Investigating cerebral oedema using poroelasticity

Modelling midline shift and ventricle collapse in cerebral oedema following acute ischaemic stroke

In ischaemic stroke, a large reduction in blood supply can lead to the breakdown of the blood-brain barrier and to cerebral oedema after reperfusion therapy. The resulting fluid accumulation in the brain may contribute to a significant rise in intracranial pressure (ICP) and tissue deformation. Changes in the level of ICP are essential for clinical decision-making and therapeutic strategies. However, the measurement of ICP is constrained by clinical techniques and obtaining the exact values of the ICP has proven challenging. In this study, we propose the first computational model for the simulation of cerebral oedema following acute ischaemic stroke for the investigation of ICP and midline shift (MLS) relationship. The model consists of three components for the simulation of healthy blood flow, occluded blood flow and oedema, respectively. The healthy and occluded blood flow components are utilized to obtain oedema core geometry and then imported into the oedema model for the simulation of oedema growth. The simulation results of the model are compared with clinical data from 97 traumatic brain injury patients for the validation of major model parameters. Midline shift has been widely used for the diagnosis, clinical decision-making, and prognosis of oedema patients. Therefore, we focus on quantifying the relationship between ICP and midline shift (MLS) and identify the factors that can affect the ICP-MLS relationship. Three major factors are investigated, including the brain geometry, blood-brain barrier damage severity and the types of oedema (including rare types of oedema). Meanwhile, the two major types (stress and tension/compression) of mechanical brain damage are also presented and the differences in the stress, tension, and compression between the intraparenchymal and periventricular regions are discussed. This work helps to predict ICP precisely and therefore provides improved clinical guidance for the treatment of brain oedema.

Poroelastic modelling of brain tissue swelling and decompressive craniectomy treatment in ischaemic stroke

Brain oedema or tissue swelling that develops after ischaemic stroke can cause detrimental effects, including brain herniation and increased intracranial pressure (ICP). These effects can be reduced by performing a decompressive craniectomy (DC) operation, in which a portion of the skull is removed to allow swollen brain tissue to expand outside the skull. In this study, a poroelastic model is used to investigate the effect of brain ischaemic infarct size and location on the severity of brain tissue swelling. Furthermore, the model will also be used to evaluate the effectiveness of DC surgery as a treatment for brain tissue swelling after ischaemia. The poroelastic model consists of two equations: one describing the elasticity of the brain tissue and the other describing the changes in the interstitial tissue pressure. The model is applied on an idealized brain geometry, and it is found that infarcts with radius larger than approximately 14 mm and located near the lateral ventricle produce worse brain midline shift, measured through lateral ventricle compression. Furthermore, the model is also able to show the positive effect of DC treatment in reducing the brain midline shift by allowing part of the brain tissue to expand through the skull opening. However, the model does not show a decrease in the interstitial pressure during DC treatment. Further improvement and validation could enhance the capability of the proposed poroelastic model in predicting the occurrence of brain tissue swelling and DC treatment post ischaemia.

MPET2: a multi-network poroelastic and transport theory for predicting absorption of monoclonal antibodies delivered by subcutaneous injection

Subcutaneous injection of monoclonal antibodies (mAbs) has attracted much attention in the pharmaceutical industry. During the injection, the drug is delivered into the tissue producing strong fluid flow and tissue deformation. While data indicate that the drug is initially uptaken by the lymphatic system due to the large size of mAbs, many of the critical absorption processes that occur at the injection site remain poorly understood. Here, we propose the MPET² approach, a multi-network poroelastic and transport model to predict the absorption of mAbs during and after subcutaneous injection. Our model is based on physical principles of tissue biomechanics and fluid dynamics. The subcutaneous tissue is modeled as a mixture of three compartments, i.e., interstitial tissue, blood vessels, and lymphatic vessels, with each compartment modeled as a porous medium. The proposed biomechanical model describes tissue deformation, fluid flow in each compartment, the fluid exchanges between compartments, the absorption of mAbs in blood vessels and lymphatic vessels, as well as the transport of mAbs in each compartment. We used our model to perform a high-fidelity simulation of an injection of mAbs in subcutaneous tissue and evaluated the long-term drug absorption. Our model results show good agreement with experimental data in depot clearance tests.

