,59 This suggests that the combination

of HP-13C metabolic imaging with other metabolic imaging models, such as PET tracers60 and steady state 1

H MRSI,61 could improve the understanding of the underlying biological processes in the abnormalities. At UCSF, we have established methods for acquiring and analyzing 1

H MRSI

for patients with brain tumors.62,63 When integrating with HP 13C data, the 1H spectral data and maps can be affinely registered to the 13C data

by applying the transformation matrix generated from the registration between the images acquired at two examinations, to enable voxel-byvoxel analysis. SIVIC can then be used to provide visual comparisons of 1

H and 13C metabolic maps, as well as maps of standardized uptake

values64 from PET.

5.3 | Workflow and data delivery

As HP methods mature and become increasingly utilized in human subjects, data flow will require further consideration, given its importance to

efficient data transfer and analysis. The use of DICOM as the standard output format from our HP packages permits us to send results freely

between scanners and research and clinical picture archiving and communication system (PACS) in our institution. Although DICOM MRSI data

can be stored in many PACS, only 3D MRI images can be visualized on most PACS workstations. To address this, we have developed a plugin49

for OsiriX65 and HOROS66 that permits individual researchers to manage their imaging MRI and MRSI data in a PACS with visualization capabilities for both.

The ability to send HP MR spectra and quantitative maps in real time from a scanner to clinical PACS for visualization and storage is a critical

element of the data flow required for clinical integration of the HP modality. In order to send viewable results to PACS and the reading room, software packages running on the scanner console support creation of static DICOM Secondary Capture reports. While these reports can be sent to

PACS for viewing, they cannot be manipulated or further processed in the reading room. The 3D quantitative metabolite maps or EPI images from

HP acquisitions can be generated on the console and sent to PACS with standard anatomical images and spatially correlated with this data.

While 3D metabolite maps derived from the analysis of MRSI acquisitions can be viewed with or without 3D anatomical images, they do not

capture spectral quality or content, and the ability to visualize spectroscopic data and correlate it with anatomical data directly in PACS would be

FIGURE 8 EPSI/EPI-derived kPL maps. Example kPL maps from human patient studies based on the fitting of dynamic HP [1-13C]lactate

production using the input-less kinetic model. Left: EPSI Kpl map overlaid on a T2-weighted image from a patient with prostate cancer, with

dynamic metabolite traces shown for the voxel indicated in green. Right: EPI kPL map overlaid on a T1 postcontrast 1

H image from a patient

treated for malignant brain tumor, with both HP [1-13C]lactate and [13C]bicarbonate production depicted within the highlighted region of normalappearing white matter

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highly advantageous. Such functional extension would require broader utilization of the DICOM MRS standard in order for PACS implementations

to provide vendor-neutral visualization tools. Several research and commercial MRS platforms already support the DICOM MRS standard, including TARQUIN,67,68 SIVIC,49,59 jMRUI69 and Philips,70 enabling vendor-neutral visualization and data interoperability. SIVIC has plugins for OsiriX65

and Horos66 PACS, which demonstrate the feasibility and benefit of integrated anatomical and spectroscopic data visualization in a PACS; however, MRS visualization in enterprise PACS implementations remains an unmet need.

6 | SUPPLEMENTARY MATERIAL

6.1 | Example EPSI data and recon

An example EPSI dataset is available online, together with reconstruction code,71 in the “Hyperpolarized MRI Toolbox”. This reconstruction routine accepts a reordered version of undersampled k-space data, along with a pseudorandom undersampling mask on which the data acquisition

was based. L1 compressed-sensing is performed to interpolate the missing k-space data, and the reconstructed k-space is saved for further quantification or visualization in SIVIC.

6.2 | Example EPI data and recon

An example EPI dataset, reconstruction code and Jupyter Notebook72 are also available online in the “Hyperpolarized MRI Toolbox”. This pseudo

reconstruction starts after the raw data has been phase corrected and Fourier-transformed into image space. The example code pre-whitens the

FIGURE 9 SIVIC visualization. Display modes for dynamic HP-13C datasets comprising a time series of spectroscopic images (top), time series

of 3D metabolite maps (middle) and dynamic views showing the evolution of the HP signal from individual resonances through time (bottom)

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multichannel data and then generates coil-combined images using the pyruvate data to estimate the sensitivity map. More information on this

‘refpeak’ reconstruction can be found in Zhu et al73. Using the coil combined data, AUC ratio maps, apparent rate constant maps, and mean arrival

time maps are also generated.

6.3 | Example dynamic EPSI data analysis utilizing DAD file

This example with software and sample data demonstrates analysis and visualization of 2D dynamic HP 13C data of the human prostate acquired

on a GE 3T scanner.74,75 The analysis uses SIVIC for data reordering, reconstruction, and to generate DICOM metabolite maps for [1-13C]pyruvate

and [1-13C]lactate at each timepoint. The end result is a set of DICOM metabolite maps of fitted kinetic parameters including kPL.

6.4 | Hyperpolarized MRI toolbox

We have created a “Hyperpolarized MRI Toolbox” to provide a set of research-level and prototyping software tools for HP MRI experiments.21 It

is primarily based on MATLAB code and includes code for simulating HP-13C MRI data, designing pulse sequences (RF pulses, readout gradients),

data reconstruction, and data analysis. This resource is hosted and maintained via GitHub as an open-source, collaborative platform to facilitate

engagement of the hyperpolarized MRI research community.

6.5 | SIVIC software, tutorials and sample data

SIVIC development has largely been driven by the need to address requirements of the HP community. The current package is available for download in source format as well as binary distributions for Linux, OsX and Windows.44,76 Since 2014, many detailed tutorials focusing on different

aspects of HP 13C analysis with SIVIC have been developed for the HMTRC77 and presented to users at hands-on symposia aimed at facilitating

the use of the SIVIC toolkit as a HP data analysis platform. All tutorials, together with sample data, are available online.78 These tutorials provide

detailed instructions for performing preprocessing, reconstruction, quantification and visualization, as well as data import and export using both

the SIVIC GUI and command line tools. These tutorials are accompanied by sample data from GE, Varian and Agilent systems and represent EPSI,

dual-band variable flip angle, EPI, and CSI acquisitions. The 2018 and 2019 tutorials also include software development tutorials to help users

who are interested in using the SIVIC command line tools to construct analysis pipelines and develop new algorithms for the framework in an

easy-to-use Docker79 development environment.

6.6 | Other software and data resources

Many other software packages are available either as freeware, or via licensed use agreements to address other aspects of data analysis and visualization, including: jMRUI,69 TARQUIN,68 and Horos.66 Although the resources described in this section contain sample data, the community

would benefit from the availability of a more comprehensive shared reference dataset for validating and comparing different algorithms and

methodologies.

