Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights

There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve functional tumour-associated blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation medi- ated by vascular targeting agents that induce occlusion/collapse of tumour blood vessels. In contrast, the therapeutic intention of normalising the abnormal structure and function of tumour vascular net- works, e.g. via alleviating stress-induced vaso-occlusion, is to improve chemo-, immuno- and radiation therapy efficacy. Although both strategies have shown therapeutic potential, it remains unclear why they often fail to control glioma invasion into the surrounding healthy brain tissue. To shed light on this issue, we propose a mathematical model of glioma invasion focusing on the interplay between the mi- gration/proliferation dichotomy (Go-or-Grow) of glioma cells and modulations of the functional tumour vasculature. Vaso-modulatory interventions are modelled by varying the degree of vaso-occlusion. We discovered the existence of a critical cell proliferation/diffusion ratio that separates glioma invasion re- sponses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the tumour front speed and increase the infiltration width, for those in the other regime the invasion speed increases and infiltration width decreases. We show how these in silico findings can be used to guide individualised approaches of vaso-modulatory treatment strategies and thereby improve success rates

Oscillatory dynamics in a model of vascular tumour growth -- implications for chemotherapy

Background\ud \ud Investigations of solid tumours suggest that vessel occlusion may occur when increased pressure from the tumour mass is exerted on the vessel walls. Since immature vessels are frequently found in tumours and may be particularly sensitive, such occlusion may impair tumour blood flow and have a negative impact on therapeutic outcome. In order to study the effects that occlusion may have on tumour growth patterns and therapeutic response, in this paper we develop and investigate a continuum model of vascular tumour growth.\ud Results\ud \ud By analysing a spatially uniform submodel, we identify regions of parameter space in which the combination of tumour cell proliferation and vessel occlusion give rise to sustained temporal oscillations in the tumour cell population and in the vessel density. Alternatively, if the vessels are assumed to be less prone to collapse, stable steady state solutions are observed. When spatial effects are considered, the pattern of tumour invasion depends on the dynamics of the spatially uniform submodel. If the submodel predicts a stable steady state, then steady travelling waves are observed in the full model, and the system evolves to the same stable steady state behind the invading front. When the submodel yields oscillatory behaviour, the full model produces periodic travelling waves. The stability of the waves (which can be predicted by approximating the system as one of λ-ω type) dictates whether the waves develop into regular or irregular spatio-temporal oscillations. Simulations of chemotherapy reveal that treatment outcome depends crucially on the underlying tumour growth dynamics. In particular, if the dynamics are oscillatory, then therapeutic efficacy is difficult to assess since the fluctuations in the size of the tumour cell population are enhanced, compared to untreated controls.\ud Conclusions\ud \ud We have developed a mathematical model of vascular tumour growth formulated as a system of partial differential equations (PDEs). Employing a combination of numerical and analytical techniques, we demonstrate how the spatio-temporal dynamics of the untreated tumour may influence its response to chemotherapy.\ud Reviewers\ud \ud This manuscript was reviewed by Professor Zvia Agur and Professor Marek Kimmel

Multiphase modelling of vascular tumour growth in two spatial dimensions

In this paper we present a continuum mathematical model of vascular tumour growth which is based on a multiphase framework in which the tissue is decomposed into four distinct phases and the principles of conservation of mass and momentum are applied to the normal/healthy cells, tumour cells, blood vessels and extracellular material. The inclusion of a diffusible nutrient, supplied by the blood vessels, allows the vasculature to have a nonlocal influence on the other phases. Two-dimensional computational simulations are carried out on unstructured, triangular meshes to allow a natural treatment of irregular geometries, and the tumour boundary is captured as a diffuse interface on this mesh, thereby obviating the need to explicitly track the (potentially highly irregular and ill-defined) tumour boundary. A hybrid finite volume/finite element algorithm is used to discretise the continuum model: the application of a conservative, upwind, finite volume scheme to the hyperbolic mass balance equations and a finite element scheme with a stable element pair to the generalised Stokes equations derived from momentum balance, leads to a robust algorithm which does not use any form of artificial stabilisation. The use of a matrix-free Newton iteration with a finite element scheme for the nutrient reaction-diffusion equations allows full nonlinearity in the source terms of the mathematical model. Numerical simulations reveal that this four-phase model reproduces the characteristic pattern of tumour growth in which a necrotic core forms behind an expanding rim of well-vascularised proliferating tumour cells. The simulations consistently predict linear tumour growth rates. The dependence of both the speed with which the tumour grows and the irregularity of the invading tumour front on the model parameters are investigated

