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

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) 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). 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

A simulation study investigating potential diffusion-based MRI signatures of microstrokes

ABSTRACT: Recent studies suggested that cerebrovascular micro-occlusions, i.e. microstokes, could lead to ischemic tissue infarctions and cognitive deficits. Due to their small size, identifying measurable biomarkers of these microvascular lesions remains a major challenge. This work aims to simulate potential MRI signatures combining arterial spin labeling (ASL) and multi-directional diffusion-weighted imaging (DWI). Driving our hypothesis are recent observations demonstrating a radial reorientation of microvasculature around the micro-infarction locus during recovery in mice. Synthetic capillary beds, randomly- and radially-oriented, and optical coherence tomography (OCT) angiograms, acquired in the barrel cortex of mice (n = 5) before and after inducing targeted photothrombosis, were analyzed. Computational vascular graphs combined with a 3D Monte-Carlo simulator were used to characterize the magnetic resonance (MR) response, encompassing the effects of magnetic field perturbations caused by deoxyhemoglobin, and the advection and diffusion of the nuclear spins. We quantified the minimal intravoxel signal loss ratio when applying multiple gradient directions, at varying sequence parameters with and without ASL. With ASL, our results demonstrate a significant difference (p < 0.05) between the signal-ratios computed at baseline and 3 weeks after photothrombosis. The statistical power further increased (p < 0.005) using angiograms measured at week 4. Without ASL, no reliable signal change was found. We found that higher ratios, and accordingly improved significance, were achieved at lower magnetic field strengths (e.g., B0 = 3T) and shorter echo time TE (< 16 ms). Our simulations suggest that microstrokes might be characterized through ASL-DWI sequence, providing necessary insights for posterior experimental validations, and ultimately, future translational trials

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.publishedVersio

The Ageing Brain: Investigating the Role of Age in Changes to the Human Cerebral Microvasculature With an in silico Model

Ageing causes extensive structural changes to the human cerebral microvasculature, which have a significant effect on capillary bed perfusion and oxygen transport. Current models of brain capillary networks in the literature focus on healthy adult brains and do not capture the effects of ageing, which is critical when studying neurodegenerative diseases. This study builds upon a statistically accurate model of the human cerebral microvasculature based on ex-vivo morphological data. This model is adapted for “healthy” ageing using in-vivo measurements from mice at three distinct age groups—young, middle-aged, and old. From this new model, blood and molecular exchange parameters are calculated such as permeability and surface-area-to-volume ratio, and compared across the three age groups. The ability to alter the model vessel-by-vessel is used to create a continuous gradient of ageing. It was found that surface-area-to-volume ratio reduced in old age by 6% and permeability by 24% from middle-age to old age, and variability within the networks also increased with age. The ageing gradient indicated a threshold in the ageing process around 75 years old, after which small changes have an amplified effect on blood flow properties. This gradient enables comparison of studies measuring cerebral properties at discrete points in time. The response of middle aged and old aged capillary beds to micro-emboli showed a lower robustness of the old age capillary bed to vessel occlusion. As the brain ages, there is thus increased vulnerability of the microvasculature—with a “tipping point” beyond which further remodeling of the microvasculature has exaggerated effects on the brain. When developing in-silico models of the brain, age is a very important consideration to accurately assess risk factors for cognitive decline and isolate early biomarkers of microvascular health.</jats:p

Rapid disruption of cortical activity and loss of cerebral blood flow in a mouse model of mild traumatic brain injury

Every year 2.8 million Americans suffer a traumatic brain injury (TBI). Despite the prevalence and debilitating consequences of TBI, effective treatment options are scarce due to the limited understanding of the neurobiological effects of injury, especially in acute phases when the cellular processes leading to neuropathology are first initiated. To identify changes in neural function and cerebral blood flow (CBF) that might account for TBI-induced cognitive and sensory deficits, we took a multidisciplinary approach, examining synaptic function, cortical activity patterns, and microvascular hemodynamics. we used a weight drop model in mice to induce mild TBI, the most common form in humans, and focused on responses within the first hours of injury where existing data are particularly limited. For synaptic function, we measured excitatory and inhibitory input onto pyramidal cells in the piriform cortex with whole-cell recordings in acute brain slices. Increased excitation appeared at one hour but excitatory-inhibitory balance was reestablished by 48 hours, highlighting the importance of studying rapid-onset injury responses. We also compared neural activity before and after TBI using in vivo two-photon calcium imaging of pyramidal cells in visual cortex. While neural activity substantially decreased in most cells one hour after injury, a minority of cells showed hyperactivation or prolonged increases in intracellular calcium, again indicating major physiological disturbances during immediate post-injury phases. Finally, we measured in vivo changes in CBF throughout the cortical microvasculature with laser speckle contrast imaging and optical coherence tomography, tracking injury effects up to three weeks after TBI. CBF and capillary flow were dramatically reduced within minutes and remained suppressed for over one hour. As neurons’ high energetic needs require a constant supply of glucose and oxygen from local vasculature, decreased CBF likely contributes to altered neural activity and loss of ion homeostasis and thus potentially cognitive and sensory deficits after TBI. Our results reveal that even mild injury creates rapid, pronounced, and heterogeneous alterations in neural activity and capillary flow. The transient nature of these effects suggests that the first two hours after injury may be a key window for delivering interventions, and that restoring CBF may reduce damage due to metabolic stress