7 | CONCLUSIONS

In the 15 years since the first demonstration of d-DNP, there has been extensive development of HP methodology for interrogating metabolism

noninvasively, with future progress towards clinical translation relying upon the harmonization of techniques and finding of strategic consensus in

this relatively young field. While numerous approaches exist for acquiring, reconstructing and analyzing data, it is vitally important that we leverage HP-13C MR technology through careful documentation and sharing of resources, which will facilitate investigative efforts by maintaining community engagement and focus. As part of that mission, this paper represents the experience gained from human studies conducted at UCSF, and

its authors encourage further contribution from other institutions regarding methodologies of interest. The NIH-funded HMTRC will continue to

lead the way in openly sharing and providing a forum for investigators to accelerate technical advancements that will impact future biological and

clinical applications.

There is a range of promising directions for improvement in the acquisitions and analyses as well as workflow. Spin-echo or steady-state

methods are promising for providing substantial improvements in SNR and resolution.80,81 Autonomous scanning methods with integrated

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frequency, power and timing corrections82 have the potential to provide more robust and reproducible results. There are promising new kinetic

models that can remove confounding factors such as perfusion, and more robust analysis methods.55 And there are unmet needs to integrate with

these methods with MRI manufacturers and PACS systems that will facilitate clinical workflows.

Going forward, there must be increased consensus in the way HP-13C acquisitions, analyses and workflows are performed, as this will be crucial for establishing standardized, comparable results and multicenter trials. This can be piloted first in small multicenter trials based on currently

emerging clinical trial results, and then expanded on by consensus-building working groups.

ACKNOWLEDGEMENTS

This paper is dedicated to the memory of Sarah J. Nelson, who passed away during the writing of this paper. She was a dedicated scientist and

contributed greatly to the field of metabolic imaging. Her leadership and friendship will be greatly missed. Jason C. Crane, Jeremy Gordon, HsinYu Chen and Adam W. Autry contributed equally to this work.

FUNDING INFORMATION

This work was supported by NIH Grants P41EB013598, R01CA183071, U01EB026412 and U01CA232320; and American Cancer Society

Research Scholar Grant #131715-RSG-18-005-01-CCE.

ORCID

Jason C. Crane https://orcid.org/0000-0002-1145-5639

Hsin-Yu Chen https://orcid.org/0000-0002-2765-1685

Peder E.Z. Larson https://orcid.org/0000-0003-4183-3634

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How to cite this article: Crane JC, Gordon JW, Chen H-Y, et al. Hyperpolarized 13C MRI data acquisition and analysis in prostate and brain

at University of California, San Francisco. NMR in Biomedicine. 2020;e4280. https://doi.org/10.1002/nbm.4280

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Translation of Carbon-13 EPI for hyperpolarized

MR molecular imaging of prostate and brain

cancer patients

研究背景

研究過程簡介

研究結(jié)果

研究對象

??????????????極?) HP) Carbon-13 (13C) ????????代謝?????????

??????????????????????????????????????? MR ??代謝?????

?????????? 13 (13C) ????????極?) DNP)????????極????? 5 ?????????

????????????????????極?) HP) 13C 代謝?????????

??代謝?? HP ???????磁??????????????????????????????????

???????????????????????? HP 13C ???????? FOV ?????

???????????????? HP 13C EPI ?????????????????????研???????

集?????極? 13C MR ????????????????

1.?? 1H T2 ??? ADC ???????????????????? 6 ?????? 13C ?????? AUC ?? ?

13C ???????????????????? ????極????? 1H ADC ???????????????

??????????????? Gleason 3+4 ????

2.????????????? AUC ???? 1H T2 ?????? AUC ????????????????代謝?

?????????????????代謝? ???????????????????????????????

??????????????? 13C ??? sinc ????? 1H ????????? AUC ??????????

??

???? (N = 3) ??????? (N = 3)

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研究結(jié)論

應用方向

??研?????? EPI ??????????????極? 13C 代謝??????? ????????????

?????代謝???? EPI ?集????????研??????????????????????? SNR???

????????????

???????????

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Magn Reson Med. 2018;1–8. wileyonlinelibrary.com/journal/mrm ? 2018 International Society for Magnetic Resonance in Medicine | 1

Received: 12 July 2018 | Revised: 22 August 2018 | Accepted: 30 August 2018

DOI: 10.1002/mrm.27549

NOTE

Translation of Carbon‐13 EPI for hyperpolarized MR molecular

imaging of prostate and brain cancer patients

Jeremy W. Gordon1 | Hsin‐Yu Chen1 | Adam Autry1 | Ilwoo Park2 |

Mark Van Criekinge1 | Daniele Mammoli1 | Eugene Milshteyn1 | Robert Bok1 |

Duan Xu1 | Yan Li1 | Rahul Aggarwal3 | Susan Chang4 | James B. Slater1 |

Marcus Ferrone5 | Sarah Nelson1 | John Kurhanewicz1 | Peder E.Z. Larson1 |

Daniel B. Vigneron1

1

Department of Radiology and Biomedical Imaging, University of California San Francisco, San Francisco, California

2

Department of Radiology, Chonnam National University Medical School and Hospital, Gwangju, Korea

3

Department of Medicine, University of California San Francisco, San Francisco, California

4

Department of Neurological Surgery, University of California San Francisco, San Francisco, California

5

Department of Clinical Pharmacy, University of California San Francisco, San Francisco, California

Correspondence

Jeremy Gordon, 1700 4th Street, Byers Hall

102, San Francisco, CA 94158.

Email: jeremy.gordon@ucsf.edu

Funding information

National Institutes of Health, Grant/Award

Numbers: R01EB017449, R01CA183071,

P41EB013598, P01CA118816, and

R01CA211150.

Purpose: To develop and translate a metabolite‐specific imaging sequence using a

symmetric echo planar readout for clinical hyperpolarized (HP) Carbon‐13 (13C)

applications.

Methods: Initial data were acquired from patients with prostate cancer (N = 3) and high‐

grade brain tumors (N = 3) on a 3T scanner. Samples of [1‐

13C]pyruvate were polarized

for at least 2 h using a 5T SPINlab system operating at 0.8 K. Following injection of the

HP substrate, pyruvate, lactate, and bicarbonate (for brain studies) were sequentially

excited with a singleband spectral‐spatial RF pulse and signal was rapidly encoded with

a single‐shot echo planar readout on a slice‐by‐slice basis. Data were acquired dynamically with a temporal resolution of 2 s for prostate studies and 3 s for brain studies.

Results: High pyruvate signal was seen throughout the prostate and brain, with conversion to lactate being shown across studies, whereas bicarbonate production was

also detected in the brain. No Nyquist ghost artifacts or obvious geometric distortion

from the echo planar readout were observed. The average error in center frequency

was 1.2 ± 17.0 and 4.5 ± 1.4 Hz for prostate and brain studies, respectively, below

the threshold for spatial shift because of bulk off‐resonance.

Conclusion: This study demonstrated the feasibility of symmetric EPI to acquire HP 13C

metabolite maps in a clinical setting. As an advance over prior single‐slice dynamic or

single time point volumetric spectroscopic imaging approaches, this metabolite‐specific

EPI acquisition provided robust whole‐organ coverage for brain and prostate studies

while retaining high SNR, spatial resolution, and dynamic temporal resolution.