MRI Visualization of Whole Brain Macro- and Microvascular Remodeling in a Rat Model of Ischemic Stroke: A Pilot Study

Using superparamagnetic iron oxide nanoparticles (SPION) as a single contrast agent, we investigated dual contrast cerebrovascular magnetic resonance imaging (MRI) for simultaneously monitoring macro- and microvasculature and their association with ischemic edema status (via apparent diffusion coefficient [ADC]) in transient middle cerebral artery occlusion (tMCAO) rat models. High-resolution T1-contrast based ultra-short echo time MR angiography (UTE-MRA) visualized size remodeling of pial arteries and veins whose mutual association with cortical ischemic edema status is rarely reported. ??R2?????R2*-MRI-derived vessel size index (VSI) and density indices (Q and MVD) mapped morphological changes of microvessels occurring in subcortical ischemic edema lesions. In cortical ischemic edema lesions, significantly dilated pial veins (p???=???0.0051) and thinned pial arteries (p???=???0.0096) of ipsilateral brains compared to those of contralateral brains were observed from UTE-MRAs. In subcortical regions, ischemic edema lesions had a significantly decreased Q and MVD values (p???<???0.001), as well as increased VSI values (p???<???0.001) than normal subcortical tissues in contralateral brains. This pilot study suggests that MR-based morphological vessel changes, including but not limited to venous blood vessels, are directly related to corresponding tissue edema status in ischemic stroke rat models

Hypoxic Cell Waves around Necrotic Cores in Glioblastoma: A Biomathematical Model and its Therapeutic Implications

Glioblastoma is a rapidly evolving high-grade astrocytoma that is distinguished pathologically from lower grade gliomas by the presence of necrosis and microvascular hiperplasia. Necrotic areas are typically surrounded by hypercellular regions known as "pseudopalisades" originated by local tumor vessel occlusions that induce collective cellular migration events. This leads to the formation of waves of tumor cells actively migrating away from central hypoxia. We present a mathematical model that incorporates the interplay among two tumor cell phenotypes, a necrotic core and the oxygen distribution. Our simulations reveal the formation of a traveling wave of tumor cells that reproduces the observed histologic patterns of pseudopalisades. Additional simulations of the model equations show that preventing the collapse of tumor microvessels leads to slower glioma invasion, a fact that might be exploited for therapeutic purposes.Comment: 29 pages, 9 figure

Combined therapies of antithrombotics and antioxidants delay in silico brain tumor progression

Glioblastoma multiforme, the most frequent type of primary brain tumor, is a rapidly evolving and spatially heterogeneous high-grade astrocytoma that presents areas of necrosis, hypercellularity and microvascular hyperplasia. The aberrant vasculature leads to hypoxic areas and results in an increase of the oxidative stress selecting for more invasive tumor cell phenotypes. In our study we assay in silico different therapeutic approaches which combine antithrombotics, antioxidants and standard radiotherapy. To do so, we have developed a biocomputational model of glioblastoma multiforme that incorporates the spatio-temporal interplay among two glioma cell phenotypes corresponding to oxygenated and hypoxic cells, a necrotic core and the local vasculature whose response evolves with tumor progression. Our numerical simulations predict that suitable combinations of antithrombotics and antioxidants may diminish, in a synergetic way, oxidative stress and the subsequent hypoxic response. This novel therapeutical strategy, with potentially low or no toxicity, might reduce tumor invasion and further sensitize glioblastoma multiforme to conventional radiotherapy or other cytotoxic agents, hopefully increasing median patient overall survival time.Comment: 8 figure

Математические модели развития и компенсации гипоксических состояний при ишемической болезни сердца у лиц летного состава

