A tracer-kinetic field theory for medical imaging

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.

Current status in spatiotemporal analysis of contrast-based perfusion MRI

In perfusion MRI, image voxels form a spatially organized network of systems, all exchanging indicator with their immediate neighbors. Yet the current paradigm for perfusion MRI analysis treats all voxels or regions-of-interest as isolated systems supplied by a single global source. This simplification not only leads to long-recognized systematic errors but also fails to leverage the embedded spatial structure within the data. Since the early 2000s, a variety of models and implementations have been proposed to analyze systems with between-voxel interactions. In general, this leads to large and connected numerical inverse problems that are intractible with conventional computational methods. With recent advances in machine learning, however, these approaches are becoming practically feasible, opening up the way for a paradigm shift in the approach to perfusion MRI. This paper seeks to review the work in spatiotemporal modelling of perfusion MRI using a coherent, harmonized nomenclature and notation, with clear physical definitions and assumptions. The aim is to introduce clarity in the state-of-the-art of this promising new approach to perfusion MRI, and help to identify gaps of knowledge and priorities for future research.

Exploring the potential of Physics-Informed Neural Networks to extract vascularization data from DCE-MRI in the presence of diffusion

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is widely used to assess tissue vascularization, particularly in oncological applications. However, the most widely used pharmacokinetic (PK) models do not account for contrast agent (CA) diffusion between neighboring voxels, which can limit the accuracy of the results, especially in cases of heterogeneous tumors. To address this issue, previous works have proposed algorithms that incorporate diffusion phenomena into the formulation. However, these algorithms often face convergence problems due to the ill-posed nature of the problem. In this work, we present a new approach to fitting DCE-MRI data that incorporates CA diffusion by using Physics-Informed Neural Networks (PINNs). PINNs can be trained to fit measured data obtained from DCE-MRI while ensuring the mass conservation equation from the PK model. We compare the performance of PINNs to previous algorithms on different 1D cases inspired by previous works from literature. Results show that PINNs retrieve vascularization parameters more accurately from diffusion-corrected tracer-kinetic models. Furthermore, we demonstrate the robustness of PINNs compared to other traditional algorithms when faced with noisy or incomplete data. Overall, our results suggest that PINNs can be a valuable tool for improving the accuracy of DCE-MRI data analysis, particularly in cases where CA diffusion plays a significant role.

Perfusion estimation using synthetic MRI-based measurements and a porous media flow model

The measurement of perfusion and filtration of blood in biological tissue give rise to important clinical parameters used in diagnosis, follow-up, and therapy. In this paper, we address techniques for perfusion analysis using processed contrast agent concentration data from dynamic MRI acquisitions. A new methodology for analysis is evaluated and verified using synthetic data generated on a tissue geometry.

Fluid Mechanics Approach to Perfusion Quantification: Vasculature Computational Fluid Dynamics Simulation, Quantitative Transport Mapping (QTM) Analysis of Dynamics Contrast Enhanced MRI, and Application in Nonalcoholic Fatty Liver Disease Classification

OBJECTIVE

We quantify liver perfusion using quantitative transport mapping (QTM) method that is free of arterial input function (AIF). QTM method is validated in a vasculature computational fluid dynamics (CFD) simulation and is applied for processing dynamic contrast enhanced (DCE) MRI images in differentiating liver with nonalcoholic fatty liver disease (NAFLD) from healthy controls using pathology reference in a preclinical rabbit model.

METHODS

QTM method was validated on a liver perfusion simulation based on fluid dynamics using a rat liver vasculature model and the mass transport equation. In the NAFLD grading task, DCE MRI images of 7 adult rabbits with methionine choline-deficient diet-induced nonalcoholic steatohepatitis (NASH), 8 adult rabbits with simple steatosis (SS) were acquired and processed using QTM method and dual-input two compartment Kety's method respectively. Statistical analysis was performed on six perfusion parameters: velocity magnitude | u | derived from QTM, liver arterial blood flow LBFa, liver venous blood flow LBFv, permeability Ktrans, blood volume Vp and extravascular space volume Ve averaged in liver ROI.

RESULTS

In the simulation, QTM method successfully reconstructed blood flow, reduced error by 48% compared to Kety's method. In the preclinical study, only QTM |u| showed significant difference between high grade NAFLD group and low grade NAFLD group.