KEYWORDS

DNP, EPI, hyperpolarization, oncology, pyruvate

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2 | GORDON ET AL.

1 | INTRODUCTION

There remains an unmet clinical need for improved molecular imaging techniques that provide relevant detection and

characterization of cancer presence and response to therapy.1

An emerging approach for metabolic imaging using

MR is dissolution dynamic nuclear polarization (DNP)2

with Carbon‐13 (13C) enriched substrates. This technique

provides as much as 5 orders of magnitude enhancement to

nuclear spin polarization and has been applied to endogenous substrates for non‐invasive, real‐time hyperpolarized

(HP) 13C metabolic imaging in pre‐clinical3-5 cancer models, a phase I clinical trial in prostate cancer patients,6

and

proof of concept clinical7-9 studies. This first‐in‐man study6

demonstrated the safety and feasibility of this approach to

detect metabolic reprogramming in human cancers that

demonstrate increased pyruvate‐to‐lactate conversion via

upregulated lactate dehydrogenase (LDH) expression. The

increased conversion of pyruvate to lactate, an outcome of

the aberrant reliance on aerobic glycolysis, is a phenomenon known as the Warburg effect and is a hallmark of advanced and malignant cancers.10

The non‐recoverable magnetization of these metabolically active HP substrates necessitates imaging sequences

that are RF-efficient, can rapidly encode both spectral and

spatial dimensions and have a high temporal resolution.

The first‐in‐man phase I trial6 used echo‐planar spectroscopic imaging (EPSI) methods for HP 13C data acquisitions. Although the acquisition methods used in this study

were adequate for establishing safety and feasibility in

prostate cancer studies, they were limited to a single‐slice

dynamic acquisition or a single time point volumetric acquisition of the prostate with a limited (8 × 8 cm2

) FOV.

Such inherent limitations hindered its broader application

for future human studies.

Clinically relevant dynamic HP 13C imaging with volumetric coverage and imaging of larger organs requires far

greater FOV coverage. An alternative approach to acquire

HP 13C data was first proposed by Cunningham et al.11 and

consisted of a spectral–spatial RF pulse to independently excite each metabolite followed by a rapid, single‐shot spiral12

or echoplanar11,13 readout. This metabolite‐specific approach

to HP 13C MRI is an appealing alternative to EPSI because

it provides higher temporal resolution, is more robust to motion, and can be scaled to large FOVs without an increase in

scan time. Compared to a spiral trajectory, echo planar readouts are more robust to off‐resonance and gradient errors,

whereas issues with Nyquist ghost artifacts can be readily

corrected by a reference scan14 or via an exhaustive search of

the phase coefficients.15

In prior work, a symmetric EPI sequence was developed

for HP 13C MRI and tested in preclinical animal models with

features based on a clinical 1H EPI product sequence that

enabled reconstruction on the scanner.13 Translating this sequence to a clinical setting faces the substantial challenges

of encoding a larger volume, along with poorer B0 homogeneity and increased susceptibility. This can hamper the

effectiveness of spectral–spatial RF pulses and potentially

lead to geometric distortion. The goal of this project was to

further develop and translate this HP 13C EPI sequence to obtain initial data in patients with prostate and brain tumors to

investigate the potential value of using this rapid acquisition

technology for hyperpolarized 13C MR molecular imaging

for clinical evaluation.

2 | METHODS

Following institutional review board (IRB) and Food and

Drug Administration investigational new drug application

(FDA IND)‐approved protocols with informed consent, patient research exams were performed on a 3T MR scanner

(MR750, GE Healthcare, Waukesha, WI) with clinical performance gradients (50 mT/m maximum gradient strength,

200 mT/m/ms maximum slew‐rate). For the prostate studies,

a 13C clamshell coil was used for RF excitation16 whereas a 1

H/13C endorectal receive coil was used for reception. For

the brain studies, a birdcage coil was used for RF excitation

and an integrated 32 channel coil was used for reception.17

An 8 M 13C urea phantom embedded in both the endorectal

and brain coil was used to set the RF transmit power and

center frequency. All data sets were acquired with a ramp‐

sampled, symmetric echo planar imaging sequence developed for clinical 13C imaging13 (Figure 1). Accompanying

spectral‐spatial (SPSP) RF pulses were designed using the

SPSP RF toolbox,18 which can be accessed at https://github.

com/LarsonLab/hyperpolarized-mri-toolbox/.

2.1 | Sample preparation and polarization

Samples containing 1.47 g of Good Manufacturing Practice

(GMP) grade [1‐

13C]pyruvate (MilliporeSigma Isotec,

Miamisburg, OH) and 15 mM electron paramagnetic agent

(EPA; AH111501, GE Healthcare) were prepared by a pharmacist the morning of the study. Samples were polarized

using a 5T clinical polarizer (SPINlab, GE Healthcare) for

at least 2 h. Following dissolution, the electron paramagnetic

agent was removed by filtration and pH, pyruvate and EPA

concentrations, polarization and temperature were measured

before injection. In parallel, the integrity of the 0.2 μm sterile

filter was tested in agreement with manufacturer specifications before injection. After release by the pharmacist, a 0.43

mL/kg dose of ~250 mM pyruvate was injected at a rate of 5

mL/s, followed by a 20 mL saline flush (0.9% sodium chloride; Baxter Healthcare, Deerfield, IL), with the acquisition

starting 5 s after the end of saline injection.

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| GORDON ET AL. 3

2.2 | Prostate imaging

HP 13C images were acquired with an 8 × 8 mm2 in‐plane resolution (12.8 × 12.8 cm2

FOV, 16 × 16 matrix size), 0.5 cm3

spatial resolution, TR/TE = 62.5 ms/15.4 ms, echo‐spacing =

0.62 ms. Metabolites were sequentially excited with a custom

echo planar single‐band spectral‐spatial RF pulse (150 Hz

FWHM, 600 Hz stopband peak‐to‐peak) using a variable flip

angle scheme (Supporting Information Figure S1) designed

to provide a robust estimate of kPL in the presence of B1

+ inhomogeneity.19 The center frequency was calibrated using an 8

M 13C‐urea standard embedded in the receive coil. Sixteen 8

mm slices were acquired per time frame, alternating between

pyruvate and lactate (Δf = 390 Hz) for each multi‐slice volume, with an effective 2 s temporal resolution and a total

acquisition time of 42 s. To correct for Nyquist ghosting, a

reference scan was acquired on the 1H channel before 13C imaging.13 After 13C imaging, non‐localized spectra (TR = 3 s,

θ = 20°, 10 time points) were acquired with a 500 μs hard

pulse to measure the error in center frequency calibration.

