Simulation of oxygen transport and estimation of tissue perfusion in extensive microvascular networks: Application to cerebral cortex

A three-dimensional, discrete-continuum model of blood pressure in microvascular networks

We present a 3D discrete-continuum model to simulate blood pressure in large microvascular tissues in the absence of known capillary network architecture. Our hybrid approach combines a 1D Poiseuille flow description for large, discrete arteriolar and venular networks coupled to a continuum-based Darcy model, point sources of flux, for transport in the capillary bed. We evaluate our hybrid approach using a vascular network imaged from the mouse brain medulla/pons using multi-fluorescence high-resolution episcopic microscopy (MF-HREM). We use the fully-resolved vascular network to predict the hydraulic conductivity of the capillary network and generate a fully-discrete pressure solution to benchmark against. Our results demonstrate that the discrete-continuum methodology is a computationally feasible and effective tool for predicting blood pressure in real-world microvascular tissues when capillary microvessels are poorly defined.

Modeling oxygen transport in the brain: An efficient coarse-grid approach to capture perivascular gradients in the parenchyma

Recent progresses in intravital imaging have enabled highly-resolved measurements of periarteriolar oxygen gradients (POGs) within the brain parenchyma. POGs are increasingly used as proxies to estimate the local baseline oxygen consumption, which is a hallmark of cell activity. However, the oxygen profile around a given arteriole arises from an interplay between oxygen consumption and delivery, not only by this arteriole but also by distant capillaries. Integrating such interactions across scales while accounting for the complex architecture of the microvascular network remains a challenge from a modelling perspective. This limits our ability to interpret the experimental oxygen maps and constitutes a key bottleneck toward the inverse determination of metabolic rates of oxygen. We revisit the problem of parenchymal oxygen transport and metabolism and introduce a simple, conservative, accurate and scalable direct numerical method going beyond canonical Krogh-type models and their associated geometrical simplifications. We focus on a two-dimensional formulation, and introduce the concepts needed to combine an operator-splitting and a Green's function approach. Oxygen concentration is decomposed into a slowly-varying contribution, discretized by Finite Volumes over a coarse cartesian grid, and a rapidly-varying contribution, approximated analytically in grid-cells surrounding each vessel. Starting with simple test cases, we thoroughly analyze the resulting errors by comparison with highly-resolved simulations of the original transport problem, showing considerable improvement of the computational-cost/accuracy balance compared to previous work. We then demonstrate the model ability to flexibly generate synthetic data reproducing the spatial dynamics of oxygen in the brain parenchyma, with sub-grid resolution. Based on these synthetic data, we show that capillaries distant from the arteriole cannot be overlooked when interpreting POGs, thus reconciling recent measurements of POGs across cortical layers with the fundamental idea that variations of vascular density within the depth of the cortex may reveal underlying differences in neuronal organization and metabolic load.

Enhancing immune modulation and bone regeneration on titanium implants by alleviating the hypoxic microenvironment and releasing bioactive ions

Bone implantation inevitably causes damage to surrounding vasculature, resulting in a hypoxic microenvironment that hinders bone regeneration. Although titanium (Ti)-based devices are widely used as bone implants, their inherent bioinert surface leads to poor osteointegration. Herein, a strontium peroxide (SrO2)-decorated Ti implant, Ti_P@SrO2, was constructed through coating with poly-L-lactic acid (PLLA) to alleviate the hypoxic microenvironment and transform the bioinert surface of the implant into a bioactive surface. PLLA degradation resulted in an acidic microenvironment and the release of SrO2 nanoparticles. The acidic microenvironment then accelerated the decomposition of SrO2, resulting in the release of O2 and Sr ions. O2 released from Ti_P@SrO2 can alleviate the hypoxic microenvironment, thus enhancing cell proliferation in an O2-insufficient microenvironment. Furthermore, under hypoxic and normal microenvironments, Ti_P@SrO2 enhanced alkaline phosphatase activity and bone-related gene expression in C3H10T1/2 cells with the continuous release of Sr ions. Meanwhile, Ti_P@SrO2 suppressed M1 polarization and promoted M2 polarization of bone marrow-derived monocytes under hypoxic and normal conditions. Furthermore, in a rat implantation model, the implant enhanced new bone formation and improved osteointegration after modification with SrO2. In summary, the newly designed O2- and Sr ion-releasing Ti implants are promising for applications in bone defects.