CONCLUSION

QTM postprocesses DCE-MRI automatically through deconvolution in space and time to solve the inverse problem of the transport equation. Comparing with Kety's method, QTM method showed higher accuracy and better differentiation in NAFLD classification task.

SIGNIFICANCE

We propose to apply QTM method in liver DCE MRI perfusion quantification.

A proof-of-concept pipeline to guide evaluation of tumor tissue perfusion by dynamic contrast-agent imaging: Direct simulation and inverse tracer-kinetic procedures

Dynamic contrast-enhanced (DCE) perfusion imaging has shown great potential to non-invasively assess cancer development and its treatment by their characteristic tissue signatures. Different tracer kinetics models are being applied to estimate tissue and tumor perfusion parameters from DCE perfusion imaging. The goal of this work is to provide an in silico model-based pipeline to evaluate how these DCE imaging parameters may relate to the true tissue parameters. As histology data provides detailed microstructural but not functional parameters, this work can also help to better interpret such data. To this aim in silico vasculatures are constructed and the spread of contrast agent in the tissue is simulated. As a proof of principle we show the evaluation procedure of two tracer kinetic models from in silico contrast-agent perfusion data after a bolus injection. Representative microvascular arterial and venous trees are constructed in silico. Blood flow is computed in the different vessels. Contrast-agent input in the feeding artery, intra-vascular transport, intra-extravascular exchange and diffusion within the interstitial space are modeled. From this spatiotemporal model, intensity maps are computed leading to in silico dynamic perfusion images. Various tumor vascularizations (architecture and function) are studied and show spatiotemporal contrast imaging dynamics characteristic of in vivo tumor morphotypes. The Brix II also called 2CXM, and extended Tofts tracer-kinetics models common in DCE imaging are then applied to recover perfusion parameters that are compared with the ground truth parameters of the in silico spatiotemporal models. The results show that tumor features can be well identified for a certain permeability range. The simulation results in this work indicate that taking into account space explicitly to estimate perfusion parameters may lead to significant improvements in the perfusion interpretation of the current tracer-kinetics models.

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.

Prediction of Lung Shunt Fraction for Yttrium-90 Treatment of Hepatic Tumors Using Dynamic Contrast Enhanced MRI with Quantitative Perfusion Processing

There is no noninvasive method to estimate lung shunting fraction (LSF) in patients with liver tumors undergoing Yttrium-90 (Y90) therapy. We propose to predict LSF from noninvasive dynamic contrast enhanced (DCE) MRI using perfusion quantification. Two perfusion quantification methods were used to process DCE MRI in 25 liver tumor patients: Kety's tracer kinetic modeling with a delay-fitted global arterial input function (AIF) and quantitative transport mapping (QTM) based on the inversion of transport equation using spatial deconvolution without AIF. LSF was measured on SPECT following Tc-99m macroaggregated albumin (MAA) administration via hepatic arterial catheter. The patient cohort was partitioned into a low-risk group (LSF ≤&amp;nbsp;10%) and a high-risk group (LSF &gt;&amp;nbsp;10%). Results: In this patient cohort, LSF was positively correlated with QTM velocity |u| (r = 0.61, F = 14.0363, p = 0.0021), and no significant correlation was observed with Kety's parameters, tumor volume, patient age and gender. Between the low LSF and high LSF groups, there was a significant difference for QTM |u| (0.0760 ± 0.0440 vs. 0.1822 ± 0.1225 mm/s, p = 0.0011), and Kety's Ktrans (0.0401 ± 0.0360 vs 0.1198 ± 0.3048, p = 0.0471) and Ve&amp;nbsp;(0.0900 ± 0.0307 vs. 0.1495 ± 0.0485, p = 0.0114). The area under the curve (AUC) for distinguishing between low LSF and high LSF was 0.87 for |u|, 0.80 for Ve and 0.74 for Ktrans. Noninvasive prediction of LSF is feasible from DCE MRI with QTM velocity postprocessing.