Anatomical Modeling of Cerebral Microvascular Structures: Application to Identify Biomarkers of Microstrokes

Les réseaux microvasculaires corticaux sont responsables du transport de l’oxygène et des substrats énergétiques vers les neurones. Ces réseaux réagissent dynamiquement aux demandes énergétiques lors d’une activation neuronale par le biais du couplage neurovasculaire. Afin d’élucider le rôle de la composante microvasculaire dans ce processus de couplage, l’utilisation de la modélisation in-formatique pourrait se révéler un élément clé. Cependant, la manque de méthodologies de calcul appropriées et entièrement automatisées pour modéliser et caractériser les réseaux microvasculaires reste l’un des principaux obstacles. Le développement d’une solution entièrement automatisée est donc important pour des explorations plus avancées, notamment pour quantifier l’impact des mal-formations vasculaires associées à de nombreuses maladies cérébrovasculaires. Une observation courante dans l’ensemble des troubles neurovasculaires est la formation de micro-blocages vascu-laires cérébraux (mAVC) dans les artérioles pénétrantes de la surface piale. De récents travaux ont démontré l’impact de ces événements microscopiques sur la fonction cérébrale. Par conséquent, il est d’une importance vitale de développer une approche non invasive et comparative pour identifier leur présence dans un cadre clinique. Dans cette thèse,un pipeline de traitement entièrement automatisé est proposé pour aborder le prob-lème de la modélisation anatomique microvasculaire. La méthode de modélisation consiste en un réseau de neurones entièrement convolutif pour segmenter les capillaires sanguins, un générateur de modèle de surface 3D et un algorithme de contraction de la géométrie pour produire des mod-èles graphiques vasculaires ne comportant pas de connections multiples. Une amélioration de ce pipeline est développée plus tard pour alléger l’exigence de maillage lors de la phase de représen-tation graphique. Un nouveau schéma permettant de générer un modèle de graphe est développé avec des exigences d’entrée assouplies et permettant de retenir les informations sur les rayons des vaisseaux. Il est inspiré de graphes géométriques déformants construits en respectant les morpholo-gies vasculaires au lieu de maillages de surface. Un mécanisme pour supprimer la structure initiale du graphe à chaque exécution est implémenté avec un critère de convergence pour arrêter le pro-cessus. Une phase de raffinement est introduite pour obtenir des modèles vasculaires finaux. La modélisation informatique développée est ensuite appliquée pour simuler les signatures IRM po-tentielles de mAVC, combinant le marquage de spin artériel (ASL) et l’imagerie multidirectionnelle pondérée en diffusion (DWI). L’hypothèse est basée sur des observations récentes démontrant une réorientation radiale de la microvascularisation dans la périphérie du mAVC lors de la récupéra-tion chez la souris. Des lits capillaires synthétiques, orientés aléatoirement et radialement, et des angiogrammes de tomographie par cohérence optique (OCT), acquis dans le cortex de souris (n = 5) avant et après l’induction d’une photothrombose ciblée, sont analysés. Les graphes vasculaires informatiques sont exploités dans un simulateur 3D Monte-Carlo pour caractériser la réponse par résonance magnétique (MR), tout en considérant les effets des perturbations du champ magnétique causées par la désoxyhémoglobine, et l’advection et la diffusion des spins nucléaires. Le pipeline graphique proposé est validé sur des angiographies synthétiques et réelles acquises avec différentes modalités d’imagerie. Comparé à d’autres méthodes effectuées dans le milieu de la recherche, les expériences indiquent que le schéma proposé produit des taux d’erreur géométriques et topologiques amoindris sur divers angiogrammes. L’évaluation confirme également l’efficacité de la méthode proposée en fournissant des modèles représentatifs qui capturent tous les aspects anatomiques des structures vasculaires. Ensuite, afin de trouver des signatures de mAVC basées sur le signal IRM, la modélisation vasculaire proposée est exploitée pour quantifier le rapport de perte de signal intravoxel minimal lors de l’application de plusieurs directions de gradient, à des paramètres de séquence variables avec et sans ASL. Avec l’ASL, les résultats démontrent une dif-férence significative (p <0,05) entre le signal calculé avant et 3 semaines après la photothrombose. La puissance statistique a encore augmenté (p <0,005) en utilisant des angiogrammes capturés à la semaine suivante. Sans ASL, aucun changement de signal significatif n’est trouvé. Des rapports plus élevés sont obtenus à des intensités de champ magnétique plus faibles (par exemple, B0 = 3) et une lecture TE plus courte (<16 ms). Cette étude suggère que les mAVC pourraient être carac-térisés par des séquences ASL-DWI, et fournirait les informations nécessaires pour les validations expérimentales postérieures et les futurs essais comparatifs.