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

Cerebral perfusion simulation using realistically generated synthetic trees for healthy and stroke patients

BACKGROUND AND OBJECTIVE

Cerebral vascular diseases are among the most burdensome diseases faced by society. However, investigating the pathophysiology of diseases as well as developing future treatments still relies heavily on expensive in-vivo and in-vitro studies. The generation of realistic, patient-specific models of the cerebrovascular system capable of simulating hemodynamics and perfusion promises the ability to simulate diseased states, therefore accelerating development cycles using in silico studies and opening opportunities for the individual assessment of diseased states, treatment planning, and the prediction of outcomes. By providing a patient-specific, anatomically detailed and validated model of the human cerebral vascular system, we aim to provide the basis for future in silico investigations of the cerebral physiology and pathology.

METHODS

In this retrospective study, a processing pipeline for patient-specific quantification of cerebral perfusion was developed and applied to healthy individuals and a stroke patient. Major arteries are segmented from 3T MR angiography data. A synthetic tree generation algorithm titled tissue-growth based optimization (GBO)1 is used to extend vascular trees beyond the imaging resolution. To investigate the anatomical accuracy of the generated trees, morphological parameters are compared against those of 7 T MRI, 9.4 T MRI, and dissection data. Using the generated vessel model, hemodynamics and perfusion are simulated by solving one-dimensional blood flow equations combined with Darcy flow equations.

RESULTS

Morphological data of three healthy individuals (mean age 47 years ± 15.9 [SD], 2 female) was analyzed. Bifurcation and physiological characteristics of the synthetically generated vessels are comparable to those of dissection data. The inability of MRI based segmentation to resolve small branches and the small volume investigated cause a mismatch in the comparison to MRI data. Cerebral perfusion was estimated for healthy individuals and a stroke patient. The simulated perfusion is compared against Arterial-Spin-Labeling MRI perfusion data. Good qualitative agreement is found between simulated and measured cerebral blood flow (CBF)2. Ischemic regions are predicted well, however ischemia severity is overestimated.

CONCLUSIONS

GBO successfully generates detailed cerebral vascular models with realistic morphological parameters. Simulations based on the resulting networks predict perfusion territories and ischemic regions successfully.

MRI-based parameter inference for cerebral perfusion modelling in health and ischaemic stroke

Cerebral perfusion modelling is a promising tool to predict the impact of acute ischaemic stroke treatments on the spatial distribution of cerebral blood flow (CBF) in the human brain. To estimate treatment efficacy based on CBF, perfusion simulations need to become suitable for group-level investigations and thus account for physiological variability between individuals. However, computational perfusion modelling to date has been restricted to a few patient-specific cases. This study set out to establish automated parameter inference for perfusion modelling based on neuroimaging data and thus enable CBF simulations of groups. Magnetic resonance imaging (MRI) data from 75 healthy senior adults were utilised. Brain geometries were computed from healthy reference subjects' T1-weighted MRI. Haemodynamic model parameters were determined from spatial CBF maps measured by arterial spin labelling (ASL) perfusion MRI. Thereafter, perfusion simulations were conducted in 75 healthy cases followed by 150 acute ischaemic stroke cases representing an occlusion and CBF cessation in the left and right middle cerebral arteries. The anatomical fitness of the brain geometries was evaluated by comparing the simulated grey (GM) and white matter (WM) volumes to measurements in healthy reference subjects. Strong positive correlations were found in both tissue types (GM: Pearson's r 0.74, P<0.001; WM: Pearson's r 0.84, P<0.001). Haemodynamic parameter tuning was verified by comparing the total volumetric blood flow rate to the brain in healthy reference subjects and simulations (Pearson's r 0.89, P<0.001). In acute ischaemic stroke cases, the simulated infarct volume using a perfusion-based estimate was 197±25 ml. Computational predictions were in agreement with anatomical and haemodynamic values from the literature concerning T1-weighted, T2-weighted, and phase-contrast MRI measurements in healthy scenarios and acute ischaemic stroke cases. The acute stroke simulations did not capture small infarcts (left tail of the distribution), which could be explained by neglected compensatory mechanisms, e.g. collaterals. The proposed parameter inference method provides a foundation for group-level CBF simulations and for in silico clinical stroke trials which could assist in medical device and drug development.

