Liangdong Zhou1, Qihao Zhang1,2, Pascal Spincemaille1, Thanh D Nguyen1, John Morgan1, Weiying Dai1, Ajay Gupta1, Martin R Prince1, and Yi Wang1,2
1Weill Medical College of Cornell University, New York, NY, United States, 2Cornell University, Ithaca, NY, United States
Synopsis
Perfusion quantification is important for the
diagnosis of many diseases. Validation of perfusion quantification methods remains challenging due to the various assumptions and lack of the ground truth. We built a numerical phantom of microvascular network in the kidney. In the phantom, the ground truth blood velocity and flow were computed from Navier-Stokes equation. Tracer concentration was simulated based on the mass transport equation. Comparison between Kety's method and our recently proposed AIF-free QTM method was performed using the numerical phantom. It turns out that QTM method reduces the flow error by more than 3 folds compare with Kety's method.
Introduction
Validation of tissue
perfusion quantification remains challenging: the microsphere deposition approach
provides arguably the best reference standard so far but is yet problematically
dependent on transcapillary extraction details1-4. We propose here to validate perfusion quantification on a numerical
phantom, where the true tissue perfusion quantity is known according to the law
of transport physics of momentum and mass fluxes or Navier-Stokes and
continuity equations5,6. Accordingly, we validate the commonly used Kety’s method for perfusion
quantification, which uses an arterial input function (AIF), a global parameter
that is not justifiable for all voxels in an imaging volume7-9. We also validate a novel quantitative transport mapping (QTM)10-12.Methods and Materials
$$$\hspace{1cm}{\bf\text{1.Numerical microvascular network of the kidney}}$$$
The 3D shape of the kidney was obtained from the segmentation of the
combination of the M0 map and ASL data. The vasculature was constructed within
the segmented 3D shape of the kidney. The MRA was used to segment the renal
arteries, and the directions of renal arterial branches were used to ensure
that the constructed vasculature follows the correct direction pattern.
Starting from the segmented renal artery branches, the microvasculature
structure in the whole kidney was generated using the bifurcation branch rule13. The process of generating renal
microvascular branches was stopped
when the renal blood volume (RBV) in the cortex reached 16%-20%14,15. The vascular structure parameters were computed for all
voxels.
We adopted the Krogh model16 to compute the blood velocity and
pressure in the constructed microvascular network, and the solution of velocity
was then voxelized to serve as the ground truth velocity. Given the microvascular model, the
intravascular blood velocity follows the steady-state Navier-Stokes equation
and the tracer concentration is governed by the continuity equation17:
$$\rho_b({\bf\,u}\cdot\nabla){\bf\,u}\,=\,-\nabla\,p+\mu\nabla\cdot\nabla{\bf\,u},\,\quad{\bf\,r}\in\Omega_v,\qquad\,(1)$$ $$\rho_b\nabla\cdot{\bf\,u}=0,\,\quad{\bf\,r}\in\Omega_v,\,\qquad(2)$$where $$$\rho_b$$$ is the density of the blood, $$$p$$$ the pressure, $$$\mu$$$ the blood viscosity, $$$\Omega_v$$$ the domain of intravascular space.
The simulated
velocity and pressure were used to simulate the tracer concentration in the
microvascular network using the analytical approach18,19 for:
$$\partial_tc({\bf\,r},t)=-\nabla\cdot(c({\bf\,r},t){\bf\,u}({\bf\,r}))+\nabla\cdot(D({\bf\,r})\nabla\,c({\bf r},t))-\gamma\,c({\bf\,r},t),\quad {\bf\,r}\in\Omega_v,\,(3)$$ The simulated
concentration was voxelized for the use of QTM algorithm10-12 to reconstruct blood
velocity and flow.
$$$\hspace{1cm}{\bf\text{2.In vivo experiment}}$$$
The QTM was tested on 7 healthy subjects with 4
post-labeling delay kidney PCASL data. 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 gating20.Results
Figure 1 shows
the simulated microvasculature based on the 3D kidney shape segmented from MRA and M0 data, and the corresponding
structural parameters calculated from the microvascular network using
voxelization.
Figure 2
demonstrates the simulated forward problem solution of pressure, velocity, flow in the numerically
generated microvascular network. These results were used to generate the ground
truth of velocity and flow maps at the voxel level.
Figure 3
presents the simulated tracer concentration at different time points with
tracer labeling duration as 1.5s. The velocity field in Figure 2 (b) was used
for the tracer delivery simulation.
Figure 4 shows
the comparison of numerical simulation results between ground truth, the QTM,
and Kety’s method. It shows that the
mean square root errors (MSRE) of estimated flow from QTM and Kety’s method are
49.7395 ml/100g/min and 169.1531 ml/100g/min, which are of 18.6% and 63.4% of
the mean of the ground truth flow 266.64ml/100g/min, respectively.
Figures 5
displays the in vivo results for one healthy volunteer. QTM provides an additional velocity field map, which is not available in Kety's method. For all seven healthy
subjects, the mean blood flow in the cortex was $$$498\pm46$$$ ml/100g/min and $$$556\pm36$$$ ml/100g/min for QTM and Kety’s method,
respectively. For the medulla region, blood flow was $$$263\pm54$$$ ml/100g/min and $$$385\pm79$$$ ml/100g/min, for QTM and Kety’s method,
respectively.Discussion and conclusion
In the
numerical phantom of kidney vasculature where the true tissue perfusion
quantity is known, QTM drastically reduces Kety’s flow error by more than 3
folds. In preliminary in vivo results,
automated QTM processing from multiple pulse labeling delays is feasible, but
QTM generates regional blood flow different in value from Kety’s flow. It seems that Kety's method is sensitive to the error in the M0 image. The QTM model
is a biophysics-based quantitative description of blood transport in the
microvascular network to the tissue in which AIF is not required. Voxelization
with the constructed microvasculature is needed to discretize the continuous
model into voxel-level discrete space. Numerical results show that the
reconstructed average blood velocity and flow maps from QTM agree well with the
ground truth, yet residual error remains likely due to approximation in
carrying out the very expensive computation of Eqs. 1&3.
In conclusion,
numerical vascular phantoms with the known ground truth of perfusion provide
validation of experimental perfusion quantification methods. The novel QTM
method is fairly accurate, while the traditional Kety’s method is quite
erroneous.Acknowledgements
No acknowledgement found.References
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