Nithin N Vajuvalli1, Shivaprasad Ashok Chikop1, and Sairam Geethanath1
1Medical Imaging Research Centre, Dayananda Sagar Institutions, Bangalore, India
Synopsis
This study is of
relevance to MR researchers interested in DCE-MRI. Tofts model is a well-established
two compartment model to determine the PharmacoKinetic (PK) maps, which is time
consuming due to the presence of iterative curve fitting for each voxel. Current
work focuses on the application of Partial Least Square (PLS) regression
modelling to determine PK maps. PLS is a statistical method based on PCA and
linear regression that provides the relationship between the predictor and
response variables. We
report 95-98% reduction in time as compared to curve fitting approaches for in silico phantoms and in vivo breast DCE data.Purpose
Current work focuses on
application of Partial Least Square (PLS) regression modelling to determine PK
maps as a faster solution as compared to curve fitting approaches to facilitate
online reconstruction of these maps. PLS is a statistical method based on PCA
and linear regression that provides the relationship between the predictor and
response variables through the determination of the regression co-efficient matrix β.
Methods
In
silico simulation: Concentration Time Curves (CTCs) were synthesized
through forward modelling of conventional
Tofts Model in Time Domain (TM-TD). Dictionary of CTCs was generated using 1000
K
trans and Ve values ranging between 0.001 – 1 and was taken as
ground truth (GT) to obtain β.
The β thus obtained was utilized
to obtain the K
trans and
Ve maps (TM-TD PLS).
Optimum β was selected by estimating
the error between the GT and PK maps obtained from TM-TD PLS for the varied number
of components values through Root Mean Square Error (RMSE). Twenty-one components
of the PLS were chosen based on the least RMSE value to obtain β. Two kinds of simulation data
were generated: randomly chosen PK value maps and the Quantitative Imaging
Biomarker Alliance (QIBA) DCE-MRI computer phantom
1. β
coefficient obtained was used for TM-TD PLS to obtain PK maps for all
simulation datasets. CTCs were fit for K
trans and Ve maps using
TM-TD, TM-FD and TM PLS. The error between the reconstructed and GT values were
quantified for both approaches through RMSE.
In-vivo
data: 7
breast DCE data were downloaded from Quantitative Imaging Network (QIN) and
details of acquisition are in ref (2). Tumor Region of Interest (ROI) selected
for determining the PK maps are shown in red outline. CTCs for the tumor ROI
pixels were curve fitted using two approaches TM-TD
3 and Tofts Model
in Frequency Domain (TM-FD)
4. Training of in vivo dictionary was performed on 2 datasets to obtain regression
coefficient matrix β using 21
components. Comparison of all approaches for
in vivo were performed with respect to either TM-TD and TM-FD as GT
in these cases and RMSE determined. Time taken for determining the PK maps for
each dataset was evaluated over 4 runs in each of these three approaches and
RMSE was calculated with respect to TM-TD or TM-FD correspondingly. The system
configuration used to carry out curve fitting and PLS regression was Intel Xeon
3.10 GHz, 8GB RAM. Computations were performed using Matlab, Mathworks Inc., USA
Results
Figure 1 depicts the PK
maps obtained from PLS, TM-TD and TM-FD approaches for both QIBA simulated data
and randomly simulated data. All three approaches
resulted in similar PK maps compared to GT as can be noticed through the
difference maps. Figure 2 depicts PK Maps obtained from TM-TD, TM-FD, TM-TD PLS
and TM-FD PLS for seven Breast DCE data with difference maps. PK maps obtained
from PLS approach is similar to the curve fitted data, as well as the PK values
lies within the physiological range.
Figure 3 depicts
computational time and RMSE for QIBA and randomly simulated data. It can be
observed that TM-TD results in more computational time and lesser error whereas
TM-FD resulted in less computational time compared to TM-TD but the RMSE values
was relatively higher. PLS resulted in less computational time compared to
TM-TD and TM-FD but RMSE values were marginally higher error compared to both
TM-TD and TM-FD, with RMSE values for PLS being much lesser than 0.01. Figure 4
depicts the table for computational time taken to obtain PK maps from three
approaches. It can be observed that PLS resulted in 95-98 % reduction in time
mean while resulting in similar PK maps.
Discussion
The difference map for
PLS approach is marginally higher for
in-vivo
PK maps compared to simulated data are due to the linear regression
coefficients approximating the time curve. However, in all these cases except
data 7
(low SNR), RMSE was lower than 0.01 indicating that the error would be within
limits of tolerance. Comparison of the computational time and RMSE depicted in
figure 3 confirms the superior performance of the TM-PLS over conventional
curve fitting model. TM-TD and TM-FD approach performs an iterative curve fit
for the model which makes computational time higher compared to TM-PLS which
operates on simple matrix multiplication and is typically not ‘data-aware’ but
only model dependent. PLS overcomes this limitation through combination of
regression as well as PCA based ‘data-awareness’. Efficient and knowledgeable
use of the number of components used during the PLS application could be
utilized for denoising of the maps through PCA.
Acknowledgements
Department of science and technology(DST), DST/TSG/NTS/2013/100References
[1] https://sites.duke.edu/dblab/
[2] Michallenges.org/dceChallenge2/clinical.html
[3] Tofts JMRI 1999
[4] Nithin N Vajuvalli et
al, ISMRM, 2015