For anatomic reference, T2‐weighted 1H images (TR/TE =

6 s/102 ms, 18 × 18 cm2 FOV, 384 × 384 matrix, 3‐mm

slice thickness, 2 averages) were acquired for co‐localization with the HP 13C data. As part of the multi‐parametric

MR exam, diffusion‐weighted 1H images were acquired

with a reduced FOV using single‐shot spin‐echo EPI. A

b = 0 s/mm2 image was acquired, followed by b = 600 s/

mm2 in 6 directions, with TR/TE = 4 s/52.4 ms, FOV = 19

× 8 cm2, matrix size = 128 × 64, NEX = 6, 16 3‐mm slices.

The geometric mean for the 6 directions was taken before

calculating the ADC.

2.3 | Brain imaging

Whole brain coverage was achieved for HP 13C studies with

8 2‐cm slices. In‐plane resolution was 1.5 × 1.5 cm2 (24.0

× 24.0 cm2 FOV, 16 × 16 matrix), with a TR of 62.5 ms,

21.7 ms TE, and 1.03 ms echo‐spacing. Similar to prostate

studies, metabolites were sequentially excited with a flyback

SPSP RF pulse (130 Hz FWHM, 868 Hz stopband peak‐to‐

peak) using a 20° pyruvate/30° lactate/30° bicarbonate flip

angle that was constant through time. The center frequency

was alternated between pyruvate, lactate (Δf = 390 Hz), and

bicarbonate (Δf = ?322 Hz) for each volume, with an effective 3 s temporal resolution. Twenty total time frames per

metabolite were acquired, yielding a total imaging time of 60

s. Following 13C imaging, non‐localized spectra (TR = 3 s, θ

= 60°, 8 time points) were acquired with a 500 μs hard pulse

to measure the relative metabolite frequencies. For anatomic

reference, T2 fluid‐attenuated inversion recovery (FLAIR) 1

H images (TR/TE = 6.25 s/142 ms, 25.6 × 25.6 cm2 FOV,

256 × 256 matrix, 5‐mm slice thickness) were acquired for

co‐localization with the HP 13C data.

2.4 | Analysis

All data sets were reconstructed using the Orchestra toolbox

(GE Healthcare). Phase coefficients from the reference scan

were first applied to the raw k‐space data. For the ramp‐sampled prostate studies, data were then interpolated to a Cartesian

grid before Fourier transform. For the multichannel brain data,

noise pre‐whitening20 was applied in k‐space before a sum‐

of‐squares coil combination. The noise covariance matrix

FIGURE 1 Multi‐slice echo planar pulse sequence. The complex single band spectral–spatial pulse (real and imaginary RF shown) is used to

selectively excite an individual hyperpolarized metabolite. An entire volume is acquired for one metabolite before switching to the next frequency.

An optional delay can be added after all metabolite volumes are acquired to achieve the desired temporal resolution

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4 | GORDON ET AL.

was calculated from the final pyruvate time frame where no

signal was present. Area under the curve (AUC) maps were

generated by summing the complex data through time, and all

1

H/13C overlay images were generated using SIVIC.21

3 | RESULTS

3.1 | Prostate studies

The RF transmit power was determined using the 8 M 13C

urea phantom embedded in the coil. Imaging the phantom

with the pyruvate flip schedule (Supporting Information

Figure S1) confirmed the RF power calibration and phase

correction coefficients before hyperpolarized imaging. The

center frequency was also set based on the 13C urea phantom

and directly measured from the spectra acquired after the end

of imaging. The average error in center frequency calibration in the prostate studies was 1.2 ± 17.0 Hz (Supporting

Information Table S1), well within the passband for excitation (150 Hz FWHM) and substantially smaller than the

bandwidth in the blip dimension (101 Hz/pixel). From the

dynamic time series, the peak SNR for pyruvate and lactate

was 30.7 ± 12.3 and 7.9 ± 1.4, respectively.

AUC maps (Figure 2) for pyruvate and lactate provide

complete coverage from the base to the apex of the prostate

with 8 × 8 × 8 mm3

(0.5 cm3) spatial resolution. Nyquist

ghost artifacts that could arise from mismatch between even

and odd lines of k‐space were not observed. These were readily corrected for with the use of the reference scan acquired

on the 1H channel, eliminating the need to directly acquire a

reference scan from the hyperpolarized 13C magnetization.

There is good spatial agreement between regions of elevated

total lactate and low 1H ADC, consistent with biopsy‐proven

Gleason 3+4 cancer in this patient.

3.2 | Brain studies

The 4D dynamics for pyruvate, lactate, and bicarbonate

(Supporting Information Figures S2–S4) were also free of

apparent geometric distortion and Nyquist ghost artifacts,

despite the larger FOV and greater potential for substantial

B0 inhomogeneity across the brain. This particular patient

had a grade 2 oligodendroglioma and received a subtotal

resection 5 y ago. Recent progression was observed on

the 1H FLAIR data, and this scan was acquired before radiotherapy. The pyruvate signal predominantly reflects the

vasculature, with the strongest signal intensity occurring in

the superior sagittal sinus and transverse sinuses. Pyruvate

conversion to lactate was observed throughout the brain

and subcutaneous tissues (Figures 3 and 4). Conversion to

bicarbonate demonstrated a different spatial distribution,

with highest apparent signal in gray matter and lower relative intensities in white matter and subcutaneous tissues.

Quantitatively, the peak SNR for pyruvate, lactate, and

FIGURE 2 Anatomic 1H T2‐weighted and ADC maps, and 13C pyruvate and lactate AUC maps for the 6 central slices covering the entire

prostate, from the base to the apex. No Nyquist ghost artifacts or geometric distortion were observed in the 13C data. There is good spatial

agreement between elevated hyperpolarized lactate and regions of low 1

H ADC (indicated by red arrows), consistent with biopsy‐proven Gleason

3+4 cancer

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| GORDON ET AL. 5

bicarbonate was 415.0 ± 27.9, 24.7 ± 7.6, and 7.0 ± 1.0,

respectively (Table 1). In all 3 studies, pyruvate signal was

present at the start of the acquisition, which began 5 s after

the end of the 20 mL saline flush.

Similar to the prostate studies, the center frequency for

hyperpolarized brain studies was also set based on the 13C

urea phantom embedded in the coil and directly measured

from the spectra acquired after the end of imaging. The average error in center frequency calibration for these studies

was 4.5 ± 1.4 Hz (Table 1), well within the passband for excitation (130 Hz FWHM) and substantially smaller than the

bandwidth in the blip dimension (61 Hz/pixel).