----------ABSTRACT Cortical microvascular networks are responsible for carrying the necessary oxygen and energy substrates to our neurons. These networks react to the dynamic energy demands during neuronal activation through the process of neurovascular coupling. A key element in elucidating the role of the microvascular component in the brain is through computational modeling. However, the lack of fully-automated computational frameworks to model and characterize these microvascular net-works remains one of the main obstacles. Developing a fully-automated solution is thus substantial for further explorations, especially to quantify the impact of cerebrovascular malformations associ-ated with many cerebrovascular diseases. A common pathogenic outcome in a set of neurovascular disorders is the formation of microstrokes, i.e., micro occlusions in penetrating arterioles descend-ing from the pial surface. Recent experiments have demonstrated the impact of these microscopic events on brain function. Hence, it is of vital importance to develop a non-invasive and translatable approach to identify their presence in a clinical setting. In this thesis, a fully automatic processing pipeline to address the problem of microvascular anatom-ical modeling is proposed. The modeling scheme consists of a fully-convolutional neural network to segment microvessels, a 3D surface model generator and a geometry contraction algorithm to produce vascular graphical models with a single connected component. An improvement on this pipeline is developed later to alleviate the requirement of water-tight surface meshes as inputs to the graphing phase. The novel graphing scheme works with relaxed input requirements and intrin-sically captures vessel radii information, based on deforming geometric graphs constructed within vascular boundaries instead of surface meshes. A mechanism to decimate the initial graph struc-ture at each run is formulated with a convergence criterion to stop the process. A refinement phase is introduced to obtain final vascular models. The developed computational modeling is then ap-plied to simulate potential MRI signatures of microstrokes, combining arterial spin labeling (ASL) and multi-directional diffusion-weighted imaging (DWI). The hypothesis is driven based on recent observations demonstrating a radial reorientation of microvasculature around the micro-infarction locus during recovery in mice. Synthetic capillary beds, randomly- and radially oriented, and op-tical coherence tomography (OCT) angiograms, acquired in the barrel cortex of mice (n=5) before and after inducing targeted photothrombosis, are analyzed. The computational vascular graphs are exploited within a 3D Monte-Carlo simulator to characterize the magnetic resonance (MR) re-sponse, encompassing the effects of magnetic field perturbations caused by deoxyhemoglobin, and the advection and diffusion of the nuclear spins. The proposed graphing pipeline is validated on both synthetic and real angiograms acquired with different imaging modalities. Compared to other efficient and state-of-the-art graphing schemes, the experiments indicate that the proposed scheme produces the lowest geometric and topological error rates on various angiograms. The evaluation also confirms the efficiency of the proposed scheme in providing representative models that capture all anatomical aspects of vascular struc-tures. Next, searching for MRI-based signatures of microstokes, the proposed vascular modeling is exploited to quantify the minimal intravoxel signal loss ratio when applying multiple gradient di-rections, at varying sequence parameters with and without ASL. With ASL, the results demonstrate a significant difference (p<0.05) between the signal-ratios computed at baseline and 3 weeks after photothrombosis. The statistical power further increased (p<0.005) using angiograms captured at week 4. Without ASL, no reliable signal change is found. Higher ratios with improved significance are achieved at low magnetic field strengths (e.g., at 3 Tesla) and shorter readout TE (<16 ms). This study suggests that microstrokes might be characterized through ASL-DWI sequences, and provides necessary insights for posterior experimental validations, and ultimately, future transla-tional trials