Indirect and direct estimation of pharmacokinetic parameters in dynamic diffuse fluorescence tomography by adaptive extended Kalman filtering

Pharmacokinetic parameter estimation with the support of dynamic diffuse fluorescence tomography (DFT) can provide helpful diagnostic information for tumor differentiation and monitoring. Adaptive extended Kalman filtering (AEKF) as a nonlinear filter method has the merits of high quantitativeness, noise robustness, and initialization independence. In this paper, indirect and direct AEKF schemes combining with a commonly used two-compartment model were studied to estimate the pharmacokinetic parameters based on our self-designed dynamic DFT system. To comprehensively compare the performances of both schemes, the selection of optimal noise covariance matrices affecting estimation results was first studied, then a series of numerical simulations with the metabolic time ranged from 4.16 min to 38 min was carried out and quantitatively evaluated. The comparison results show that the direct AEKF outperforms the indirect EKF in estimation accuracy at different metabolic velocity and demonstrates stronger stability at the large metabolic velocity. Furtherly, the in vivo experiment was conducted to achieve the indocyanine green pharmacokinetic-rate images in the mouse liver. The experimental results confirmed the capability of both schemes to estimate the pharmacokinetic-rate images and were in agreement with the theory predictions and the numerical simulation results.

Quantitative transport mapping (QTM) for differentiating benign and malignant breast lesion: Comparison with traditional kinetics modeling and semi-quantitative enhancement curve characteristics

PURPOSE

To test the feasibility of using quantitative transport mapping (QTM) method, which is based on the inversion of transport equation using spatial deconvolution without any arterial input function, for automatically postprocessing dynamic contrast enhanced MRI (DCE-MRI) to differentiate malignant and benign breast tumors.

MATERIALS AND METHODS

Breast DCE-MRI data with biopsy confirmed malignant (n = 13) and benign tumors (n = 13) was used to assess QTM velocity (|u|) and diffusion coefficient (D), volume transfer constant (K^trans), volume fraction of extravascular extracellular space (V_e) from kinetics method, and traditional enhancement curve characteristics (ECC: amplitude A, wash-in rate α, wash-out rate β). A Mann-Whitney U test and receiver operating characteristic curve (ROC) analysis were performed to assess the diagnostic performance of these parameters for distinguishing between benign and malignant tumors.

RESULTS

Between malignant and benign tumors, there was a significant difference in |u| and K^trans, (p = 0.0066, 0.0274, respectively), but not in D, V_e, A, α and β (p = 0.1119, 0.2382, 0.4418,0.2592 and 0.9591, respectively). ROC area-under-the-curve was 0.82, 0.75 (95% confidence level 0.60-0.95, 0.51-0.90) for |u| and K^trans, respectively.

CONCLUSION

QTM postprocesses DCE-MRI automatically through deconvolution in space and time to solve the inverse problem of the transport equation. Comparing with traditional kinetics method and ECC, QTM method showed better diagnostic accuracy in differentiating benign from malignant breast tumors in this study.

New Pharmacokinetic Parameters of Imaging Substrates Quantified from Rat Liver Compartments

Hepatobiliary imaging is increasingly used by pharmacologists to quantify liver concentrations of transporter-dependent drugs. However, liver imaging does not quantify concentrations in extracellular space, hepatocytes, and bile canaliculi. Our study compared the compartmental distribution of two hepatobiliary substrates gadobenate dimeglumine [BOPTA; 0.08 liver extraction ratio (ER)] and mebrofenin (MEB; 0.93 ER) in a model of perfused rat liver. A gamma counter placed over livers measured liver concentrations. Livers were preperfused with gadopentetate dimeglumine to measure extracellular concentrations. Concentrations coming from bile canaliculi and hepatocytes were calculated. Transporter activities were assessed by concentration ratios between compartments and pharmacokinetic parameters that describe the accumulation and decay profiles of hepatocyte concentrations. The high liver concentrations of MEB relied mainly on hepatocyte and bile canaliculi concentrations. In contrast, the three compartments contributed to the low liver concentrations obtained during BOPTA perfusion. Nonlinear regression analysis of substrate accumulation in hepatocytes revealed that cellular efflux is measurable ∼4 minutes after the start of perfusion. The hepatocyte-to-extracellular concentration ratio measured at this time point was much higher during MEB perfusion. BOPTA transport by multidrug resistance associated protein 2 induced an aquaporin-mediated water transport, whereas MEB transport did not. BOPTA clearance from hepatocytes to bile canaliculi was higher than MEB clearance. MEB did not efflux back to sinusoids, whereas BOPTA basolateral efflux contributed to the decrease in hepatocyte concentrations. In conclusion, our ex vivo model quantifies substrate compartmental distribution and transport across hepatocyte membranes and provides an additional understanding of substrate distribution in the liver. SIGNIFICANCE STATEMENT: When transporter-dependent drugs target hepatocytes, cellular concentrations are important to investigate. Low concentrations on cellular targets impair drug therapeutic effects, whereas excessive hepatocyte concentrations may induce cellular toxicity. With a gamma counter placed over rat perfused livers, we measured substrate concentrations in the extracellular space, hepatocytes, and bile canaliculi. Transport across hepatocyte membranes was calculated. The study provides an additional understanding of substrate distribution in the liver.