Modeling and hexahedral meshing of cerebral arterial networks from centerlines

Computational fluid dynamics (CFD) simulation provides valuable information on blood flow from the vascular geometry. However, it requires extracting precise models of arteries from low-resolution medical images, which remains challenging. Centerline-based representation is widely used to model large vascular networks with small vessels, as it encodes both the geometric and topological information and facilitates manual editing. In this work, we propose an automatic method to generate a structured hexahedral mesh suitable for CFD directly from centerlines. We addressed both the modeling and meshing tasks. We proposed a vessel model based on penalized splines to overcome the limitations inherent to the centerline representation, such as noise and sparsity. The bifurcations are reconstructed using a parametric model based on the anatomy that we extended to planar n-furcations. Finally, we developed a method to produce a volume mesh with structured, hexahedral, and flow-oriented cells from the proposed vascular network model. The proposed method offers better robustness to the common defects of centerlines and increases the mesh quality compared to state-of-the-art methods. As it relies on centerlines alone, it can be applied to edit the vascular model effortlessly to study the impact of vascular geometry and topology on hemodynamics. We demonstrate the efficiency of our method by entirely meshing a dataset of 60 cerebral vascular networks. 92% of the vessels and 83% of the bifurcations were meshed without defects needing manual intervention, despite the challenging aspect of the input data. The source code is released publicly.

A network-based model of dynamic cerebral autoregulation

Cerebrovascular diseases continue to be one of the leading causes of morbidity and mortality in humans. Abnormalities in dynamic cerebral autoregulation (dCA) have been implicated in many of these disease conditions. Accurate models are therefore needed to better understand the complex pathophysiology behind impaired dCA. We thus present here a simple framework for modelling a vessel-driven network model of dCA in the microvasculature, as opposed to the conventional compartmental modelling approach. Network models incorporate the actual connectivity and anatomy of the vasculature, thereby allowing us to include and trace changes in the calibre and morphology of individual vessels, investigate the spatial specificity and heterogeneity of the various control mechanisms to help disentangle their contributions, and link the model parameters to the actual network physiology. The proposed control feedback mechanisms are incorporated at the level of the individual vessel, and the dynamic pressure and flow fields are solved for here within a simple vessel network. In response to an upstream pressure drop, the network is found to be able to recover cerebral blood flow (CBF) while exhibiting the characteristic autoregulatory behaviour in terms of changes in vessel calibre and the biphasic flow response. We assess the feasibility of our formulation in larger networks by comparing the simulation results to those obtained using a one-dimensional (1D) model of CBF applied to the same microvasculature network and find that our model results are in very good agreement with the 1D solution, while significantly reducing the computational cost, thus enabling more detailed models of network behaviour to be adopted in the future. Accurate and computationally feasible models of dCA that are more representative of the vasculature can help increase the translatability of haemodynamic models into the clinical environment, which would help develop more informed treatment guidelines for patients with cerebrovascular diseases.

Modeling a 3-D multiscale blood-flow and heat-transfer framework for realistic vascular systems

Modeling of biological domains and simulation of biophysical processes occurring in them can help inform medical procedures. However, when considering complex domains such as large regions of the human body, the complexities of blood vessel branching and variation of blood vessel dimensions present a major modeling challenge. Here, we present a Voxelized Multi-Physics Simulation (VoM-PhyS) framework to simulate coupled heat transfer and fluid flow using a multi-scale voxel mesh on a biological domain obtained. In this framework, flow in larger blood vessels is modeled using the Hagen–Poiseuille equation for a one-dimensional flow coupled with a three-dimensional two-compartment porous media model for capillary circulation in tissue. The Dirac distribution function is used as Sphere of Influence (SoI) parameter to couple the one-dimensional and three-dimensional flow. This blood flow system is coupled with a heat transfer solver to provide a complete thermo-physiological simulation. The framework is demonstrated on a frog tongue and further analysis is conducted to study the effect of convective heat exchange between blood vessels and tissue, and the effect of SoI on simulation results.

A 1D-0D-3D coupled model for simulating blood flow and transport processes in breast tissue

In this work, we present mixed dimensional models for simulating blood flow and transport processes in breast tissue and the vascular tree supplying it. These processes are considered, to start from the aortic inlet to the capillaries and tissue of the breast. Large variations in biophysical properties and flow conditions exist in this system necessitating the use of different flow models for different geometries and flow regimes. In total, we consider four different model types. First, a system of 1D nonlinear hyperbolic partial differential equations (PDEs) is considered to simulate blood flow in larger arteries with highly elastic vessel walls. Second, we assign 1D linearized hyperbolic PDEs to model the smaller arteries with stiffer vessel walls. The third model type consists of ODE systems (0D models). It is used to model the arterioles and peripheral circulation. Finally, homogenized 3D porous media models are considered to simulate flow and transport in capillaries and tissue within the breast volume. Sink terms are used to account for the influence of the venous and lymphatic systems. Combining the four model types, we obtain two different 1D-0D-3D coupled models for simulating blood flow and transport processes: The first model results in a fully coupled 1D-0D-3D model covering the complete path from the aorta to the breast combining a generic arterial network with a patient specific breast network and geometry. The second model is a reduced one based on the separation of the generic and patient specific parts. The information from a calibrated fully coupled model is used as inflow condition for the patient specific sub-model allowing a significant computational cost reduction. Several numerical experiments are conducted to calibrate the generic model parameters and to demonstrate realistic flow simulations compared to existing data on blood flow in the human breast and vascular system. Moreover, we use two different breast vasculature and tissue data sets to illustrate the robustness of our reduced sub-model approach.