The increase of pilots’ labor intensity caused by rapid development of flight technologies and increasing of complexity of combat missions faced by flight crew members increases the loads on organisms of flight personnel in general and in particular on their cardiovascular system. Domestic and foreign sources contain statistics indicating an increase in the number of flight accidents caused by cardiovascular pathologies in pilots, an increase in the number of flight personnel unsuitable for flight work due to the same reasons, a decrease in the age of flight crew members with cardiovascular pathologies. Therefore, issues of early detection and optimization of treatment processes of cardiovascular diseases in flight crew members are really necessary.Збільшення інтенсивності праці льотчиків, викликане швидкими темпами розвитку льотної техніки і ускладненням бойових завдань, що стоять перед членами льотних екіпажів, збільшує навантаження на організм осіб льотного складу в цілому, і зокрема на серцево-судинну систему. Вітчизняні та зарубіжні джерела містять статистику, яка свідчить про збільшення кількості льотних пригод, викликаних серцево-судинними патологіями у льотчиків, зростанні кількості осіб льотного складу, визнаними непридатними до льотної роботи з тих же причин, зниженням віку членів льотних екіпажів, що мають патології серцево-судинної системи. Тому актуальними є питання своєчасного виявлення та оптимізації процесу лікування серцево-судинних захворюваньу членів льотних екіпажів.Увеличение интенсивности труда летчиков, вызванное быстрыми темпами развития летной техники и усложнением боевых задач, стоящих перед членами летных экипажей увеличивает нагрузку на организм лиц летного состава в целом и а частности на сердечно-сосудистую систему. Отечественные и зарубежные источники содержат статистику, свидетельствующую об увеличении числа летных происшествий, вызванных сердечно-сосудистыми патологиями у летчиков, росте числа лиц летного состава, признанными непригодными к летной работе по тем же причинам, снижением возраста членов летных экипажей, имеющих патологии сердечно-сосудистой системы. Поэтому актуальными являются вопросы своевременного выявления и оптимизации процесса лечения сердечно-сосудистых заболеваний у членов летных экипажей

A mathematical model for simulation of fetal heart rate decelerations in labor

Fetal wellbeing during labor and delivery is commonly monitored through the cardiotocogram (CTG), the combined registration of uterus contractions and fetal heart rate (FHR). From the CTG, the fetal oxygen state is estimated as the main indicator of the fetal condition. However, this estimate is difficult to make, due to the complex relation between CTG and oxygen state. Mathematical models can be used to assist in interpretation of the CTG, since they enable quantitative modeling of the flow of events through which uterine contractions affect fetal oxygenation and FHR. This thesis describes the development of a model that can be used to reproduce FHR response to uterine contractions during several clinical scenarios. First, a model was developed that describes the relation between uterine contractions, maternal and fetal hemodynamics, oxygen distribution within the feto-maternal circulation and cardiovascular (reflex) regulation in the fetus in response to deviations in blood- and oxygen pressures. The model is partly based on previously presented models for cardiac function, chemoreceptor control in adults and oxygen distribution in the fetal circulation. These modules are coupled and scaled to meet requirements for the (pregnant) maternal and fetal condition. The model is completed with a module for uterine contractions and a module of the vascular system of both mother and fetus. A first clinical scenario was simulated with the model to test model response to changes in cerebral blood flow during the descent of the fetal head in the birth canal. A validation pilot was performed to investigate the quality of model outcome via expert opinion. Experts were unable to discriminate between real and simulated signals, suggesting that the model can be used for educational training. Second, the model was extended with the baroreceptor reflex. This allowed simulation of a second clinical scenario, where both chemo- and baroreflex pathways lead to a FHR deceleration in response to uterine flow reduction during contractions. Results for the uncompromised fetus show that partial oxygen pressures reduce in relation to the strength and duration of the contraction. Furthermore, decelerations during several scenarios of uteroplacental insufficiency were studied. Results for reduced uterine blood supply or reduced placental diffusion capacity, demonstrated lower baseline FHR and smaller decelarations during contraction. Reduced uteroplacental blood volume was found to lead to deeper decelerations only. The model response in several nerve blocking simulations is similar to experimental findings. Third, the model was used to simulate a third type of decelerations, i.e. variable heart rate decelerations, originating from umbilical cord compression. Different degrees of compression were investigated. An increase in contraction amplitude and duration leads to increased umbilical cord compression grade and thus affects the extent of blood pressure increase, flow redistribution and FHR response. There is a clear relation between fetal oxygenation, blood pressure and the resulting FHR. The extent of umbilical compression and thus FHR deceleration is positively related to increased contraction duration and amplitude, and increased sensitivity of the umbilical resistance to uterine pressure. Fourth, gynaecologists, midwives and residents were asked to rate a set of both model-generated CTGs and real CTGs for the three clinical scenarios. Although real tracings were more likely to be recognized correctly, the suitability for use in simulation training was found to be almost equal for real and computer-generated tracings. Due to limited numbers for early and variable deceleration evaluation, statistical analysis turned out to be valid only for the CTG’s with late decelerations. Additional comments from the respondents revealed that variability and regularity of the simulated signals greatly influence the perception of a tracing. Clinicians agreed that a tracing is suitable for use in simulation training when it is clear and free of physiological incompatibilities, which is the case for all simulated tracings. Fifth, the model was used to test the clinical hypothesis that administration of oxygen to the mother may increase FHR during variable fetal heart rate decelerations. The model was used to test the response of fetal oxygenation and heart rate to maternal oxygen increase following 100% oxygen administration. Model outcome suggests that FHR benefits from oxygen administration as the duration and depth of FHR decelerations and fetal oxygenation improves. However, the beneficial effect of maternal hyperoxygenation on FHR and oxygenation reduces during more severe variable decelerations. In conclusion, a model was developed to simulate the physiologic cascade from uterine contraction to changes in fetal heart rate. Model outcome for various scenarios is in correspondence with findings from animal experiments. The model can be used in an educational setting for the simulation of short-term changes in fetal hemodynamics and oxygenation status in response to uterine contractions to increase insight into the complex physiology. In addition, it can be integrated in a full-body delivery simulator to enhance obstetric team training