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

Predictions of tumour perfusion are key determinants of drug delivery and responsiveness to therapy. Pharmacokinetic models allow for the estimation of perfusion properties of tumour tissues but many assume no dispersion associated with tracer transport away from the capillaries and through the tissue. At the level of a voxel, this translates to assuming no cross-voxel tracer exchange, often leading to the misinterpretation of derived perfusion parameters. Tofts model (TM), a compartmental model widely used in oncology, also makes this assumption. A more realistic description is required to quantify kinetic properties of tracers, such as convection and diffusion. We propose a Cross-Voxel Exchange Model (CVXM) for analysing cross-voxel tracer kinetics.In silicodatasets quantifying the roles of convection and diffusion in tracer transport (which TM ignores) were employed to investigate the interpretation of Tofts' perfusion parameters compared to CVXM. TM returned inaccurate values ofKtransandvewhere diffusive and convective mechanisms are pronounced (up to 20% and 300% error respectively). A mathematical equation, developed in this work, predicts and gives the correct physiological interpretation of Tofts've.Finally, transport parameters were derived from dynamic contrast enhanced-magnetic resonance imaging of a TS-415 human cervical carcinoma xenograft by using TM and CVXM. The latter deduced lower values ofKtransandvecompared to TM (lower by up to 63% and 76% respectively). It also allowed the detection of a diffusive flux (mean diffusivity 155μm²s^-1) in the tumour tissue, as well as an increased convective flow at the periphery (mean velocity 2.3μm s^-1detected). The results serve as a proof of concept establishing the feasibility of using CVXM for accurately determining transport metrics that characterize the exchange of tracer between voxels. CVXM needs to be investigated further as its parameters can be linked to the tumour microenvironment properties (permeability, pressure…), potentially leading to enhanced personalized treatment planning.

Concentrations and pharmacokinetic parameters of MRI and SPECT hepatobiliary agents in rat liver compartments

Background

In hepatobiliary imaging, systems detect the total amount of agents originating from extracellular space, bile canaliculi, and hepatocytes. They add in situ concentration of each compartment corrected by its respective volume ratio to provide liver concentrations. In vivo contribution of each compartment to liver concentration is inaccessible. Our aim was to quantify the compartmental distribution of two hepatobiliary agents in an ex vivo model and determine how their liver extraction ratios and cholestasis (livers lacking canalicular transporters) might modify it.

Methods

We perfused labelled gadobenate dimeglumine (Bopta, 200 μM, 7% liver extraction ratio) and mebrofenin (Meb, 64 μM, 94% liver extraction ratio) in normal (n = 18) and cholestatic (n = 6) rat livers. We quantified liver concentrations with a gamma counter placed over livers. Concentrations in hepatocytes and bile canaliculi were calculated. Mann-Whitney and Kruskal-Wallis tests were used.

Results

Hepatocyte concentrations were 2,043 ± 333 μM (Meb) versus 360 ± 69 μM (Bopta, p < 0.001). Meb extracellular concentrations did not contribute to liver concentrations (1.3 ± 0.3%). The contribution of Bopta extracellular concentration was 12.4 ± 1.9% (p < 0.001 versus Meb). Contribution of canaliculi was similar for both agents (16%). Cholestatic livers had no Bopta in canaliculi but their hepatocyte concentrations increased in comparison to normal livers.

Conclusion

Hepatocyte concentrations are correlated to liver extraction ratios of hepatobiliary agents. When Bopta is not present in canaliculi of cholestatic livers, hepatocyte concentrations increase in comparison to normal livers. This new understanding extends the interpretation of clinical liver images.