FIGURE 3 Pyruvate, lactate, and bicarbonate AUC maps for the 8 slices covering the entire brain. The red arrowheads indicate the external 13C urea phantom, 1

H FLAIR abnormality, and resection cavity, respectively. 13C data have been zero‐filled 4‐fold for display. For anatomic

reference, 1

H T2 FLAIR images are shown below

FIGURE 4 Pyruvate, lactate, and bicarbonate AUC maps overlaid on 1H T2‐weighted images. The AUC maps reflect pyruvate uptake and

metabolism over the course of the experiment, with lactate metabolism observed throughout the brain and subcutaneous tissues. Conversion to

bicarbonate demonstrated a different spatial distribution, with highest signal in gray matter and relatively lower intensities in white matter and

subcutaneous tissues. 13C data were sinc‐interpolated to match the resolution of the 1

H images, and AUCs were normalized to the peak pyruvate

intensity

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4 | DISCUSSION

The goal of this study was to translate and investigate the feasibility of a new frequency‐specific EPI approach designed

for human studies to acquire HP 13C metabolite images from

cancer patients. In this research, we acquired first‐ever volumetric data of HP [1‐

13C]pyruvate and its metabolic products [1‐

13C]lactate and 13C‐bicarbonate using a multi‐slice,

single‐shot echo planar readout in prostate cancer and brain

cancer patients. Dynamic imaging and whole‐organ coverage are crucial in translating this technology for clinical studies. This approach represents a significant advantage over

prior single‐slice acquisitions by enabling greater coverage

of tumor location(s) and over single time point approaches

that preclude kinetic rate measurements. The latter is important because simple ratio calculations are time‐dependent

and sub‐optimal because patient variations in perfusion can

introduce quantification errors in ratio calculations. In the

phase 1 trial of prostate cancer patients,6 one approach used

was a 2D dynamic EPSI sequence to acquire a single slice

(10 × 10 mm2 in‐plane resolution, 12–40 mm through‐plane)

every 5 s. Another approach used a single time point 3D EPSI

to acquire an entire volume with 0.5 cm3 spatial resolution

over 8–12 s with an FOV of ~8 × 8 cm2. In contrast, the EPI

approach investigated in this study enabled both improved

temporal resolution (2 s resolution for prostate studies and

3 s resolution for brain studies) and whole‐organ coverage

(12.8 × 12.8 × 12.8 cm3 for the prostate, 24 × 24 × 16 cm3

for the brain) without sacrificing spatial coverage or temporal resolution.

The dynamic time course and AUC maps of pyruvate

metabolism in the brain highlights the ability of HP 13C‐

pyruvate EPI to detect multiple biochemical conversions with

multi‐slice volumetric coverage of the entire brain for the first

time. The differential metabolism observed between gray and

white matter may be because of physiological differences or

the coil reception profile, which accentuates signal from the

cortex and subcutaneous tissue closest to the receive array.

Nevertheless, the peak SNR was nearly an order of magnitude

higher for pyruvate than for lactate or bicarbonate in the 3 initial brain studies. This difference in signal provides a potential

opportunity to improve SNR for bicarbonate and lactate by

optimizing the flip angle for each metabolite.22,23 Ultimately,

the achievable spatial resolution will be determined by the

metabolite of interest with the lowest SNR, which was bicarbonate in the 3 patient studies performed here.

The multichannel brain data in this work were combined

using a sum‐of‐squares approach. This resulted in spatial intensity variation throughout the raw images because of the

receive profile of each coil. Although this variation is implicitly removed when computing the apparent rate constant

or AUC ratio map, the individual dynamic images reflect the

sensitivity profile of the 32‐channel array. This non‐uniform

intensity could potentially be corrected using fiducial markers to analytically calculate the reception profile using the

Biot‐Savart law,24 from coil sensitivity maps obtained from

a thermal 13C phantom, or from reception profiles extracted

from the fully sampled hyperpolarized data using ESPIRiT.25

Improved coil combination methods26 could also be used to

improve image quality over the conventional sum‐of‐squares

approach used in this work.

Although the specific absorption rate (SAR) is nucleus‐

independent,27 the lower 13C gyromagnetic ratio places

greater demands on gradient performance, potentially resulting in long ramp times at maximum slew‐rate that may cause

peripheral nerve stimulation (PNS). Using a low bandwidth

readout or increasing the rise time will minimize PNS but

will further increase the echo‐spacing, increasing the sensitivity to off‐resonance. The ability to accurately set the transmit center frequency is therefore crucial to the success of this

approach, as off‐resonance can impact the effectiveness of

SPSP RF pulses because of their narrow passband and can

result in a bulk shift in the phase‐encode (blip) dimension

for EPI studies. The frequencies measured based on residual HP 13C signal after the EPI acquisition indicated that this

TABLE 1 Summary of EPI brain studies

Study Δf (Hz)

13C polarization

(%)

Time to

injection

(s)

Pyruvate Lactate Bicarbonate

Peak SNR

TTP

(s) Peak SNR

TTP

(s) Peak SNR

TTP

(s)

1 +3.7 41.3 54 447 9 30 12 6 15

2 +3.7 41.9 60 396 3 28 6 7 9

3 +6.1 33.1 53 402 9 16 9 8 15

Abbreviation: TTP, time‐to‐peak.

All brain data were acquired with 1.5 × 1.5 cm2 in‐plane resolution using a constant 20° pyruvate/30° lactate/30° bicarbonate flip angle scheme and an integrated birdcage

and 32 channel head coil. TTP signal is referenced from the start of acquisition, and the reported polarization is referenced to the start of dissolution. The error in center

frequency calibration (Δf) was measured with non‐localized spectroscopy after dynamic imaging

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| GORDON ET AL. 7

was not a substantial effect in these studies. EPI shift artifacts

due to larger receive frequency errors can be corrected for

by phase‐modulating the data in k‐space or by reversing the

blip polarity every other time frame.28 For setups where a

urea phantom is impractical, the center frequency can also be

calibrated using the water frequency. In this case, a B1

+ map

could be acquired from the hyperpolarized substrate using

a Bloch‐Siegert approach29 to calibrate the transmit power.

Conversely, the transmit B1 field would not be uniform when

using a surface coil for excitation. Although a urea phantom

could still be used for power calibration, it would require a

known, pre‐measured change in power to provide the desired

flip angle at depth.

Finally, in these initial studies, the total readout time for

each slice was 9.9 ms for prostate studies and 16.5 ms for

brain studies. Although this resulted in short echo‐spacing

and made the acquisitions more robust to B0 inhomogeneity,

we anticipate that the SNR could readily be improved by increasing the total readout duration, given the relatively long

T2

*

of 13C substrates.30 However, this will place more of a

burden on shimming and frequency calibration, as a further

increase in echo‐spacing would make the acquisition more

susceptible to geometric distortion and bulk shifts in the blip

dimension. In this case, alternating the blip polarity each time

frame31 or using a dual‐echo EPI acquisition32,33 could potentially be used to correct for distortion and signal loss arising

from B0 inhomogeneity.

5 | CONCLUSION

This study demonstrated the feasibility of symmetric EPI

to acquire hyperpolarized 13C metabolite maps in brain and

prostate cancer patients. As an advance over prior spectroscopic imaging approaches, this metabolite‐specific EPI acquisition provided robust whole organ coverage for brain and

prostate studies while retaining high SNR, spatial resolution,

and dynamic temporal resolution.