Research progress on the multi-omics and survival status of circulating tumor cells

In the dynamic process of metastasis, circulating tumor cells (CTCs) emanate from the primary solid tumor and subsequently acquire the capacity to disengage from the basement membrane, facilitating their infiltration into the vascular system via the interstitial tissue. Given the pivotal role of CTCs in the intricate hematogenous metastasis, they have emerged as an essential resource for a deeper comprehension of cancer metastasis while also serving as a cornerstone for the development of new indicators for early cancer screening and new therapeutic targets. In the epoch of precision medicine, as CTC enrichment and separation technologies continually advance and reach full fruition, the domain of CTC research has transcended the mere straightforward detection and quantification. The rapid advancement of CTC analysis platforms has presented a compelling opportunity for in-depth exploration of CTCs within the bloodstream. Here, we provide an overview of the current status and research significance of multi-omics studies on CTCs, including genomics, transcriptomics, proteomics, and metabolomics. These studies have contributed to uncovering the unique heterogeneity of CTCs and identifying potential metastatic targets as well as specific recognition sites. We also review the impact of various states of CTCs in the bloodstream on their metastatic potential, such as clustered CTCs, interactions with other blood components, and the phenotypic states of CTCs after undergoing epithelial-mesenchymal transition (EMT). Within this context, we also discuss the therapeutic implications and potential of CTCs.

An integral blood-brain barrier in adulthood relies on microglia-derived PDGFB

Pericyte is an indispensable cellular constituent of blood-brain barrier (BBB) and its homeostasis heavily rely on PDGFB-PDGFRβ signaling. However, the primary cellular sources of PDGFB in the central nervous system (CNS) are unclear. Microglia is not considered a component of BBB and its role in maintaining BBB integrity in steady state is controversial. In this study, by analyzing transcriptomic data and performing in situ hybridization, we revealed a transition of the primary central PDGFB producers from endothelial cells in newborns to microglia in adults. Acute loss of microglial PDGFB profoundly impaired BBB integrity in adult but not newborn mice, and thus, adult mice deficient of microglial PDGFB could not survive from a sublethal endotoxin challenge due to rampant microhemorrhages in the CNS. In contrast, acute abrogation of endothelial PDGFB had minimal effects on the BBB of adult mice but led to a severe impairment of CNS vasculature in the neonates. Moreover, we found that microglia would respond to a variety of BBB insults by upregulating PDGFB expression. These findings underscore the physiological importance of the microglia-derived PDGFB to the BBB integrity of adult mice both in steady state and under injury.

Mesh-free high-resolution simulation of cerebrocortical oxygen supply with fast Fourier preconditioning

Oxygen transfer from blood vessels to cortical brain tissue is representative of a class of problems with mixed-domain character. Large-scale efficient computation of tissue oxygen concentration is dependent on the manner in which the tubular network of blood vessels is coupled to the tissue mesh. Models which explicitly resolve the interface between the tissue and vasculature with a contiguous mesh are prohibitively expensive for very dense cerebral microvasculature. We propose a mixed-domain mesh-free technique whereby a vascular anatomical network (VAN) represented as a thin directed graph serves for convection of blood oxygen, and the surrounding extravascular tissue is represented as a Cartesian grid of 3D voxels throughout which oxygen is transported by diffusion. We split the network and tissue meshes by the Schur complement method of domain decomposition to obtain a reduced set of system equations for the tissue oxygen concentration at steady state. The use of a Cartesian grid allows the corresponding matrix equation to be solved approximately with a fast Fourier transform-based Poisson solver, which serves as an effective preconditioner for Krylov subspace iteration. The performance of this method enables the steady-state simulation of cortical oxygen perfusion for anatomically accurate vascular networks down to single micron resolution without the need for supercomputers.