Multi-compartmental model of glymphatic clearance of solutes in brain tissue

The glymphatic system is the subject of numerous pieces of research in biology. Mathematical modelling plays a considerable role in this field since it can indicate the possible physical effects of this system and validate the biologists' hypotheses. The available mathematical models that describe the system at the scale of the brain (i.e. the macroscopic scale) are often solely based on the diffusion equation and do not consider the fine structures formed by the perivascular spaces. We therefore propose a mathematical model representing the time and space evolution of a mixture flowing through multiple compartments of the brain. We adopt a macroscopic point of view in which the compartments are all present at any point in space. The equations system is composed of two coupled equations for each compartment: One equation for the pressure of a fluid and one for the mass concentration of a solute. The fluid and solute can move from one compartment to another according to certain membrane conditions modelled by transfer functions. We propose to apply this new modelling framework to the clearance of 14C-inulin from the rat brain.

Insights into Infusion-Based Targeted Drug Delivery in the Brain: Perspectives, Challenges and Opportunities

Targeted drug delivery in the brain is instrumental in the treatment of lethal brain diseases, such as glioblastoma multiforme, the most aggressive primary central nervous system tumour in adults. Infusion-based drug delivery techniques, which directly administer to the tissue for local treatment, as in convection-enhanced delivery (CED), provide an important opportunity; however, poor understanding of the pressure-driven drug transport mechanisms in the brain has hindered its ultimate success in clinical applications. In this review, we focus on the biomechanical and biochemical aspects of infusion-based targeted drug delivery in the brain and look into the underlying molecular level mechanisms. We discuss recent advances and challenges in the complementary field of medical robotics and its use in targeted drug delivery in the brain. A critical overview of current research in these areas and their clinical implications is provided. This review delivers new ideas and perspectives for further studies of targeted drug delivery in the brain.

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.

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.

Parameter-robust multiphysics algorithms for Biot model with application in brain edema simulation

In this paper, we develop parameter-robust numerical algorithms for Biot model and apply the algorithms in brain edema simulations. By introducing an intermediate variable, we derive a multiphysics reformulation of the Biot model. Based on the reformulation, the Biot model is viewed as a generalized Stokes subproblem combining with a reaction-diffusion subproblem. Solving the two subproblems together or separately leads to a coupled or a decoupled algorithm. We conduct extensive numerical experiments to show that the two algorithms are robust with respect to the key physical parameters. The algorithms are applied to study the brain swelling caused by abnormal accumulation of cerebrospinal fluid in injured areas. The effects of the key physical parameters on brain swelling are carefully investigated. It is observed that the permeability has the biggest influence on intracranial pressure (ICP) and tissue deformation; the Young's modulus and the Poisson ratio do not affect the maximum value of ICP too much but have big influence on the tissue deformation and the developing speed of brain swelling.

Exploring neurodegenerative disorders using a novel integrated model of cerebral transport: Initial results

The neurovascular unit (NVU) underlines the complex and symbiotic relationship between brain cells and the cerebral vasculature, and dictates the need to consider both neurodegenerative and cerebrovascular diseases under the same mechanistic umbrella. Importantly, unlike peripheral organs, the brain was thought not to contain a dedicated lymphatics system. The glymphatic system concept (a portmanteau of glia and lymphatic) has further emphasized the importance of cerebrospinal fluid transport and emphasized its role as a mechanism for waste removal from the central nervous system. In this work, we outline a novel multiporoelastic solver which is embedded within a high precision, subject specific workflow that allows for the co-existence of a multitude of interconnected compartments with varying properties (multiple-network poroelastic theory, or MPET), that allow for the physiologically accurate representation of perfused brain tissue. This novel numerical template is based on a six-compartment MPET system (6-MPET) and is implemented through an in-house finite element code. The latter utilises the specificity of a high throughput imaging pipeline (which has been extended to incorporate the regional variation of mechanical properties) and blood flow variability model developed as part of the VPH-DARE@IT research platform. To exemplify the capability of this large-scale consolidated pipeline, a cognitively healthy subject is used to acquire novel, biomechanistically inspired biomarkers relating to primary and derivative variables of the 6-MPET system. These biomarkers are shown to capture the sophisticated nature of the NVU and the glymphatic system, paving the way for a potential route in deconvoluting the complexity associated with the likely interdependence of neurodegenerative and cerebrovascular diseases. The present study is the first, to the best of our knowledge, that casts and implements the 6-MPET equations in a 3D anatomically accurate brain geometry.