Magnetic Resonance Imaging of Neural and Pulmonary Vascular Function: A Dissertation

Magnetic resonance imaging (MRI) has emerged as the imaging modality of choice in a wide variety experimental and clinical applications. In this dissertation, I will describe novel MRI techniques for the characterization of neural and pulmonary vascular function in preclinical models of disease. In the first part of this dissertation, experimental results will be presented comparing the identification of ischemic lesions in experimental stroke using dynamic susceptibility contrast (DSC) and a well validated arterial spin labeling (ASL). We show that DSC measurements of an index of cerebral blood flow are sensitive to ischemia, treatment, and stroke subregions. Further, we derived a threshold of cerebral blood flow for ischemia as measured by DSC. Finally, we show that ischemic lesion volumes as defined by DSC are comparable to those defined by ASL. In the second part of this dissertation, a methodology of visualizing clots in experimental animal models of stroke is presented. Clots were rendered visible by MRI through the addition of a gadolinium based contrast agent during formation. Modified clots were used to induce an experimental embolic middle cerebral artery occlusion. Clots in the cerebral vasculature were visualized in vivousing MRI. Further, the efficacy of recombinant tissue plasminogen activator (r-tPA) and the combination of r-tPA and recombinant annexin-2 (rA2) was characterized by clot visualization during lysis. In the third part of this dissertation, we present results of the application of hyperpolarized helium (HP-He) in the characterization of new model of experimental pulmonary ischemia. The longitudinal relaxation time of HP-He is sensitive to the presence of paramagnetic oxygen. During ischemia, oxygen exchange from the airspaces of the lungs to the capillaries is hindered resulting in increased alveolar oxygen content which resulted in the shortening of the HP-He longitudinal relaxation time. Results of measurements of the HP-He relaxation time in both normal and ischemic animals are presented. In the final part of this dissertation, I will present results of a new method to measure pulmonary blood volume (PBV) using proton based MRI. A T1 weighted, inversion recovery spin echo sequence with cardiac and respiratory gating was developed to measure the changes in signal intensity of lung parenchyma before and after the injection of a long acting intravascular contrast agent. PBV is related to the signal change in the lung parenchyma and blood before and after contrast agent. We validate our method using a model of hypoxic pulmonary vasoconstriction in rats

A multiscale model for collagen alignment in wound healing

It is thought that collagen alignment plays a significant part in scar tissue formation during dermal wound healing. We present a multiscale model for collagen deposition and alignment during this process. We consider fibroblasts as discrete units moving within an extracellular matrix of collagen and fibrin modelled as continua. Our model includes flux induced alignment of collagen by fibroblasts, and contact guidance of fibroblasts by collagen fibres. We can use the model to predict the effects of certain manipulations, such as varying fibroblast speed, or placing an aligned piece of tissue in the wound. We also simulate experiments which alter the TGF-β concentrations in a healing dermal wound and use the model to offer an explanation of the observed influence of this growth factor on scarring