Multi-scale multi-physics model of brain interstitial water flux by transcranial Direct Current Stimulation

Objective. Transcranial direct current stimulation (tDCS) generates sustained electric fields in the brain, that may be amplified when crossing capillary walls (across blood-brain barrier, BBB). Electric fields across the BBB may generate fluid flow by electroosmosis. We consider that tDCS may thus enhance interstitial fluid flow.Approach. We developed a modeling pipeline novel in both (1) spanning the mm (head),μm (capillary network), and then nm (down to BBB tight junction (TJ)) scales; and (2) coupling electric current flow to fluid current flow across these scales. Electroosmotic coupling was parametrized based on prior measures of fluid flow across isolated BBB layers. Electric field amplification across the BBB in a realistic capillary network was converted to volumetric fluid exchange.Main results. The ultrastructure of the BBB results in peak electric fields (per mA of applied current) of 32-63Vm-1across capillary wall and >1150Vm-1in TJs (contrasted with 0.3Vm-1in parenchyma). Based on an electroosmotic coupling of 1.0 × 10-9- 5.6 × 10-10m3s-1m2perVm-1, peak water fluxes across the BBB are 2.44 × 10-10- 6.94 × 10-10m3s-1m2, with a peak 1.5 × 10-4- 5.6 × 10-4m3min-1m3interstitial water exchange (per mA).Significance. Using this pipeline, the fluid exchange rate per each brain voxel can be predicted for any tDCS dose (electrode montage, current) or anatomy. Under experimentally constrained tissue properties, we predicted tDCS produces a fluid exchange rate comparable to endogenous flow, so doubling fluid exchange with further local flow rate hot spots ('jets'). The validation and implication of such tDCS brain 'flushing' is important to establish.

Operational Modal Analysis of Near-Infrared Spectroscopy Measure of 2-Month Exercise Intervention Effects in Sedentary Older Adults with Diabetes and Cognitive Impairment

The Global Burden of Disease Study (GBD 2019 Diseases and Injuries Collaborators) found that diabetes significantly increases the overall burden of disease, leading to a 24.4% increase in disability-adjusted life years. Persistently high glucose levels in diabetes can cause structural and functional changes in proteins throughout the body, and the accumulation of protein aggregates in the brain that can be associated with the progression of Alzheimer's Disease (AD). To address this burden in type 2 diabetes mellitus (T2DM), a combined aerobic and resistance exercise program was developed based on the recommendations of the American College of Sports Medicine. The prospectively registered clinical trials (NCT04626453, NCT04812288) involved two groups: an Intervention group of older sedentary adults with T2DM and a Control group of healthy older adults who could be either active or sedentary. The completion rate for the 2-month exercise program was high, with participants completing on an average of 89.14% of the exercise sessions. This indicated that the program was practical, feasible, and well tolerated, even during the COVID-19 pandemic. It was also safe, requiring minimal equipment and no supervision. Our paper presents portable near-infrared spectroscopy (NIRS) based measures that showed muscle oxygen saturation (SmO2), i.e., the balance between oxygen delivery and oxygen consumption in muscle, drop during bilateral heel rise task (BHR) and the 6 min walk task (6MWT) significantly (p < 0.05) changed at the post-intervention follow-up from the pre-intervention baseline in the T2DM Intervention group participants. Moreover, post-intervention changes from pre-intervention baseline for the prefrontal activation (both oxyhemoglobin and deoxyhemoglobin) showed statistically significant (p < 0.05, q < 0.05) effect at the right superior frontal gyrus, dorsolateral, during the Mini-Cog task. Here, operational modal analysis provided further insights into the 2-month exercise intervention effects on the very-low-frequency oscillations (<0.05 Hz) during the Mini-Cog task that improved post-intervention in the sedentary T2DM Intervention group from their pre-intervention baseline when compared to active healthy Control group. Then, the 6MWT distance significantly (p < 0.01) improved in the T2DM Intervention group at post-intervention follow-up from pre-intervention baseline that showed improved aerobic capacity and endurance. Our portable NIRS based measures have practical implications at the point of care for the therapists as they can monitor muscle and brain oxygenation changes during physical and cognitive tests to prescribe personalized physical exercise doses without triggering individual stress response, thereby, enhancing vascular health in T2DM.