Quantitative transport mapping (QTM) of the kidney with an approximate microvascular network

Purpose

Proof‐of‐concept study of mapping renal blood flow vector field according to the inverse solution to a mass transport model of time resolved tracer‐labeled MRI data.

Theory and Methods

To determine tissue perfusion according to the underlying physics of spatiotemporal tracer concentration variation, the mass transport equation is integrated over a voxel with an approximate microvascular network for fitting time‐resolved tracer imaging data. The inverse solution to the voxelized transport equation provides the blood flow vector field, which is referred to as quantitative transport mapping (QTM). A numerical microvascular network modeling the kidney with computational fluid dynamics reference was used to verify the accuracy of QTM and the current Kety’s method that uses a global arterial input function. Multiple post‐label delay arterial spin labeling (ASL) of the kidney on seven subjects was used to assess QTM in vivo feasibility.

Results

Against the ground truth in the numerical model, the error in flow estimated by QTM (18.6%) was smaller than that in Kety’s method (45.7%, 2.5‐fold reduction). The in vivo kidney perfusion quantification by QTM (cortex: 443 ± 58 mL/100 g/min and medulla: 190 ± 90 mL/100 g/min) was in the range of that by Kety’s method (482 ± 51 mL/100 g/min in the cortex and 242 ± 73 mL/100 g/min in the medulla), and QTM provided better flow homogeneity in the cortex region.

Conclusions

QTM flow velocity mapping is feasible from multi‐delay ASL MRI data based on inverting the transport equation. In a numerical simulation, QTM with deconvolution in space and time provided more accurate perfusion quantification than Kety’s method with deconvolution in time only.

Radiomic features of Pk-DCE MRI parameters based on the extensive Tofts model in application of breast cancer

To explore radiomic features of pharmacokinetic dynamic contrast-enhanced (Pk-DCE) MRI on the extensive Tofts model to diagnose breast cancer and predict molecular phenotype. Breast lesions enrolled must undergo Pk-DCE MRI before treatment or puncture, and be identified as primary lesions by pathology. K^trans, K_ep, V_e and V_p were generated on the extensive Tofts model. Radiomic features (histogram, geometry and texture features) were extracted from parametric maps and selected by LASSO. The subjects were divided into training and validation cohort with a ratio of 4:1 to construct model in diagnosis of breast cancer. Feature analysis was made to predict the molecular phenotype. Area under curve (AUC), sensitivity, specificity and accuracy were used to evaluate radiomic features. DeLong's test was performed to compare AUC values. 228 breast lesions met the criteria were used to discrimination and 126 malignant lesions were used to study molecular phenotypes. The number of training cohort and validation cohort were 182 and 46, respectively. The AUC of K^trans, K_ep, V_e, and V_p was 0.95, 0.93, 0.89, and 0.96, and their accuracy was 85%, 89%, 89%, 94% respectively in diagnosis of breast lesions, while their AUC was 0.71 to 0.77, 0.61 to 0.68, and 0.67 to 0.74 to predict ER/PR, Her-2, and Ki-67. There was no significant difference among parameters (P > 0.05). Radiomic features based on Pk-DCE MRI have an advantage to diagnose breast cancer and less ability to predict molecular phenotypes, which are beneficial to guide clinical treatment of breast lesions in some extent.

Optimal mass transport kinetic modeling for head and neck DCE-MRI: Initial analysis

PURPOSE

Current state-of-the-art models for estimating the pharmacokinetic parameters do not account for intervoxel movement of the contrast agent (CA). We introduce an optimal mass transport (OMT) formulation that naturally handles intervoxel CA movement and distinguishes between advective and diffusive flows.

METHOD

Ten patients with head and neck squamous cell carcinoma (HNSCC) were enrolled in the study between June 2014 and October 2015 and underwent DCE MRI imaging prior to beginning treatment. The CA tissue concentration information was taken as the input in the data-driven OMT model. The OMT approach was tested on HNSCC DCE data that provides quantitative information for forward flux ( Φ F ) and backward flux ( Φ B ). OMT-derived Φ F was compared with the volume transfer constant for CA, K trans , derived from the Extended Tofts Model (ETM).