A nonlinear multi-scale model for blood circulation in a realistic vascular system

In the last decade, numerical models have become an increasingly important tool in biological and medical science. Numerical simulations contribute to a deeper understanding of physiology and are a powerful tool for better diagnostics and treatment. In this paper, a nonlinear multi-scale model framework is developed for blood flow distribution in the full vascular system of an organ. We couple a quasi one-dimensional vascular graph model to represent blood flow in larger vessels and a porous media model to describe flow in smaller vessels and capillary bed. The vascular model is based on Poiseuille's Law, with pressure correction by elasticity and pressure drop estimation at vessels' junctions. The porous capillary bed is modelled as a two-compartment domain (artery and venous) using Darcy's Law. The fluid exchange between the artery and venous capillary bed compartments is defined as blood perfusion. The numerical experiments show that the proposed model for blood circulation: (i) is closely dependent on the structure and parameters of both the larger vessels and of the capillary bed, and (ii) provides a realistic blood circulation in the organ. The advantage of the proposed model is that it is complex enough to reliably capture the main underlying physiological function, yet highly flexible as it offers the possibility of incorporating various local effects. Furthermore, the numerical implementation of the model is straightforward and allows for simulations on a regular desktop computer.

In silico trials for treatment of acute ischemic stroke: Design and implementation

An in silico trial simulates a disease and its corresponding therapies on a cohort of virtual patients to support the development and evaluation of medical devices, drugs, and treatment. In silico trials have the potential to refine, reduce cost, and partially replace current in vivo studies, namely clinical trials and animal testing. We present the design and implementation of an in silico trial for treatment of acute ischemic stroke. We propose an event-based modelling approach for the simulation of a disease and injury, where changes to the state of the system (the events) are assumed to be instantaneous. Using this approach we are able to combine a diverse set of models, spanning multiple time scales, to model acute ischemic stroke, treatment, and resulting brain tissue injury. The in silico trial is designed to be modular to aid development and reproducibility. It provides a comprehensive framework for application to any potential in silico trial. A statistical population model is used to generate cohorts of virtual patients. Patient functional outcomes are also predicted with a statistical model, using treatment and injury results and the patient's clinical parameters. We demonstrate the functionality of the event-based modelling approach and trial framework by running proof of concept in silico trials. The proof of concept trials simulate the same cohort of patients twice: once with successful treatment (successful recanalisation) and once with unsuccessful treatment (unsuccessful treatment). Ways to overcome some of the challenges and difficulties in setting up such an in silico trial are discussed, such as validation and computational limitations.

On the Sensitivity Analysis of Porous Finite Element Models for Cerebral Perfusion Estimation

Computational physiological models are promising tools to enhance the design of clinical trials and to assist in decision making. Organ-scale haemodynamic models are gaining popularity to evaluate perfusion in a virtual environment both in healthy and diseased patients. Recently, the principles of verification, validation, and uncertainty quantification of such physiological models have been laid down to ensure safe applications of engineering software in the medical device industry. The present study sets out to establish guidelines for the usage of a three-dimensional steady state porous cerebral perfusion model of the human brain following principles detailed in the verification and validation (V&V 40) standard of the American Society of Mechanical Engineers. The model relies on the finite element method and has been developed specifically to estimate how brain perfusion is altered in ischaemic stroke patients before, during, and after treatments. Simulations are compared with exact analytical solutions and a thorough sensitivity analysis is presented covering every numerical and physiological model parameter. The results suggest that such porous models can approximate blood pressure and perfusion distributions reliably even on a coarse grid with first order elements. On the other hand, higher order elements are essential to mitigate errors in volumetric blood flow rate estimation through cortical surface regions. Matching the volumetric flow rate corresponding to major cerebral arteries is identified as a validation milestone. It is found that inlet velocity boundary conditions are hard to obtain and that constant pressure inlet boundary conditions are feasible alternatives. A one-dimensional model is presented which can serve as a computationally inexpensive replacement of the three-dimensional brain model to ease parameter optimisation, sensitivity analyses and uncertainty quantification. The findings of the present study can be generalised to organ-scale porous perfusion models. The results increase the applicability of computational tools regarding treatment development for stroke and other cerebrovascular conditions.