Cortical microvascular blood flow velocity mapping by combining dynamic light scattering optical coherence tomography and two-photon microscopy

Significance

The accurate large-scale mapping of cerebral microvascular blood flow velocity is crucial for a better understanding of cerebral blood flow (CBF) regulation. Although optical imaging techniques enable both high-resolution microvascular angiography and fast absolute CBF velocity measurements in the mouse cortex, they usually require different imaging techniques with independent system configurations to maximize their performances. Consequently, it is still a challenge to accurately combine functional and morphological measurements to co-register CBF speed distribution from hundreds of microvessels with high-resolution microvascular angiograms.

Aim

We propose a data acquisition and processing framework to co-register a large set of microvascular blood flow velocity measurements from dynamic light scattering optical coherence tomography (DLS-OCT) with the corresponding microvascular angiogram obtained using two-photon microscopy (2PM).

Approach

We used DLS-OCT to first rapidly acquire a large set of microvascular velocities through a sealed cranial window in mice and then to acquire high-resolution microvascular angiograms using 2PM. The acquired data were processed in three steps: (i) 2PM angiogram coregistration with the DLS-OCT angiogram, (ii) 2PM angiogram segmentation and graphing, and (iii) mapping of the CBF velocities to the graph representation of the 2PM angiogram.

Results

We implemented the developed framework on the three datasets acquired from the mice cortices to facilitate the coregistration of the large sets of DLS-OCT flow velocity measurements with 2PM angiograms. We retrieved the distributions of red blood cell velocities in arterioles, venules, and capillaries as a function of the branching order from precapillary arterioles and postcapillary venules from more than 1000 microvascular segments.

Conclusions

The proposed framework may serve as a useful tool for quantitative analysis of large microvascular datasets obtained by OCT and 2PM in studies involving normal brain functioning, progression of various diseases, and numerical modeling of the oxygen advection and diffusion in the realistic microvascular networks.

Effects of apolipoprotein E polymorphism on cerebral oxygen saturation, cerebral perfusion, and early prognosis after traumatic brain injury

OBJECTIVE

To investigate the effects of the apolipoprotein E (APOE) gene on oxygen saturation and cerebral perfusion in the early stages of traumatic brain injury (TBI).

METHODS

This study included 136 consecutive TBI patients and 51 healthy individuals. The APOE genotypes of all subjects were determined using quantitative fluorescence polymerase chain reaction (QF-PCR). Regional cerebral oxygen saturation (rScO2) of patients with TBI and normal subjects was monitored using near-infrared spectroscopy (NIRS). Computed tomography (CT) perfusion was used to obtain cerebral perfusion in patients with TBI and normal subjects.

RESULTS

In the TBI group, the rScO2 of APOEε4 carriers (53.06 ± 6.87%) was significantly lower than that of non-carriers (58.19 ± 5.83%, p < 0.05). Meanwhile, the MTT of APOEε4 carriers (6.75 ± 1.30 s) was significantly longer than that of non-carriers (5.87 ± 1.00 s, p < 0.05). Furthermore, correlation analysis showed a negative correlation between rSCO2 and MTT in patients with TBI. Both the univariate and multifactorial logistic regression analyses revealed that APOE ε4, hypoxia, MTT >5.75 s, Marshall CT Class, and GCS were independent risk factors for early poor prognosis in patients with TBI.

CONCLUSION

Both cerebral perfusion and cerebral oxygen were significantly impaired after TBI, and low cerebral perfusion and hypoxia were related to poor prognosis of patients with TBI. Compared with APOE ε4 non-carriers, APOE ε4 carriers not only had poorer cerebral perfusion and cerebral oxygen metabolism but also worse prognosis in the early stages of TBI. Furthermore, a negative correlation was observed between the rSCO2 and MTT levels. In addition, both CT perfusion scanning (CTP) and NIRS are reliable for monitoring the condition of patients with TBI in the neurological intensive care unit (NICU).