RESULTS

The OMT-derived flows showed a consistent jump in the CA diffusive behavior across the images in accordance with the known CA dynamics. The mean forward flux was 0.0082 ± 0.0091 ( min - 1 ) whereas the mean advective component was 0.0052 ± 0.0086 ( min - 1 ) in the HNSCC patients. The diffusive percentages in forward and backward flux ranged from 8.67% to 18.76% and 12.76% to 30.36%, respectively. The OMT model accounts for intervoxel CA movement and results show that the forward flux ( Φ F ) is comparable with the ETM-derived K trans .

CONCLUSIONS

This is a novel data-driven study based on optimal mass transport principles applied to patient DCE imaging to analyze CA flow in HNSCC.

A new framework for assessing subject-specific whole brain circulation and perfusion using MRI-based measurements and a multi-scale continuous flow model

A large variety of severe medical conditions involve alterations in microvascular circulation. Hence, measurements or simulation of circulation and perfusion has considerable clinical value and can be used for diagnostics, evaluation of treatment efficacy, and for surgical planning. However, the accuracy of traditional tracer kinetic one-compartment models is limited due to scale dependency. As a remedy, we propose a scale invariant mathematical framework for simulating whole brain perfusion. The suggested framework is based on a segmentation of anatomical geometry down to imaging voxel resolution. Large vessels in the arterial and venous network are identified from time-of-flight (ToF) and quantitative susceptibility mapping (QSM). Macro-scale flow in the large-vessel-network is accurately modelled using the Hagen-Poiseuille equation, whereas capillary flow is treated as two-compartment porous media flow. Macro-scale flow is coupled with micro-scale flow by a spatially distributing support function in the terminal endings. Perfusion is defined as the transition of fluid from the arterial to the venous compartment. We demonstrate a whole brain simulation of tracer propagation on a realistic geometric model of the human brain, where the model comprises distinct areas of grey and white matter, as well as large vessels in the arterial and venous vascular network. Our proposed framework is an accurate and viable alternative to traditional compartment models, with high relevance for simulation of brain perfusion and also for restoration of field parameters in clinical brain perfusion applications.

Estimating the discretization dependent accuracy of perfusion in coupled capillary flow measurements

One-compartment models are widely used to quantify hemodynamic parameters such as perfusion, blood volume and mean transit time. These parameters are routinely used for clinical diagnosis and monitoring of disease development and are thus of high relevance. However, it is known that common estimation techniques are discretization dependent and values can be erroneous. In this paper we present a new model that enables systematic quantification of discretization errors. Specifically, we introduce a continuous flow model for tracer propagation within the capillary tissue, used to evaluate state-of-the-art one-compartment models. We demonstrate that one-compartment models are capable of recovering perfusion accurately when applied to only one compartment, i.e. the whole region of interest. However, substantial overestimation of perfusion occurs when applied to fractions of a compartment. We further provide values of the estimated overestimation for various discretization levels, and also show that overestimation can be observed in real-life applications. Common practice of using compartment models for fractions of tissue violates model assumptions and careful interpretation is needed when using the computed values for diagnosis and treatment planning.

The effects of intravoxel contrast agent diffusion on the analysis of DCE-MRI data in realistic tissue domains

PURPOSE

Quantitative evaluation of dynamic contrast enhanced MRI (DCE-MRI) allows for estimating perfusion, vessel permeability, and tissue volume fractions by fitting signal intensity curves to pharmacokinetic models. These compart mental models assume rapid equilibration of contrast agent within each voxel. However, there is increasing evidence that this assumption is violated for small molecular weight gadolinium chelates. To evaluate the error introduced by this invalid assumption, we simulated DCE-MRI experiments with volume fractions computed from entire histological tumor cross-sections obtained from murine studies.

METHODS

A 2D finite element model of a diffusion-compensated Tofts-Kety model was developed to simulate dynamic T₁ signal intensity data. Digitized histology slices were segmented into vascular (v_p ), cellular and extravascular extracellular (v_e ) volume fractions. Within this domain, K^trans (the volume transfer constant) was assigned values from 0 to 0.5 min^-1 . A representative signal enhancement curve was then calculated for each imaging voxel and the resulting simulated DCE-MRI data analyzed by the extended Tofts-Kety model.

RESULTS

Results indicated parameterization errors of -19.1% ± 10.6% in K^trans , -4.92% ± 3.86% in v_e , and 79.5% ± 16.8% in v_p for use of Gd-DTPA over 4 tumor domains.