ACKNOWLEDGMENTS

This research was supported by NIH grants R01EB017449,

R01CA183071, P41EB013598, P01CA118816, and

R01CA211150.

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SUPPORTING INFORMATION

Additional supporting information may be found online in

the Supporting Information section at the end of the article.

FIGURE S1 Variable flip angle schedule for [1‐

13C]pyruvate and [1‐

13C]lactate used in prostate studies (A). An 8 M

13C urea phantom embedded in the endorectal coil was used

for center frequency and RF power calibration during the

study. Imaging the 13C urea phantom with the pyruvate flip

schedule (B) confirms the RF power is properly calibrated

before hyperpolarized 13C imaging

FIGURE S2 4D dynamics of [1‐

13C]pyruvate, with a 3‐s

temporal resolution. For anatomic reference, 1H FLAIR images are on the left. Data are displayed in arbitrary units with

a fixed window/level across all slices and time frames

FIGURE S3 4D dynamics of [1‐

13C]lactate, with a 3‐s temporal resolution. For anatomic reference, 1

H FLAIR images

are on the left. Data are displayed in arbitrary units with a

fixed window/level across all slices and time frames

FIGURE S4 4D dynamics of 13C bicarbonate, with a 3‐s

temporal resolution. The 13C urea phantom, visible in the 4th

slice, was excited by the edge of the SPSP RF pulse. For anatomic reference, 1

H FLAIR images are on the left. Data are

displayed in arbitrary units with a fixed window/level across

all slices and time frames

TABLE S1 Summary of EPI prostate studies. Prostate data

was acquired with 0.8 × 0.8 × 0.8 cm3

spatial resolution

using a variable flip angle schedule (Supporting Information

Figure S1) and an endorectal receive coil. The error in center

frequency calibration (Δf) was measured with non‐localized

spectroscopy following dynamic imaging

How to cite this article: Gordon JW, Chen H‐Y,

Autry A, et al. Translation of Carbon‐13 EPI for

hyperpolarized MR molecular imaging of prostate and

brain cancer patients. Magn Reson Med. 2018;00:1–8.

https://doi.org/10.1002/mrm.27549

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Technique development of 3D dynamic CS-EPSI

for hyperpolarized 13C pyruvate MR molecular

imaging of human prostate cancer

研究背景

研究過程簡介

研究結(jié)果

研究對象

?研??????????? 3D ??? 13 ???????????) ?EPSI) MR ??????????????

??????????????????極??代謝?????] ?1- 13C] ????] 1-13C] ??????????

?????全?????

???????極?) dDNP) ??極?) HP)13C MR ???? 100 ????????研?????????????

13C ?????????????????????????????????????????????

???????????????????集???????????????????? HP ????????

???????? 3D ?????????????) ?3Ddynamic CS-EPSI) ?????????????????

???? RF ????????? blip ??????? EPSI ????????????研????? 3D ?????

?????????????? (TRAMP) ?????????????????????????????????

???????????????????????? B1 ?????

???????????????????? Gleason 4 + 3 ????? HP ?????????????? (A) T2-

FSE ????? (B) ??????????????? ???? ADC ????????? ADC ????? (C) ???

????????????????????????????????????????? (D) ? t 5 36 s ???

???代????? (E) ???????? ?kPL ???????????????? kPL ????????????

???????? 4 + 3 ?????

????ǖ????

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研究結(jié)論

應用方向

???? 3D ?? MRSI ?集?????????????????FID??????? CS ????????研??

???????????????????????? ????????研?????????????????

SNR ????????????????????集?????????????? ??????????? 3D

?? HP MR ???] 1-C] ?????] ?1-C] ?????????? kPL ???????????????????

??代謝???????????????????

????????

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FULL PAPER

Technique development of 3D dynamic CS-EPSI for

hyperpolarized 13C pyruvate MR molecular imaging of human

prostate cancer

Hsin-Yu Chen1 | Peder E.Z. Larson1 | Jeremy W. Gordon1 | Robert A. Bok1 |

Marcus Ferrone2 | Mark van Criekinge1 | Lucas Carvajal1 | Peng Cao1 |

John M. Pauly3 | Adam B. Kerr3 | Ilwoo Park4 | James B. Slater1 |

Sarah J. Nelson1 | Pamela N. Munster5 | Rahul Aggarwal5 | John Kurhanewicz1 |

Daniel B. Vigneron1

1Department of Radiology and Biomedical Imaging, University of California, San Francisco, California

2

Department of Clinical Pharmacy, University of California, San Francisco, California

3

Electrical Engineering, Stanford University, Stanford, California

4

Department of Radiology, Chonnam National University Medical School and Hospital, Gwangju, Chonnam, Korea

5

Department of Medicine, University of California, San Francisco, California

Correspondence

Hsin-Yu Chen, Department of Radiology

and Biomedical Imaging, University of

California, San Francisco, 1700 Fourth

Street, Byers Hall Suite 102,

San Francisco, CA 94158, USA.

Email: Hsin-yu.Chen@ucsf.edu

Funding information

National Institutes of Health, Grant/

Award Numbers: R01EB017449,

R01EB013427, R01CA166655, and

P41EB013598

Purpose: The purpose of this study was to develop a new 3D dynamic carbon-13

compressed sensing echoplanar spectroscopic imaging (EPSI) MR sequence and test

it in phantoms, animal models, and then in prostate cancer patients to image the metabolic conversion of hyperpolarized [1-13C]pyruvate to [1-13C]lactate with whole

gland coverage at high spatial and temporal resolution.

Methods: A 3D dynamic compressed sensing (CS)-EPSI sequence with spectral–

spatial excitation was designed to meet the required spatial coverage, time and spatial

resolution, and RF limitations of the 3T MR scanner for its clinical translation for

prostate cancer patient imaging. After phantom testing, animal studies were performed in rats and transgenic mice with prostate cancers. For patient studies, a GE

SPINlab polarizer (GE Healthcare, Waukesha, WI) was used to produce hyperpolarized sterile GMP [1-13C]pyruvate. 3D dynamic 13C CS-EPSI data were acquired

starting 5 s after injection throughout the gland with a spatial resolution of 0.5 cm3

,

18 time frames, 2-s temporal resolution, and 36 s total acquisition time.

Results: Through preclinical testing, the 3D CS-EPSI sequence developed in this

project was shown to provide the desired spectral, temporal, and spatial 5D HP 13C

MR data. In human studies, the 3D dynamic HP CS-EPSI approach provided firstever simultaneously volumetric and dynamic images of the LDH-catalyzed conversion of [1-13C]pyruvate to [1-13C]lactate in a biopsy-proven prostate cancer patient

with full gland coverage.

Conclusion: The results demonstrate the feasibility to characterize prostate cancer

metabolism in animals, and now patients using this new 3D dynamic HP MR technique to measure kPL, the kinetic rate constant of [1-13C]pyruvate to [1-13C]lactate

conversion.

