Dictionary based approach for accelerated determination of Pharmacokinetic maps using Partial Least Square regression
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 Ktrans 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 Ktrans 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 phantom1. β coefficient obtained was used for TM-TD PLS to obtain PK maps for all simulation datasets. CTCs were fit for Ktrans 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-TD3 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/2013/100

References

[1] https://sites.duke.edu/dblab/

[2] Michallenges.org/dceChallenge2/clinical.html

[3] Tofts JMRI 1999

[4] Nithin N Vajuvalli et al, ISMRM, 2015

Figures

Figure 1 (a) Pharmacokinetics maps of randomly generated values of size 50 x 50 and (b) representative of QIBA generated values of size 180 x 60 along with differences of three approaches with respect to the GT

Figure 2 (a) Pharmacokinetics maps from TM-TD , TM-FD ,TM-TD PLS and TM-FD PLS on the seven breast data set from QIN for (a) Ktrans and (b) Ve with difference map

Figure 3 Plots of computational time vs RMSE for three approaches for (a) QIBA simulated data and (b) Random simulated data

Table 1 Comparison of computation time and RMSE for TM-TD, TM-FD and PLS for seven breast DCE data



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
1482