Liangdong Zhou1, Jinwei Zhang1,2, Qihao Zhang1,2, Pascal Spincemaille1, Thanh D Nguyen1, Yi Wang1,2, and Liangdong Zhou3
1Weill Medical School of Cornell University, New York, NY, United States, 2Cornell University, Ithaca, NY, United States, 3Radiology, Weill Medical School of Cornell University, New York, NY, United States
Synopsis
Perfusion
parameters, including blood flow (BF), apparent blood velocity (V), blood
volume (BV) and arterial transit time (ATT) are useful for the disgnosis of
many dieases. Typically, perfusion quantification methods utilize the tracer
concentration (ASL, DEC, DSC, etc.) as input and blood flow map as output. We proposed a deep learning-based
perfusion parameters mapping (DL-PPM), which uses 4D
time-revolved tracer concentration as input and perfusion parameters (BF, V,
BV, ATT) as output. We tested the propose method using simulated data and in vivo data in kidney.
Introduction
Blood perfusion quantification is of essential importance
for the diagnosis of many diseases, including stroke, heart attack, cancer,
Alzheimer’s disease and other diseases that affect blood flow. Perfusion
parameters, including blood flow (BF), apparent blood velocity (V), blood
volume (BV) and arterial transit time (ATT) are useful for the diagnosis of
many diseases1-5. Typically, perfusion
quantification methods utilize the tracer concentration (ASL, DEC, DSC, etc.)
as input and blood flow map as output6. Mapping all the perfusion
parameters mentioned from one dataset using the conventional perfusion quantification
method could be challenging. We proposed a deep learning-based perfusion
parameter mapping (PPM), which uses a dataset of simulated 4D time series of
tracer concentration as input and produces perfusion parameters (BF, V, BV, ATT)7,8. To validate DL-PPM method, we simulated a microvascular network in the kidney and the corresponding blood velocity using the
Navier-Stokes equation and tracer concentration based on mass transport
equation9. The ground truth of the
perfusion parameters was calculated from the simulation settings and served as
a training label. A recurrent neural network (RNN) was used to capture the data
relation between time frames.Methods and material
$$${\bf 1.\,Numerical\,simulation\,for\,training\,data}$$$
The blood velocity in the microvascular network follows the
static state Navier-Stokes equation10
$$\rho_b({\bf\,u}\cdot\nabla){\bf\,u}\,=\,\nabla\,p+\mu\nabla\cdot\nabla{\bf\,u},\,\quad{\bf\,r}\in\Omega_v,\qquad\,(1)$$ $$\rho_b\nabla\cdot{\bf\,u}=0,\,\quad{\bf\,r}\in\Omega_v,\,\qquad(2)$$ in which $$$\rho_b$$$ is the blood density, $$$p$$$ the blood pressure, $$$\mu$$$ the blood viscosity, and $$$\Omega_v$$$ the intravascular space. The blood pulsation
was ignored for simplicity.
Assume that the blood tracer has the same velocity as the
blood. The tracer concentration $$$c({\bf r},t))$$$ in the blood vascular space is governed by the
mass transport equation11
$$\partial_tc({\bf\,r},t)=-\nabla\cdot(c({\bf\,r},t){\bf\,u}({\bf\,r}))+\nabla\cdot(D({\bf\,r})\nabla\,c({\bf r},t))-\gamma\,c({\bf\,r},t),\quad {\bf\,r}\in\Omega_v,\,(3)$$ where $$$D$$$ is the diffusion coefficient, $$$\gamma$$$ is the tracer signal decay rate.
$$${\bf 2.\,Recurrent\,neural\,network}$$$
As the constructed ground truth of the perfusion parameters $$$G=(BF, V, BV, ATT)$$$ and the simulated tracer concentration data $$$C({\bf r},t)$$$ were obtained,
the recurrent neural network (RNN) was feed with $$$(G, C_{t_i}), i = 1, \ldots,N$$$ data pairs for training and validation, where $$$i$$$ is the time indicator and $$$N$$$ is the total number of time frames12. $$S_i=f(S_{i-1}W_{rec }+C_{t_i}W_c),\qquad(4)$$ where $$$S_i$$$ is the state at the time $$$t_i$$$, $$$C_{t_i}$$$ the exogenous input at time $$$t_i$$$, $$$W_{rec}$$$ and $$$W_c$$$ are weight parameters like that in feedforward
net. The fitting term to optimize during the training is defined as $$\min_{W_{rec}, W_c}\|Y_N-G\|_2.$$ Stochastic gradient descent on image patches was used during
the training.
$$${\bf 3.\,In\,vivo\,experiments}$$$
Renal arterial spin labeling (ASL) data was acquired with
multiple post-labeling delays (PLD) for seven healthy volunteers. The data
acquisition parameters are: 3D FSE PCASL, GE MR750 3T scanner, 32 channel body
coil, 2.5x2.5x4 mm3 voxel size, 128x128x36 matrix
size, 10.4840ms TE, 111o flip angle, three signal averages, ~4.5 min
scan time, PLD = 1025ms, 1525ms, 2025ms, 2525ms, background suppression,
synchronized breathing. At the same image acquisition session, non-contrast 3D
MR angiogram (MRA) IFIR data were acquired for each subject. Acquisition
parameters for the MRA include: 0.625x0.625x2 mm3 voxel size,
512x512x128 matrix size, 4.0240ms TR, 2.0120ms TE, 50o flip angle,
with breath gating13.
The numerical microvascular network for each volunteer was
constructed based on the hemodynamic principles with the anatomical information
from ASL, M0 and MRA images. The blood volume (BV) is computed from the
microvascular network structure. These microvascular networks serve as the
domain for equations (1)-(3). Therefore, the velocity (V), tracer concentration
(C) can be calculated by solving (1)-(3). ATT is obtained from the dynamics of tracer
transportation. The blood flow (BF) is computed from the velocity and the
microvascular network cross-sectional area. All of these parameters (BF, V, BV,
ATT) were then voxelized to the image voxel scale and set as the ground
truth (label image for training).
Results
Figure 1. shows the RNN architecture used for the training.
There are four input layers corresponding to the four PLDs of ASL data used.
Figure 2. presents the numerical simulation solutions in the
microvascular network. The ground truth of RBV is generated from the simulated
microvasculature, blood velocity (V) and flow (BF) are generated from the
voxelization of (b) and (c), ATT was captured from the time curve of tracer
concentration. These perfusion parameters ground truth and voxelized tracer
concentration data together serve as the training data.
Figure 3. displays the reconstruction results from the
proposed DL-PPM and the comparison of the results between DL-PPM, Kety’s method3,14 and the ground truth.
Figure 4. shows the quantitative estimation of the
reconstruction error for DL-PPM and Kety’s method in Figure 3.
Figure 5. shows the application of trained DL-PPM to in
vivo health volunteer data. The results were compared with the conventional
Kety’s method.Discussion and conclusion
The preliminary results from the numerically simulated data
and the in vivo data show that DL-PPM is able to generate four perfusion
parameters (BF, V, BV, ATT) from the multiple PLDs ASL data with acceptable accuracy. The quantitative
analysis of the blood velocity and flow implies that DL-PPM outperforms Kety’s
method. DL-PPM quantifies the perfusion parameters without using assumptions
that are generally required in Kety’s method15.
And DL-PPM does not need the AIF which might introduce bias or errors in the
conventional perfusion quantification methods.Acknowledgements
No acknowledgement found.References
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