Modeling and simulation of blood circulation and perfusion

Numeriske simuleringer har hatt vesentlig betydning for vår forståelse av perfusjon og blodsirkulasjon, og simuleringer gir også viktig innsikt under utviklingen av medisinske anvendelser. Teknologiske fremskritt har muliggjort bruken av mer realistiske modeller, ikke bare i form av mer kompleks fysikk, men også ved at en kan studere sirkulasjonen i hele organer. Disse kjennetegnene er ofte av interesse da fysiologiske egenskaper er forskjellige på tvers av romlige størrelsesordener. Denne avhandlingen fokuserer på modellering og simulering av blodstrøm, sporstofftransport og perfusjon i organvev. De fysiske prosessene er uttrykt i en flerskala strømningsmodell der segmenterte arterier og vener danner en nettverksmodell for vaskulær strømning, og som er knyttet til en mikrosirkulasjonsmodell. Den ikkeobserverbare vaskulaturen beskrevet av modellen simuleres både med en kontinuerlig og en diskretisert tilnærming. Vi presenterer et flerskala rammeverk for å studere blodsirkulasjon. Det nytenkende aspektet ved rammeverket består i å kombinere en eksisterende hybrid strømningsmodell for flerskala sirkulasjon med vaskulærfremkalte ikke-lineariteter som har opphav i bl.a. veggelastisiteten og kurvaturen til blodkarene. Anvendelsen av en passende betingelse fra lineær algebra gjør at vi effektivt kan løse det tilknyttede ikke-lineære systemet ved bruk av en iterativ Newtons metode, og det relativt enkle rammeverket beskriver slik blodsirkulasjon i et komplekst fysisk domene med en lav beregningsmessig kostnad. Modellene og deres tilhørende implementeringer presenteres i artiklene som utgjør Del II i avhandlingen. Her foreslår vi et rammeverk for å generere digitale fantomer for avbildning av perfusjon, og ved å evaluere kinetikkmodeller for sporstoff demonstrerer vi de betydelige verdiene som finnes i etterbehandling av medisinske data. I tillegg undersøker vi optimale vaskulære nettverk som avslører en kompleks gjensidig avhengighet mellom geometrien til det vaskulære nettverket, kapillærene og organene. Resultatene fra denne avhandlingen bidrar til en bedre forståelse av blodperfusjonsmodeller i vev og potensialet til disse, samt potensialet som vitenskapelig databehandling har i medisinske anvendelser utover perfusjonsavbildning.Numerical simulations have become essential for understanding blood circulation and perfusion, as well as providing important insights for medical applications. More realistic models have become possible with technological advances, not only in the form of more complex physics, but also in the flow detail of an entire organ circulation. These characteristics are frequently of interest because blood vessels at different spatial scales have different physiological properties. This thesis focuses on the modeling and simulations of blood flow, tracer transport, and perfusion in an organ tissue. The physical processes are expressed in a multiscale flow model with segmented arteries and veins forming a vascular network flow model that is connected to a microcirculation model. The unobservable vasculature, including small vessels and capillaries, represented by the connection model, is simulated by using a continuum and discrete approach. A multiscale framework for solving blood circulation is presented. The novelty of this framework comes from combining an existing hybrid flow model for a multiscale circulation with vasculature-induced nonlinearities such as vessel wall elasticity and vessel curvature. By using an appropriate linear algebra precondition, the corresponding nonlinear system can be efficiently solved by using an iterative Newton method. This allows us to formulate more realistic blood circulation in a complex physical domain by employing a relatively simple framework with a low computational cost. The models and their implementation are presented in the papers that constitute Part II of this thesis. In the paper section, we propose a framework to generate a digital phantom for perfusion imaging. Moreover, we evaluate tracer kinetic models demonstrating the significant value of post-processing of medical data. We also investigate optimal vascular networks revealing a complex interdependence between the geometry of the vascular network, the capillary bed and organ shape. The results of this thesis contribute to a better understanding of blood perfusion models in tissue and their potential, as well as the potential of scientific computing, for medical applications not limited to perfusion imaging.Doktorgradsavhandlin

A CFD and FEM Approach to a Multicompartmental Poroelastic Model for CSF Production and Circulation with Applicationsin Hydrocephalus Treatment and Cerebral Oedema