Magn Reson Med. 2018;1–11. wileyonlinelibrary.com/journal/mrm VC 2018 International Society for Magnetic Resonance in Medicine | 1

Received: 19 October 2017 | Revised: 23 February 2018 | Accepted: 23 February 2018

DOI: 10.1002/mrm.27179

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KEYWORDS

human prostate cancer, hyperpolarized C-13 pyruvate, 3D dynamic imaging

1 | INTRODUCTION

Hyperpolarized (HP) 13C MR using dissolution dynamic

nuclear polarization (dDNP) has been shown in over 100

published animal studies to provide unprecedented information on previously inaccessible aspects of biological processes by detecting endogenous, nontoxic 13C-labeled probes

that can monitor enzymatic conversions through key biochemical pathways.1–11 A human Phase 1 clinical trial using

a custom-designed polarizer in a cleanroom demonstrated the

safety and feasibility of HP 13C-pyruvate MRI in prostate

cancer patients.12 This clinical trial indicated the potential to

characterize the extent and aggressiveness of prostate cancer

in individual subjects to ultimately benefit clinical treatment

decisions and to monitor treatment response that is an unmet

clinical need.12 However, the acquisition techniques used in

that first human study provided only slice dynamic information on the conversion of [1-13C]pyruvate to [1-13C]lactate

and single time point 3D 13C MRSI data acquired over 12 s.

To be clinically useful, dynamic 3D acquisitions with full

gland coverage are required and with a spatial resolution fine

enough to study 0.5 cm3 tumors and a temporal resolution

adequate to measure quantitatively the conversion rate, kPL,

of pyruvate to lactate.

The goal of this project was to develop a new dynamic

and volumetric acquisition to detect HP pyruvate uptake

and enzymatic conversion throughout the prostate with

high spatial and temporal resolution. A new 3D dynamic

compressed sensing echoplanar spectroscopic imaging (3D

dynamic CS-EPSI) sequence was developed and comprised

of spectral–spatial RF excitations with multiband and

variable-flip schemes, followed by a compressed-sensing

EPSI readout using random blip encoding. The 3D

dynamic imaging protocol was tested in phantoms, transgenic mice of prostate cancer (TRAMPs), and rats before

translating this approach for human studies. The translational challenges, including larger imaging volume, reduced

peak RF power and lower B1 inhomogeneity were

addressed through the optimization of pulse design and

sequence parameters.

2 | METHODS

2.1 | Pulse sequences

A 3D dynamic CS-EPSI sequence was designed and optimized to provide more efficient, higher SNR hyperpolarized

13C MR scans of pyruvate metabolism in animals and

humans. The backbone of this sequence consists of a spectral–spatial RF excitation pulse, followed by a compressed

sensing EPSI readout. Prior TRAMP studies1,13 used a

double-spin echo (DSE) refocusing pulse to provide narrow

spectral lines and improve SNR (TE/TR 5 150/250 ms)

(Figure 1A). For patient studies, no spin-echo refocusing

pulses were used (Figure 1B) because of peak power limitations and the increased B1 inhomogeneity for the clamshell

transmit coil. The estimated SAR of the 3D CS-EPSI

sequence was well below the Food and Drug Administration

(FDA) requirements. The 3D readout scheme used pseudorandom “blip” encoding in the kx-ky-dynamic directions and

flyback EPSI in the kz-kt dimensions. The compressed sensing reconstruction takes advantage of the sparsity in the spatial and temporal-wavelet dimensions to recover

undersampled k-space locations using L1-minimization with

total variation penalty, achieving 18 3 acceleration. The

EPSI readout enabled another 16-fold acceleration compared

to conventional chemical-shift imaging by the rapid simultaneous spectral–spatial encoding.14,15 A combined

288 3 acceleration factor condenses a 10-min fully sampled

MRSI acquisition into a 2-s undersampled time interval.

Acquiring data without DSE refocusing pulses required modification of the prior compressed sensing reconstruction algorithm1,15 to incorporate spectral phasing and minimize

linewidth broadening. The reconstruction included a linear

phase correction to account for the additional phase caused

by sampling delay.

2.2 | RF pulses design

The RF excitation pulse provided multiband excitation to

account for the metabolic conversions between 13C pyruvate

and lactate. Moreover, a “variable flip angle” scheme was

applied, where the excitation flip angle on each metabolite

was progressively increased to account for the loss from previous excitations and the intrinsic T1 relaxation. The flip

angles were calculated based on a “T1-effective” scheme,

ensuring adequate pyruvate SNR while maximizing total lactate SNR for robust modeling of metabolic conversion and

parameter estimation.16 The spectral–spatial pulses were

designed using the SS-RF toolbox developed by Larson

et al.17

A new spectral-spatial RF pulse was designed and generated to account for the limitation on peak power in the clinical setup (Figure 2A). The new SSRF pulse has a peak B1 of

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0.597G and duration of 6.3 ms, which is a 67% reduction of

peak power and 30% reduction in length compared to our

preclinical designs (peak B1 5 1.796 G, duration 5 8.9 ms,

applied in the preclinical data sets in this study). The pulse

bandwidth was 793 Hz. The ripple was set to <1% in both

passband and stopband to ensure reasonably homogeneous

pulse profile. The 13C RF calibration protocol is summarized

in the Supporting Information.

2.3 | 3D imaging coverage

The 3D CS-EPSI sequence15 was designed to offer full 3D

coverage for the regions of interest with high spatiotemporal

resolution in both preclinical1 and now clinical research in

this study. In TRAMP mice studies, the sequence was configured to cover the entire animal, which has 2 advantages.

First, the coverage allows for blood vessels such as the iliac

FIGURE 1 The HP-13C 3D CS-EPSI sequence diagram designed for in vivo studies. (A) The double spin-echo enabled (DSE mode) was used in a

previous report of mouse prostate cancer imaging.1 (B) The imaging mode (FID mode) in this study was chosen for larger imaging volumes and to account

for peak B1 limitations with the human coil setup.

FIGURE 2 New spectral–spatial RF pulses were designed using the ss-RF toolbox by Larson et al.17 (A) The 6.3 ms-long RF pulse excites 13C pyruvate and lactate with independent variable flip angles. Red is magnitude, blue is real, and green is imaginary components. The peak B1 of 0.597 G is a 67%

reduction from that used for preclinical studies. (B) Phantom data excited with progressive-increasing flip RF showed good agreement with simulated

profile.

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artery to be included, and therefore enables acquisition of the

arterial input function (AIF) and potentially factor perfusion

into the dynamic modeling. Second, it allows not only imaging the primary tumor, but common metastatic sites, such as

peri-arterial (PA) and peri-renal (PR) lymph nodes. In addition, it monitors key physiological regions (e.g., kidney and

liver) for possible abnormalities associated with prostate cancer. In rat studies, the FOV was chosen to extend through the

rat trunk for similar reasoning. In clinical exams, the

sequence covers the full prostate gland from base to apex,

including the peripheral, central, and transition zones. The

581 Hz-spectral bandwidth ensures inclusion of the 2 main

biomarkers in preclinical studies (i.e., HP-13C pyruvate and

lactate). Note the urea phantom was spectrally aliased to conserve spectral bandwidth for improved SNR efficiency.