CONCLUSION

These results indicate a need for revising the standard model of DCE-MRI to incorporate a correction for slow diffusion of contrast agent. Magn Reson Med 80:330-340, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Direct reconstruction in CT-analogous pharmacokinetic diffuse fluorescence tomography: two-dimensional simulative and experimental validations

We present a generalized strategy for direct reconstruction in pharmacokinetic diffuse fluorescence tomography (DFT) with CT-analogous scanning mode, which can accomplish one-step reconstruction of the indocyanine-green pharmacokinetic-rate images within in vivo small animals by incorporating the compartmental kinetic model into an adaptive extended Kalman filtering scheme and using an instantaneous sampling dataset. This scheme, compared with the established indirect and direct methods, eliminates the interim error of the DFT inversion and relaxes the expensive requirement of the instrument for obtaining highly time-resolved date-sets of complete 360 deg projections. The scheme is validated by two-dimensional simulations for the two-compartment model and pilot phantom experiments for the one-compartment model, suggesting that the proposed method can estimate the compartmental concentrations and the pharmacokinetic-rates simultaneously with a fair quantitative and localization accuracy, and is well suitable for cost-effective and dense-sampling instrumentation based on the highly-sensitive photon counting technique.

Clinical Diagnostic Biomarkers from the Personalization of Computational Models of Cardiac Physiology

Computational modelling of the heart is rapidly advancing to the point of clinical utility. However, the difficulty of parameterizing and validating models from clinical data indicates that the routine application of truly predictive models remains a significant challenge. We argue there is significant value in an intermediate step towards prediction. This step is the use of biophysically based models to extract clinically useful information from existing patient data. Specifically in this paper we review methodologies for applying modelling frameworks for this goal in the areas of quantifying cardiac anatomy, estimating myocardial stiffness and optimizing measurements of coronary perfusion. Using these indicative examples of the general overarching approach, we finally discuss the value, ongoing challenges and future potential for applying biophysically based modelling in the clinical context.

Performance Enhancement of Pharmacokinetic Diffuse Fluorescence Tomography by Use of Adaptive Extended Kalman Filtering

Due to both the physiological and morphological differences in the vascularization between healthy and diseased tissues, pharmacokinetic diffuse fluorescence tomography (DFT) can provide contrast-enhanced and comprehensive information for tumor diagnosis and staging. In this regime, the extended Kalman filtering (EKF) based method shows numerous advantages including accurate modeling, online estimation of multiparameters, and universal applicability to any optical fluorophore. Nevertheless the performance of the conventional EKF highly hinges on the exact and inaccessible prior knowledge about the initial values. To address the above issues, an adaptive-EKF scheme is proposed based on a two-compartmental model for the enhancement, which utilizes a variable forgetting-factor to compensate the inaccuracy of the initial states and emphasize the effect of the current data. It is demonstrated using two-dimensional simulative investigations on a circular domain that the proposed adaptive-EKF can obtain preferable estimation of the pharmacokinetic-rates to the conventional-EKF and the enhanced-EKF in terms of quantitativeness, noise robustness, and initialization independence. Further three-dimensional numerical experiments on a digital mouse model validate the efficacy of the method as applied in realistic biological systems.

Modeling the effect of intra-voxel diffusion of contrast agent on the quantitative analysis of dynamic contrast enhanced magnetic resonance imaging

Quantitative dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) provides estimates of physiologically relevant parameters related to tissue blood flow, vascular permeability, and tissue volume fractions which can then be used for prognostic and diagnostic reasons. However, standard techniques for DCE-MRI analysis ignore intra-voxel diffusion, which may play an important role in contrast agent distribution and voxel signal intensity and, thus, will affect quantification of the aforementioned parameters. To investigate the effect of intra-voxel diffusion on quantitative DCE-MRI, we developed a finite element model of contrast enhancement at the voxel level. For diffusion in the range of that expected for gadolinium chelates in tissue (i.e., 1×10⁻⁴ to 4×10⁻⁴ mm²/s), parameterization errors range from −58% to 12% for K^trans, −9% to 8% for v_e, and −60% to 213% for v_p over the range of K^trans, v_e, v_p, and temporal resolutions investigated. Thus the results show that diffusion has a significant effect on parameterization using standard techniques.