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.This study introduces a Multiple-Network Poroelastic Theory (MPET) model, coupled with finite-volume based Computational fluid dynamics (CFD) for the purpose of studying, in detail, the effects of obstructing Cerebrospinal fluid (CSF) transport within an image-derived cerebral environment. The MPET representation allows the investigation of fluid transport between CSF, brain parenchyma and cerebral blood, in an integral and comprehensive manner. Key novelties of this model are the casting of multidimensional MPET in a Finite Element Method (FEM) framework, the amalgamation of anatomically accurate choroid plexuses with their feeding arteries and a simple relationship relaxing the constraint of a unique permeability for the CSF compartment. This model is used to demonstrate the impact of fourth ventricle outlet obstruction (FVOO). The implications of treating such a clinical condition with the aid of endoscopic third (ETV) and endoscopic fourth (EFV) ventriculostomy are considered. Finally, we outline the impact of the FEM based MPET framework in understanding oedema, and its ongoing evolution

Inferring Geodesic Cerebrovascular Graphs: Image Processing, Topological Alignment and Biomarkers Extraction

A vectorial representation of the vascular network that embodies quantitative features - location, direction, scale, and bifurcations - has many potential neuro-vascular applications. Patient-specific models support computer-assisted surgical procedures in neurovascular interventions, while analyses on multiple subjects are essential for group-level studies on which clinical prediction and therapeutic inference ultimately depend. This first motivated the development of a variety of methods to segment the cerebrovascular system. Nonetheless, a number of limitations, ranging from data-driven inhomogeneities, the anatomical intra- and inter-subject variability, the lack of exhaustive ground-truth, the need for operator-dependent processing pipelines, and the highly non-linear vascular domain, still make the automatic inference of the cerebrovascular topology an open problem. In this thesis, brain vessels’ topology is inferred by focusing on their connectedness. With a novel framework, the brain vasculature is recovered from 3D angiographies by solving a connectivity-optimised anisotropic level-set over a voxel-wise tensor field representing the orientation of the underlying vasculature. Assuming vessels joining by minimal paths, a connectivity paradigm is formulated to automatically determine the vascular topology as an over-connected geodesic graph. Ultimately, deep-brain vascular structures are extracted with geodesic minimum spanning trees. The inferred topologies are then aligned with similar ones for labelling and propagating information over a non-linear vectorial domain, where the branching pattern of a set of vessels transcends a subject-specific quantized grid. Using a multi-source embedding of a vascular graph, the pairwise registration of topologies is performed with the state-of-the-art graph matching techniques employed in computer vision. Functional biomarkers are determined over the neurovascular graphs with two complementary approaches. Efficient approximations of blood flow and pressure drop account for autoregulation and compensation mechanisms in the whole network in presence of perturbations, using lumped-parameters analog-equivalents from clinical angiographies. Also, a localised NURBS-based parametrisation of bifurcations is introduced to model fluid-solid interactions by means of hemodynamic simulations using an isogeometric analysis framework, where both geometry and solution profile at the interface share the same homogeneous domain. Experimental results on synthetic and clinical angiographies validated the proposed formulations. Perspectives and future works are discussed for the group-wise alignment of cerebrovascular topologies over a population, towards defining cerebrovascular atlases, and for further topological optimisation strategies and risk prediction models for therapeutic inference. Most of the algorithms presented in this work are available as part of the open-source package VTrails

An inextensible model for the robotic manipulation of textiles

We introduce a new isometric strain model for the study of the dynamics of cloth garments in a moderate stress environment, such as robotic manipulation in the neighborhood of humans. This model treats textiles as surfaces that are inextensible, admitting only isometric motions. Inextensibility is derived in a continuous setting, prior to any discretization, which gives consistency with respect to remeshing and prevents the problem of locking even with coarse meshes. The simulations of robotic manipulation using the model are compared to the actual manipulation in the real world, finding that the difference between the simulated and the real position of each point in the garment is lower than 1cm in average even when a coarse mesh is used. Aerodynamic contributions to motion are incorporated to the model through the virtual uncoupling of the inertial and gravitational mass of the garment. This approach results in an accurate, when compared to the recorded dynamics of real textiles, description of cloth motion incorporating aerodynamic effects by using only two parameters.Peer ReviewedPostprint (published version

Modélisation de l'écoulement sanguin et du transport de molécules dans la microcirculation sanguine cérébrale : impact des occlusions capillaires dans la maladie d'Alzheimer