2.4 | MRI experiments

Eleven sets of hyperpolarized 13C dynamic MRSI were

acquired on a total of 6 TRAMP mice and 3 healthy rats

using the 3D dynamic CS-EPSI. 3 TRAMPs had histologically aggressive late stage, and 3 had early stage tumors in

this study. Data sets (N 5 8) were collected from TRAMP

experiments, with 2 mice studied twice (on different days)

among the cohort of 6.

Two mice were studied twice among the cohort of 6.

[1-13C]pyruvate was polarized by a GE SPINlab clinical

polarizer (GE Healthcare, Waukesha, WI) using the dDNP

technique for 2 h, yielding 25–35% pyruvate polarization.

The 13C substrate was rapidly dissolved and injected into the

subject animal through a tail vein catheter. For the TRAMP

studies, !350 lL bolus was injected over 15 s, whereas the

rats received !3 mL bolus over 12 s. In both cases, the

sequence was initiated at t 5 15 s since the beginning of

injection. All studies were performed on a 3T clinical scanner (GE Healthcare). The mouse and rat studies were done

using custom-built, dual-tuned 1

H and 13C mouse and rat

coils, respectively. Dose per unit weight was !10 mL/kg for

TRAMP mouse and 6 mL/kg for rat, both injected with

80 mM solution.

For TRAMP mouse studies, the 3D CS-EPSI sequence

was chosen to provide a spatial resolution of

3.3 3 3.3 3 5.4 mm, a temporal resolution of 2 s, a FOV of

4 3 4 3 8.6 cm, a spectral BW of 581 Hz, and 18 time frames

in 36 s. For rats, the FOV and the spatial voxel size were

both doubled to provide larger coverage (spatial resolution 5 6.7 3 6.7 3 10.8 mm, FOV 5 8 3 8 3 17.2 cm),

whereas temporal resolution and acquisition window

remained the same as TRAMP scans. The HP-13C voxel volume for mouse and rat scans were 0.059 and 0.480 cm3

,

respectively. A proton T2-FSE sequence was prescribed for

anatomical reference in TRAMP exams, whereas a bSSFP

sequence served as the reference in rat studies.

Phantom studies were conducted using the full clinical configuration with clamshell transmit and endorectal receive coils.

The phantom setup includes a built-in 13C-urea phantom positioned on the receive coil (8M, 600 lL) and 2 ethylene glycol

phantoms (natural abundance, 13C concentration 5 0.17M).

The pulse sequence for the clinical studies was used.

For the human study (N 5 1), GMP-grade sterile [1-13C]

pyruvic acid with 15 mM trityl radical was polarized in Spinlab for !2 h, dissolved with sterile water, and subjected to

radical filtration, neutralization, and sterile filtration into a

Medrad syringe. An automatic post-dissolution QC reported

key parameters including pyruvate concentration (253 mM),

polarization level (37%), radical concentration (0.7 lM), pH

(7.8), and temperature (32.9 8C), and a pharmacist determined that the bolus met all safety standards for injection.

Dosage was calculated based on patient weight for 0.43 mL/

kg of the 250 mM sterile pyruvate solution. The injection

used a power injector (Spectris Solaris, Medrad, Saxonburg,

PA) at a rate of 5 mL/s, followed by flush of saline. Total

injection time was !10–15 s depending on patient weight.

In the clinical setup, a clamshell volume coil was used

for 13C transmit and a dual-tuned endorectal coil for receive.

The resolution for the patient study was as follows (spatial

resolution 5 8 3 8 3 8 mm isotropic, FOV 5 9.6 3 9.6 3

12.8 cm). Acquisition window was 36 s for the patient study,

with voxel volume of 0.5 cm3

. The proton acquisitions were

done using a 4-channel pelvic phased coil array in

FIGURE 3 Phantom studies using the clinical setup, the 3D CS-EPSI sequence, and the new RF pulses showed good spatial homogeneity in a urea

syringe.

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combination with the 1H-tuned endorectal coil element. A

T2-weighted fast-spin echo sequence provided anatomical

reference, with the following parameters: FOV

18 3 18 3 7.2 cm, spatial resolution 5 0.35 3 0.35 3 3 mm,

TE/TR 5 102/5000 ms, and NEX 5 3.

The human research was conducted with the approval

from Institutional Review Board, and all animal studies were

conducted in accordance with the policies of Institutional

Animal Care and Use Committee at University of California,

San Francisco.

2.5 | Data analysis

The hyperpolarized 13C 3D CS-EPSI data were reconstructed

using an in-house command-line script combined with MATLAB (The MathWorks, Natick, MA) routine.1,15 A combination of an open-source SIVIC image processing software18

and MATLAB was used for examination of the fully 3D

spectrum voxel-by-voxel, over a specific slice and orientation, or across a given time frame. Overlay of HP-13C

images, image-based statistics or modeled metabolic and perfusion indices such as kPL and ktrans, with the anatomical reference scans was performed for better lesion identification

and analysis.

Dynamic modeling of the pyruvate to lactate conversion

was calculated using a 2-site exchange model including a

pyruvate arterial input function (AIF) assumed to be a boxcar

function, defined by injection rate r0, similar to the model

reported by Zierhut et al.19 The model used is described in

the following ODE form

dMpyretT=dt5r0 # e2qt # ?uetT2uet2aT%2eq1kPLTMpyretT;

(1)

dMlacetT=dt5kPL # MpyretT2q # MlacetT; (2)

where Mx is the magnetization of metabolite x and kPL is the

pyruvate-to-lactate conversion rate constant. q is the relaxation coefficient, where q 5 1/T1, uetT is the unit step function, and a is the bolus duration. Here, the alanine fitting was

included as it could improve the quantitative accuracy of

kPL.

The rate coefficient for pyruvate-to-lactate conversion,

kPL, was computed by applying the metabolic models to the

in vivo HP-13C dynamic profile. The signal curves were fitted

to the dynamic models using the non-linear least squares analysis. The mean was calculated over the manually selected

tumor ROI for the kPL estimation, where only voxels with

>85% tumor were incorporated. RF excitations and relaxation

T1 were included in the model to account for signal loss,

FIGURE 4 Similar to the “DSE” mode, the in vivo dynamics of 13C biomarker acquired using the 3D dynamic CS-EPSI “FID” mode can be quantitatively analyzed by compartmental exchange models. Pyruvate and lactate dynamics were overlaid on T2-FSE scan in a low-grade TRAMP tumor. The calculated kPL value was 0.0297 (s21

).

FIGURE 5 Pyruvate-to-lactate conversion in the kidneys of healthy rat is visualized in this 13C image overlaid on bSSFP reference. The calculated

kPL was 0.0058 (s21).

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