MESH-FREE HIGH-RESOLUTION SIMULATION OF CEREBROCORTICAL OXYGEN SUPPLY WITH FAST FOURIER PRECONDITIONING

Oxygen transfer from blood vessels to cortical brain tissue is representative of a class of problems with mixed-domain character. Large-scale efficient computation of tissue oxygen concentration is dependent on the manner in which the tubular network of blood vessels is coupled to the tissue mesh. Models which explicitly resolve the interface between the tissue and vasculature with a contiguous mesh are prohibitively expensive for very dense cerebral microvasculature. We propose a mixed-domain mesh-free technique whereby a vascular anatomical network (VAN) represented as a thin directed graph serves for convection of blood oxygen, and the surrounding extravascular tissue is represented as a Cartesian grid of 3D voxels throughout which oxygen is transported by diffusion. We split the network and tissue meshes by the Schur complement method of domain decomposition to obtain a reduced set of system equations for the tissue oxygen concentration. The use of a Cartesian grid allows the corresponding matrix equation to be solved approximately with a fast Fourier transform based Poisson solver, which serves as an effective preconditioner for Krylov subspace iteration. The performance of this method enables the steady state simulation of cortical oxygen perfusion for anatomically accurate vascular networks down to single micron resolution without the need for supercomputers.

Practitioner Points

We present a novel mixed-domain framework for efficiently modeling O ₂ extraction kinetics in the brain. Model equations are generated by graph-theoretic methods for mixed domains.Dual mesh domain decomposition with FFT preconditioning yields very fast simulation times for extremely high spatial resolution.

Could respiration-driven blood oxygen changes modulate neural activity?

Oxygen is critical for neural metabolism, but under most physiological conditions, oxygen levels in the brain are far more than are required. Oxygen levels can be dynamically increased by increases in respiration rate that are tied to the arousal state of the brain and cognition, and not necessarily linked to exertion by the body. Why these changes in respiration occur when oxygen is already adequate has been a long-standing puzzle. In humans, performance on cognitive tasks can be affected by very high or very low oxygen levels, but whether the physiological changes in blood oxygenation produced by respiration have an appreciable effect is an open question. Oxygen has direct effects on potassium channels, increases the degradation rate of nitric oxide, and is rate limiting for the synthesis of some neuromodulators. We discuss whether oxygenation changes due to respiration contribute to neural dynamics associated with attention and arousal.

Quantification of hypoxic regions distant from occlusions in cerebral penetrating arteriole trees

The microvasculature plays a key role in oxygen transport in the mammalian brain. Despite the close coupling between cerebral vascular geometry and local oxygen demand, recent experiments have reported that microvascular occlusions can lead to unexpected distant tissue hypoxia and infarction. To better understand the spatial correlation between the hypoxic regions and the occlusion sites, we used both in vivo experiments and in silico simulations to investigate the effects of occlusions in cerebral penetrating arteriole trees on tissue hypoxia. In a rat model of microembolisation, 25 μm microspheres were injected through the carotid artery to occlude penetrating arterioles. In representative models of human cortical columns, the penetrating arterioles were occluded by simulating the transport of microspheres of the same size and the oxygen transport was simulated using a Green’s function method. The locations of microspheres and hypoxic regions were segmented, and two novel distance analyses were implemented to study their spatial correlation. The distant hypoxic regions were found to be present in both experiments and simulations, and mainly due to the hypoperfusion in the region downstream of the occlusion site. Furthermore, a reasonable agreement for the spatial correlation between hypoxic regions and occlusion sites is shown between experiments and simulations, which indicates the good applicability of in silico models in understanding the response of cerebral blood flow and oxygen transport to microemboli.