Le système microvasculaire est un acteur essentiel du fonctionnement cérébral. Il est en effet responsable de l’approvisionnement des cellules en oxygène et glucose ainsi que de l’évacuation des déchets métaboliques comme le dioxyde de carbone. Ce système est composé d’une multitude de petit vaisseaux appelés artérioles, veinules et capillaires, qui sont entourés de tissu cérébral. Ces vaisseaux forment un immense réseau qui étend ses ramifications à travers tout le cerveau. A cause de son rôle prépondérant dans l’homéostasie cérébrale le système microvasculaire est impliqué dansde nombreuses pathologies, allant de l’accident vasculaire cérébral aux maladies neurodégénératives. Ces dernières décennies ont été marquées par des avancées significatives dans le domaine de l’imagerie du vivant (e.g. la microscopie multi-photonique) qui ont permis l’observation du système microvasculaire cérébral avec un niveau de précision sans précédent. Ces techniques génèrent cependant de grandes quantités de données qu’il est difficile d’analyser sans outils théoriques adaptés. C’est pourquoi, dans cette thèse, nous développons des modèles capables de décrire l’écoulement sanguin ainsi que le transport de soluté au sein de vastes réseaux microvasculaires anatomiques. La principale difficulté dans la résolution de tels problèmes, vient de la taille de ces réseaux. En effet, même s’ils ne représentent qu’une fraction du système microvasculaire, ils sont composés de plusieurs dizaines de milliers de vaisseaux et possèdent des géométries complexes. Il est donc inenvisageable de résoudre l’écoulement sanguin et le transport de soluté par le biais de méthodes classiques comme les volumes finis ou les éléments finis. Afin de surmonter cette difficulté, nous combinons une approche réseau de pores avec des méthodes de changement d’échelles (prise de moyenne volumique et développements asymptotiques) et des fonctions de Green. Cela nous permet de simplifier à la fois la description de l’écoulement sanguin et du transport de soluté tout en restant cohérent avec la physique sous-jacente. Pour nous assurer de la pertinence de ces simplifications nous validons systématiquement nos modèles en les comparant à des mesures in vitro et in vivo si elles existent et à des solutions analytiques de référence sinon. Une fois validés, nous utilisons nos modèles afin d’élucider le rôle joué par le système microvas- culaire aux stades précoces de la maladie d’Alzheimer. En effet, il a été récemment montré qu’une baisse du débit sanguin cérébral était le premier marqueur quantitatif de la maladie. Simultanément, nos collaborateurs, les professeurs Schaffer et Nishimura de l’université de Cornell, ont observé chez les souris malades qu’une faible proportion (2%-4%) des capillaires étaient obstrués par des globules blancs. En conséquence ils ont injecté un anticorps inhibant l’adhésion de ces derniers. Les vaisseaux se sont alors débloqués, entraînant une augmentation du débit sanguin ainsi qu’une amélioration des capacités cognitives chez les souris malades. Si l’on suppose qu’après l’injection le débit sanguin retrouve sa valeur de référence, on peut estimer que les occlusions capillaires réduisent de 20 % à 30 % le débit sanguin. Une si faible proportion de capillaires obstrués peut-elle avoir un impact aussi important sur le débit sanguin cérébral ? Il est difficile de répondre simplement à cette question en se fiant uniquement à l’expérience puisqu’il est quasiment impossible d’isoler un tel phénomène in vivo que ce soit chez la souris ou chez l’humain. Pour contourner ce problème nous utilisons nos modèles et simulons numériquement l’impact de ces occlusions sur le débit sanguin. Nous trouvons que 2% à 4% d’occlusions capillaires conduisent à une baisse de débit pouvant aller jusqu’à 12%, faisant de ces occlusions un mécanisme important dans l’apparition de la maladie d’Alzheimer. Pour finir, nous quantifions leurs conséquences sur les échanges moléculaires

Direct numerical simulation of a pulsatile flow in a stenotic channel using immersed boundary method

A three-dimensional direct numerical simulation model coupled with the immersed boundary method has been developed to simulate a pulsatile flow in a planar channel with single and double one-sided semicircular constrictions. For relevance to blood flow in large arteries, simulations have been performed at Reynolds numbers of 750 and 1000. Flow physics and resultant wall shear stress (WSS)-based hemodynamic parameters are presented. The instantaneous vortex dynamics, mean flow characteristics, and turbulent energy spectra are evaluated for flow physics. Subsequently, three WSS-based parameters, namely the time-averaged WSS, oscillatory shear index, and relative residence time, are calculated over the stenotic wall and correlated with flow physics to identify the regions prone to atherosclerotic plaque progression. Results show that the double stenotic channel leads to high-intensity and broadband turbulent characteristics downstream, promoting critical values of the WSS-based parameters in the post-stenotic areas. In addition, the inter-space area between two stenoses displays multiple strong recirculations, making this area highly prone to atherosclerosis progression. The effect of stenosis degree on the WSS-based parameters is studied up to 60% degree. As the degree of occlusion is increased, larger regions are involved with the nonphysiological ranges of the WSS-based parameters