Incorporating cross-voxel exchange into the analysis of dynamic contrast-enhanced imaging data: theory, simulations and experimental results

Model discovery approach enables noninvasive measurement of intra-tumoral fluid transport in dynamic MRI

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a routine method to noninvasively quantify perfusion dynamics in tissues. The standard practice for analyzing DCE-MRI data is to fit an ordinary differential equation to each voxel. Recent advances in data science provide an opportunity to move beyond existing methods to obtain more accurate measurements of fluid properties. Here, we developed a localized convolutional function regression that enables simultaneous measurement of interstitial fluid velocity, diffusion, and perfusion in 3D. We validated the method computationally and experimentally, demonstrating accurate measurement of fluid dynamics in situ and in vivo. Applying the method to human MRIs, we observed tissue-specific differences in fluid dynamics, with an increased fluid velocity in breast cancer as compared to brain cancer. Overall, our method represents an improved strategy for studying interstitial flows and interstitial transport in tumors and patients. We expect that our method will contribute to the better understanding of cancer progression and therapeutic response.

Identifiability of spatiotemporal tissue perfusion models

Objective.Standard models for perfusion quantification in DCE-MRI produce a bias by treating voxels as isolated systems. Spatiotemporal models can remove this bias, but it is unknown whether they are fundamentally identifiable. The aim of this study is to investigate this question in silico using one-dimensional toy systems with a one-compartment blood flow model and a two-compartment perfusion model.Approach.For each of the two models, identifiability is explored theoretically and in-silico for three systems. Concentrations over space and time are simulated by forward propagation. Different levels of noise and temporal undersampling are added to investigate sensitivity to measurement error. Model parameters are fitted using a standard gradient descent algorithm, applied iteratively with a stepwise increasing time window. Model fitting is repeated with different initial values to probe uniqueness of the solution. Reconstruction accuracy is quantified for each parameter by comparison to the ground truth.Main results.Theoretical analysis shows that flows and volume fractions are only identifiable up to a constant, and that this degeneracy can be removed by proper choice of parameters. Simulations show that in all cases, the tissue concentrations can be reconstructed accurately. The one-compartment model shows accurate reconstruction of blood velocities and arterial input functions, independent of the initial values and robust to measurement error. The two-compartmental perfusion model was not fully identifiable, showing good reconstruction of arterial velocities and input functions, but multiple valid solutions for the perfusion parameters and venous velocities, and a strong sensitivity to measurement error in these parameters.Significance.These results support the use of one-compartment spatiotemporal flow models, but two-compartment perfusion models were not sufficiently identifiable. Future studies should investigate whether this degeneracy is resolved in more realistic 2D and 3D systems, by adding physically justified constraints, or by optimizing experimental parameters such as injection duration or temporal resolution.

Model discovery approach enables non-invasive measurement of intra-tumoral fluid transport in dynamic MRI

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a routine method to non-invasively quantify perfusion dynamics in tissues. The standard practice for analyzing DCE-MRI data is to fit an ordinary differential equation to each voxel. Recent advances in data science provide an opportunity to move beyond existing methods to obtain more accurate measurements of fluid properties. Here, we developed a localized convolutional function regression that enables simultaneous measurement of interstitial fluid velocity, diffusion, and perfusion in 3D. We validated the method computationally and experimentally, demonstrating accurate measurement of fluid dynamics in situ and in vivo. Applying the method to human MRIs, we observed tissue-specific differences in fluid dynamics, with an increased fluid velocity in breast cancer as compared to brain cancer. Overall, our method represents an improved strategy for studying interstitial flows and interstitial transport in tumors and patients. We expect that it will contribute to the better understanding of cancer progression and therapeutic response.

Incorporating cross-voxel exchange for the analysis of dynamic contrast-enhanced imaging data: pre-clinical results

Tumours exhibit abnormal interstitial structures and vasculature function often leading to impaired and heterogeneous drug delivery. The disproportionate spatial accumulation of a drug in the interstitium is determined by several microenvironmental properties (blood vessel distribution and permeability, gradients in the interstitial fluid pressure). Predictions of tumour perfusion are key determinants of drug delivery and responsiveness to therapy. Pharmacokinetic models allow for the quantification of tracer perfusion based on contrast enhancement measured with non-invasive imaging techniques. An advanced cross-voxel exchange model (CVXM) was recently developed to provide a comprehensive description of tracer extravasation as well as advection and diffusion based on cross-voxel tracer kinetics (Sinnoet al2021). Transport parameters were derived from DCE-MRI of twenty TS-415 human cervical carcinoma xenografts by using CVXM. Tracer velocity flows were measured at the tumour periphery (mean 1.78-5.82μm.s^-1) pushing the contrast outward towards normal tissue. These elevated velocity measures and extravasation rates explain the heterogeneous distribution of tracer across the tumour and its accumulation at the periphery. Significant values for diffusivity were deduced across the tumours (mean 152-499μm².s^-1). CVXM resulted in generally smaller values for the extravasation parameterKext(mean 0.01-0.04 min^-1) and extravascular extracellular volume fractionve(mean 0.05-0.17) compared to the standard Tofts parameters, suggesting that Toft model underestimates the effects of inter-voxel exchange. The ratio of Tofts' extravasation parameters over CVXM's was significantly positively correlated to the cross-voxel diffusivity (P< 0.0001) and velocity (P= 0.0005). Tofts' increasedvemeasurements were explained using Sinnoet al(2021)'s theoretical work. Finally, a scan time of 15 min renders informative estimations of the transport parameters. However, a duration as low as 7.5 min is acceptable to recognize the spatial variation of transport parameters. The results demonstrate the potential of utilizing CVXM for determining metrics characterizing the exchange of tracer between the vasculature and the tumour tissue. Like for many earlier models, additional work is strongly recommended, in terms of validation, to develop more confidence in the results, motivating future laboratory work in this regard.