The brain function depends on the continuous oxygen supply through the bloodstream inside the microvasculature. Occlusions in the microvascular network will disturb the oxygen delivery in the brain and result in hypoxic tissues that can lead to infarction and cognitive dysfunction. To aid in understanding the formation of hypoxic tissues caused by micro-occlusions in the penetrating arteriole trees, we use rodent experiments and simulations of human vascular networks to study the spatial correlations between the hypoxic regions and the occlusion locations. Our results suggest that hypoxic regions can form distally from the occlusion site, which agrees with the previous observations in the rat brain. These distant hypoxic regions are primarily due to the lack of blood flow in the brain tissues downstream of the occlusion. Moreover, a reasonable agreement of the spatial relationship is found between the experiments and the simulations, which indicates the applicability of in silico models to study the effects of microemboli on the brain tissue.

Altered linear coupling between stimulus-evoked blood flow and oxygen metabolism in the aging human brain

Neural-vascular coupling (NVC) is the process by which oxygen and nutrients are delivered to metabolically active neurons by blood vessels. Murine models of NVC disruption have revealed its critical role in healthy neural function. We hypothesized that, in humans, aging exerts detrimental effects upon the integrity of the neural-glial-vascular system that underlies NVC. To test this hypothesis, calibrated functional magnetic resonance imaging (cfMRI) was used to characterize age-related changes in cerebral blood flow (CBF) and oxygen metabolism during visual cortex stimulation. Thirty-three younger and 27 older participants underwent cfMRI scanning during both an attention-controlled visual stimulation task and a hypercapnia paradigm used to calibrate the blood-oxygen-level-dependent signal. Measurement of stimulus-evoked blood flow and oxygen metabolism permitted calculation of the NVC ratio to assess the integrity of neural-vascular communication. Consistent with our hypothesis, we observed monotonic NVC ratio increases with increasing visual stimulation frequency in younger adults but not in older adults. Age-related changes in stimulus-evoked cerebrovascular and neurometabolic signal could not fully explain this disruption; increases in stimulus-evoked neurometabolic activity elicited corresponding increases in stimulus-evoked CBF in younger but not in older adults. These results implicate age-related, demand-dependent failures of the neural-glial-vascular structures that comprise the NVC system.

A two-layer continuously distributed capillary O2 transport model applied to blood flow regulation in resting skeletal muscle

The microcirculation is the site of direct oxygen transfer from blood to tissue, and also of oxygen delivery control via regulation of local blood flow. In addition, a number of diseases including type II diabetes mellitus (DMII) and sepsis are known to produce microcirculatory dysfunction in their early phases. Given the complexity of microvascular structure and physiology, and the difficulty of measuring tissue oxygenation at the micro-scale, mathematical modelling has been necessary for understanding the physiology and pathophysiology of O₂ transport in the microcirculation and for interpreting in vivo experiments. To advance this area, a model of blood-tissue O₂ transport in skeletal muscle was recently developed which uses continuously distributed capillaries and includes O₂ diffusion, convection, and consumption. The present work extends this model to two adjacent layers of skeletal muscle with different blood flow rates and applies it to study steady-state O₂ transport when flow regulation is stimulated using an O₂ exchange chamber. To generate a model which may be validated through in vivo experiments, an overlying O₂ permeable membrane is included. The model is solved using traditional methods including separation of variables and Fourier decomposition, and to ensure smooth profiles at the muscle-muscle and muscle-membrane interfaces matching conditions are developed. The study presents qualitative verification for the model, using visualizations of tissue PO₂ distributions for varying capillary density (CD), and presents capillary velocity response values in the near layer for varying chamber PO₂ under the assumption that outlet capillary O₂ saturation is equalized between adjacent layers. These compensatory velocity profiles, along with effective 'no-flux' chamber PO₂ values, are presented for varying CD and tissue O₂ consumption values. Insights gained from the two-layer model provide guidance for interpreting and planning future in-vivo experiments, and also provide motivation for further development of the model to improve understanding of the interaction between O₂ transport and blood flow regulation.

