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

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.

The ISMRM Open Science Initiative for Perfusion Imaging (OSIPI): Results from the OSIPI-Dynamic Contrast-Enhanced challenge

PURPOSE

K trans $$ {K}^{\mathrm{trans}} $$ has often been proposed as a quantitative imaging biomarker for diagnosis, prognosis, and treatment response assessment for various tumors. None of the many software tools forK trans $$ {K}^{\mathrm{trans}} $$ quantification are standardized. The ISMRM Open Science Initiative for Perfusion Imaging-Dynamic Contrast-Enhanced (OSIPI-DCE) challenge was designed to benchmark methods to better help the efforts to standardizeK trans $$ {K}^{\mathrm{trans}} $$ measurement.

METHODS

A framework was created to evaluateK trans $$ {K}^{\mathrm{trans}} $$ values produced by DCE-MRI analysis pipelines to enable benchmarking. The perfusion MRI community was invited to apply their pipelines forK trans $$ {K}^{\mathrm{trans}} $$ quantification in glioblastoma from clinical and synthetic patients. Submissions were required to include the entrants'K trans $$ {K}^{\mathrm{trans}} $$ values, the applied software, and a standard operating procedure. These were evaluated using the proposedOSIP I gold $$ \mathrm{OSIP}{\mathrm{I}}_{\mathrm{gold}} $$ score defined with accuracy, repeatability, and reproducibility components.

RESULTS

Across the 10 received submissions, theOSIP I gold $$ \mathrm{OSIP}{\mathrm{I}}_{\mathrm{gold}} $$ score ranged from 28% to 78% with a 59% median. The accuracy, repeatability, and reproducibility scores ranged from 0.54 to 0.92, 0.64 to 0.86, and 0.65 to 1.00, respectively (0-1 = lowest-highest). Manual arterial input function selection markedly affected the reproducibility and showed greater variability inK trans $$ {K}^{\mathrm{trans}} $$ analysis than automated methods. Furthermore, provision of a detailed standard operating procedure was critical for higher reproducibility.

CONCLUSIONS

This study reports results from the OSIPI-DCE challenge and highlights the high inter-software variability withinK trans $$ {K}^{\mathrm{trans}} $$ estimation, providing a framework for ongoing benchmarking against the scores presented. Through this challenge, the participating teams were ranked based on the performance of their software tools in the particular setting of this challenge. In a real-world clinical setting, many of these tools may perform differently with different benchmarking methodology.

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.

A Generalized Kinetic Model of Fractional Order Transport Dynamics with Transit Time Heterogeneity in Microvascular Space

The aim of this study is to develop and validate a unifying kinetic model for microvascular transport by introducing an impulse response function that incorporates essential physiological parameters and integrates key features of existing models. This new methodology combines a one-compartment model of fractional order with a model that uses the gamma distribution to describe the distribution of capillary transit times. Central to this model are two primary parameters: [Formula: see text], representing the kurtosis of residue times, and [Formula: see text], signifying the width of the distribution of capillary transit times within a tissue voxel. To validate this proposed model, data from dynamic contrast-enhanced magnetic resonance imaging (DCI-MRI) were employed and the findings were compared with three existing models. Using the Akaike information criterion for model selection, the results demonstrate that the integrative model, especially at elevated blood flow rates, frequently offers superior fits in comparison to constrained models.

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.

Novel fast FFR derived from coronary CT angiography based on static first-pass algorithm: a comparison study

BACKGROUND

Fractional flow reserve (FFR) is the invasive gold standard for evaluating coronary arterial stenosis. However, there have been a few non-invasive methods such as computational fluid dynamics FFR (CFD-FFR) with coronary CT angiography (CCTA) images that can perform FFR assessment. This study aims to develop a new method based on the principle of static first-pass of CT perfusion imaging technique (SF-FFR) and evaluate the efficacy in direct comparisons between CFD-FFR and the invasive FFR.

METHODS

A total of 91 patients (105 coronary artery vessels) who were admitted from January 2015 to March 2019 were enrolled in this study, retrospectively. All patients underwent CCTA and invasive FFR. 64 patients (75 coronary artery vessels) were successfully analyzed. The correlation and diagnostic performance of SF-FFR method on per-vessel basis were analyzed, using invasive FFR as the gold standard. As a comparison, we also evaluated the correlation and diagnostic performance of CFD-FFR.

RESULTS

The SF-FFR showed a good Pearson correlation (r = 0.70, P < 0.001) and intra-class correlation (r = 0.67, P < 0.001) with the gold standard. The Bland-Altman analysis showed that the average difference between the SF-FFR and invasive FFR was 0.03 (0.11-0.16); between CFD-FFR and invasive FFR was 0.04 (-0.10-0.19). Diagnostic accuracy and area under the ROC curve on a per-vessel level were 0.89, 0.94 for SF-FFR, and 0.87, 0.89 for CFD-FFR, respectively. The SF-FFR calculation time was about 2.5 s per case while CFD calculation was about 2 min on an Nvidia Tesla V100 graphic card.

CONCLUSIONS

The SF-FFR method is feasible and shows high correlation compared to the gold standard. This method could simplify the calculation procedure and save time compared to the CFD method.

Fractional calculus tracer kinetic compartment model for quantification of microvascular perfusion

Objective. We evaluate a tracer kinetic model for quantification of physiological perfusion and microvascular residue time kurtosis (RTK) in skeletal muscle vasculature with first pass bolus experiments in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI).Approach. A decreasing stretched Mittag-Leffler function (f1C model) was obtained as the impulse response solution of a rate equation of real-valued ('fractional') derivation order. The method was validated in skeletal muscle in the lower limb of seven female pigs examined by DCE-MRI. Dynamic imaging during blood pool contrast agent elimination was performed using a 3D gradient echo sequence with k-space sharing. Blood flow was augmented by continuous infusion of the vasodilator adenosine into the femoral artery increasing blood flow up to four times. Blood flow measured by a Doppler flow probe placed at the femoral artery served as ground truth.Main results. Goodness of fit and correlation with the Doppler measurements,r= 0.80 (P< 0.001), of the 4-parameter f1C model was comparable with the results obtained with a previously tested 6-parameter two-compartment (2C) model. The derivation orderαof the f1C model can be interpreted as a measure of microvascular RTK. With increasing blood flow,αdropped significantly, leading to an increase in RTK.Significance. The f1C model is a practical approach based on hemodynamic principles to quantify physiological microvascular perfusion but it is impaired due to its compartmental nature.

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.