Modelling the impact of clot fragmentation on the microcirculation after thrombectomy

Many ischaemic stroke patients who have a mechanical removal of their clot (thrombectomy) do not get reperfusion of tissue despite the thrombus being removed. One hypothesis for this 'no-reperfusion' phenomenon is micro-emboli fragmenting off the large clot during thrombectomy and occluding smaller blood vessels downstream of the clot location. This is impossible to observe in-vivo and so we here develop an in-silico model based on in-vitro experiments to model the effect of micro-emboli on brain tissue. Through in-vitro experiments we obtain, under a variety of clot consistencies and thrombectomy techniques, micro-emboli distributions post-thrombectomy. Blood flow through the microcirculation is modelled for statistically accurate voxels of brain microvasculature including penetrating arterioles and capillary beds. A novel micro-emboli algorithm, informed by the experimental data, is used to simulate the impact of micro-emboli successively entering the penetrating arterioles and the capillary bed. Scaled-up blood flow parameters-permeability and coupling coefficients-are calculated under various conditions. We find that capillary beds are more susceptible to occlusions than the penetrating arterioles with a 4x greater drop in permeability per volume of vessel occluded. Individual microvascular geometries determine robustness to micro-emboli. Hard clot fragmentation leads to larger micro-emboli and larger drops in blood flow for a given number of micro-emboli. Thrombectomy technique has a large impact on clot fragmentation and hence occlusions in the microvasculature. As such, in-silico modelling of mechanical thrombectomy predicts that clot specific factors, interventional technique, and microvascular geometry strongly influence reperfusion of the brain. Micro-emboli are likely contributory to the phenomenon of no-reperfusion following successful removal of a major clot.

A porous circulation model of the human brain for in silico clinical trials in ischaemic stroke

The advancement of ischaemic stroke treatment relies on resource-intensive experiments and clinical trials. In order to improve ischaemic stroke treatments, such as thrombolysis and thrombectomy, we target the development of computational tools for in silico trials which can partially replace these animal and human experiments with fast simulations. This study proposes a model that will serve as part of a predictive unit within an in silico clinical trial estimating patient outcome as a function of treatment. In particular, the present work aims at the development and evaluation of an organ-scale microcirculation model of the human brain for perfusion prediction. The model relies on a three-compartment porous continuum approach. Firstly, a fast and robust method is established to compute the anisotropic permeability tensors representing arterioles and venules. Secondly, vessel encoded arterial spin labelling magnetic resonance imaging and clustering are employed to create an anatomically accurate mapping between the microcirculation and large arteries by identifying superficial perfusion territories. Thirdly, the parameter space of the problem is reduced by analysing the governing equations and experimental data. Fourthly, a parameter optimization is conducted. Finally, simulations are performed with the tuned model to obtain perfusion maps corresponding to an open and an occluded (ischaemic stroke) scenario. The perfusion map in the occluded vessel scenario shows promising qualitative agreement with computed tomography images of a patient with ischaemic stroke caused by large vessel occlusion. The results highlight that in the case of vessel occlusion (i) identifying perfusion territories is essential to capture the location and extent of underperfused regions and (ii) anisotropic permeability tensors are required to give quantitatively realistic estimation of perfusion change. In the future, the model will be thoroughly validated against experiments.

In-Silico Trials for Treatment of Acute Ischemic Stroke

Despite improved treatment, a large portion of patients with acute ischemic stroke due to a large vessel occlusion have poor functional outcome. Further research exploring novel treatments and better patient selection has therefore been initiated. The feasibility of new treatments and optimized patient selection are commonly tested in extensive and expensive randomized clinical trials. in-silico trials, computer-based simulation of randomized clinical trials, have been proposed to aid clinical trials. In this white paper, we present our vision and approach to set up in-silico trials focusing on treatment and selection of patients with an acute ischemic stroke. The INSIST project (IN-Silico trials for treatment of acute Ischemic STroke, www.insist-h2020.eu) is a collaboration of multiple experts in computational science, cardiovascular biology, biophysics, biomedical engineering, epidemiology, radiology, and neurology. INSIST will generate virtual populations of acute ischemic stroke patients based on anonymized data from the recent stroke trials and registry, and build on the existing and emerging in-silico models for acute ischemic stroke, its treatment (thrombolysis and thrombectomy) and the resulting perfusion changes. These models will be used to design a platform for in-silico trials that will be validated with existing data and be used to provide a proof of concept of the potential efficacy of this emerging technology. The platform will be used for preliminary evaluation of the potential suitability and safety of medication, new thrombectomy device configurations and methods to select patient subpopulations for better treatment outcome. This could allow generating, exploring and refining relavant hypotheses on potential causal pathways (which may follow from the evidence obtained from clinical trials) and improving clinical trial design. Importantly, the findings of the in-silico trials will require validation under the controlled settings of randomized clinical trials.