Modelling the effects of cerebral microthrombi on tissue oxygenation and cell death

Thrombectomy, the mechanical removal of a clot, is the most common way to treat ischaemic stroke with large vessel occlusions. However, perfusion cannot always be restored after such an intervention. It has been hypothesised that the absence of reperfusion is at least partially due to the clot fragments that block the downstream vessels. In this paper, we present a new way of quantifying the effects of cerebral microthrombi on oxygen transport to tissue in terms of hypoxia and ischaemia. The oxygen transport was simulated with the Green's function method on physiologically representative microvascular cubes, which was found independent of both microvascular geometry and length scale. The microthrombi occlusions were then simulated in the microvasculature, which were extravasated over time with a new thrombus extravasation model. The tissue hypoxic fraction was fitted as a sigmoidal function of vessel blockage fraction, which was then taken to be a function of time after the formation of microthrombi occlusions. A novel hypoxia-based 3-state cell death model was finally proposed to simulate the hypoxic tissue damage over time. Using the cell death model, the impact of a certain degree of microthrombi occlusions on tissue viability and microinfarct volume can be predicted over time. Quantifying the impact of microthrombi on oxygen transport and tissue death will play an important role in full brain models of ischaemic stroke and thrombectomy.

A Mesoscale Computational Model for Microvascular Oxygen Transfer

We address a mathematical model for oxygen transfer in the microcirculation. The model includes blood flow and hematocrit transport coupled with the interstitial flow, oxygen transport in the blood and the tissue, including capillary-tissue exchange effects. Moreover, the model is suited to handle arbitrarily complex vascular geometries. The purpose of this study is the validation of the model with respect to classical solutions and the further demonstration of its adequacy to describe the heterogeneity of oxygenation in the tissue microenvironment. Finally, we discuss the importance of these effects in the treatment of cancer using radiotherapy.

Simulation of angiogenesis in three dimensions: Application to cerebral cortex

The vasculature is a dynamic structure, growing and regressing in response to embryonic development, growth, changing physiological demands, wound healing, tumor growth and other stimuli. At the microvascular level, network geometry is not predetermined, but emerges as a result of biological responses of each vessel to the stimuli that it receives. These responses may be summarized as angiogenesis, remodeling and pruning. Previous theoretical simulations have shown how two-dimensional vascular patterns generated by these processes in the mesentery are consistent with experimental observations. During early development of the brain, a mesh-like network of vessels is formed on the surface of the cerebral cortex. This network then forms branches into the cortex, forming a three-dimensional network throughout its thickness. Here, a theoretical model is presented for this process, based on known or hypothesized vascular response mechanisms together with experimentally obtained information on the structure and hemodynamics of the mouse cerebral cortex. According to this model, essential components of the system include sensing of oxygen levels in the midrange of partial pressures and conducted responses in vessel walls that propagate information about metabolic needs of the tissue to upstream segments of the network. The model provides insights into the effects of deficits in vascular response mechanisms, and can be used to generate physiologically realistic microvascular network structures.

Blood flow regulation and oxygen transport in a heterogeneous model of the mouse retina

Elevated intraocular pressure is the primary risk factor for glaucoma, yet vascular health and ocular hemodynamics have also been established as important risk factors for the disease. The precise physiological mechanisms and processes by which flow impairment and reduced tissue oxygenation relate to retinal ganglion cell death are not fully known. Mathematical modeling has emerged as a useful tool to help decipher the role of hemodynamic alterations in glaucoma. Several previous models of the retinal microvasculature and tissue have investigated the individual impact of spatial heterogeneity, flow regulation, and oxygen transport on the system. This study combines all three of these components into a heterogeneous mathematical model of retinal arterioles that includes oxygen transport and acute flow regulation in response to changes in pressure, shear stress, and oxygen demand. The metabolic signal (S_i) is implemented as a wall-derived signal that reflects the oxygen deficit along the network, and three cases of conduction are considered: no conduction, a constant signal, and a flow-weighted signal. The model shows that the heterogeneity of the downstream signal serves to regulate flow better than a constant conducted response. In fact, the increases in average tissue PO₂ due to a flow-weighted signal are often more significant than if the entire level of signal is increased. Such theoretical work supports the importance of the non-uniform structure of the retinal vasculature when assessing the capability and/or dysfunction of blood flow regulation in the retinal microcirculation.