An implicit discontinuous Galerkin method for modeling acute edema and resuscitation in the small intestine

Edema, also termed oedema, is a generalized medical condition associated with an abnormal aggregation of fluid in a tissue matrix. In the intestine, excessive edema can lead to serious health complications associated with reduced motility. A $7.5\%$ solution of hypertonic saline (HS) has been hypothesized as an effective means to reduce the effects of edema following surgery or injury. However, detailed clinical edema experiments can be difficult to implement, or costly, in practice. In this manuscript we introduce an implicit in time discontinuous Galerkin method with novel adaptations for modeling edema in the 3D layered physiology of the intestine. The model improves over early work via inclusion of the tissue intrinsic storage coefficient, and the effects of Starling overestimation for high venous pressures. Validation against a recent clinical experiment in HS resuscitation of acute edema is presented; the results support the clinical hypothesis that 7.5% HS solution may be effective in the resuscitation of acute edema formation. New results include an improved view into the effects of resuscitation on the hydrostatic pressure profile of edematous rats, effects on lumenal volume attenuation, relative fluid gain and an estimation of the impacts of both acute edema and resuscitation on intestinal motility.

Highly integrated workflows for exploring cardiovascular conditions: Exemplars of precision medicine in Alzheimer's disease and aortic dissection

For precision medicine to be implemented through the lens of in silico technology, it is imperative that biophysical research workflows offer insight into treatments that are specific to a particular illness and to a particular subject. The boundaries of precision medicine can be extended using multiscale, biophysics-centred workflows that consider the fundamental underpinnings of the constituents of cells and tissues and their dynamic environments. Utilising numerical techniques that can capture the broad spectrum of biological flows within complex, deformable and permeable organs and tissues is of paramount importance when considering the core prerequisites of any state-of-the-art precision medicine pipeline. In this work, a succinct breakdown of two precision medicine pipelines developed within two Virtual Physiological Human (VPH) projects are given. The first workflow is targeted on the trajectory of Alzheimer's Disease, and caters for novel hypothesis testing through a multicompartmental poroelastic model which is integrated with a high throughput imaging workflow and subject-specific blood flow variability model. The second workflow gives rise to the patient specific exploration of Aortic Dissections via a multi-scale and compliant model, harnessing imaging, computational fluid-dynamics (CFD) and dynamic boundary conditions. Results relating to the first workflow include some core outputs of the multiporoelastic modelling framework, and the representation of peri-arterial swelling and peri-venous drainage solution fields. The latter solution fields were statistically analysed for a cohort of thirty-five subjects (stratified with respect to disease status, gender and activity level). The second workflow allowed for a better understanding of complex aortic dissection cases utilising both a rigid-wall model informed by minimal and clinically common datasets as well as a moving-wall model informed by rich datasets.

On the Validation of a Multiple-Network Poroelastic Model Using Arterial Spin Labeling MRI Data

The Multiple-Network Poroelastic Theory (MPET) is a numerical model to characterize the transport of multiple fluid networks in the brain, which overcomes the problem of conducting separate analyses on individual fluid compartments and losing the interactions between tissue and fluids, in addition to the interaction between the different fluids themselves. In this paper, the blood perfusion results from MPET modeling are partially validated using cerebral blood flow (CBF) data obtained from arterial spin labeling (ASL) magnetic resonance imaging (MRI), which uses arterial blood water as an endogenous tracer to measure CBF. Two subjects—one healthy control and one patient with unilateral middle cerebral artery (MCA) stenosis are included in the validation test. The comparison shows several similarities between CBF data from ASL and blood perfusion results from MPET modeling, such as higher blood perfusion in the gray matter than in the white matter, higher perfusion in the periventricular region for both the healthy control and the patient, and asymmetric distribution of blood perfusion for the patient. Although the partial validation is mainly conducted in a qualitative way, it is one important step toward the full validation of the MPET model, which has the potential to be used as a testing bed for hypotheses and new theories in neuroscience research.

Subject-specific multi-poroelastic model for exploring the risk factors associated with the early stages of Alzheimer's disease

There is emerging evidence suggesting that Alzheimer's disease is a vascular disorder, caused by impaired cerebral perfusion, which may be promoted by cardiovascular risk factors that are strongly influenced by lifestyle. In order to develop an understanding of the exact nature of such a hypothesis, a biomechanical understanding of the influence of lifestyle factors is pursued. An extended poroelastic model of perfused parenchymal tissue coupled with separate workflows concerning subject-specific meshes, permeability tensor maps and cerebral blood flow variability is used. The subject-specific datasets used in the modelling of this paper were collected as part of prospective data collection. Two cases were simulated involving male, non-smokers (control and mild cognitive impairment (MCI) case) during two states of activity (high and low). Results showed a marginally reduced clearance of cerebrospinal fluid (CSF)/interstitial fluid (ISF), elevated parenchymal tissue displacement and CSF/ISF accumulation and drainage in the MCI case. The peak perfusion remained at 8 mm s⁻¹ between the two cases.