Browsing by Subject "mathematical model"

Now showing 1 - 6 of 6
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    Blood circulation and aqueous humor flow in the eye : multi-scale modeling and clinical applications
    (2016-06-14) Cassani, Simone; Guidoboni, Giovanna; Arciero, Julia Concetta; Harris, Alon
    Glaucoma is a multi-factorial ocular disease associated with death of retinal ganglion cells and irreversible vision loss. Many risk factors contribute to glaucomatous damage, including elevated intraocular pressure (IOP), age, genetics, and other diseases such as diabetes and systemic hypertension. Interestingly, alterations in retinal hemodynamics have also been associated with glaucoma. A better understanding of the factors that contribute to these hemodynamic alterations could lead to improved and more appropriate clinical approaches to manage and hopefully treat glaucoma patients. In this thesis, we develop several mathematical models aimed at describing ocular hemodynamics and oxygenation in health and disease. Precisely we describe: (i) a time-dependent mathematical model for the retinal circulation that includes macrocirculation, microcirculation, phenomenological vascular regulation, and the mechanical effect of IOP on the retinal vasculature; (ii) a steady-state mathematical model for the retinal circulation that includes macrocirculation, microcirculation, mechanistic vascular regulation, the effect of IOP on the central retinal artery and central retinal vein, and the transport of oxygen in the retinal tissue using a Krogh cylinder type model; (iii) a steady-state mathematical model for the transport of oxygen in the retinal microcirculation and tissue based on a realistic retinal anatomy; and (iv) a steady-state mathematical model for the production and drainage of aqueous humor (AH). The main objective of this work is to study the relationship between IOP, systemic blood pressure, and the functionality of vascular autoregulation; the transport and exchange of oxygen in the retinal vasculature and tissue; and the production and drainage of AH, that contributes to the level of IOP. The models developed in this thesis predict that (i) the autoregulation plateau occurs for different values of IOP in hypertensive and normotensive patients. Thus, the level of blood pressure and functionality of autoregulation affect the changes in retinal hemodynamics caused by IOP and might explain the inconsistent outcomes of clinical studies; (ii) the metabolic and carbon dioxide mechanisms play a major role in the vascular regulation of the retina. Thus, the impairment of either of these mechanisms could cause ischemic damage to the retinal tissue; (iii) the multi-layer description of transport of oxygen in the retinal tissue accounts for the effect of the inner and outer retina, thereby improving the predictive ability of the model; (iv) a greater reduction in IOP is obtained if topical medications target AH production rather that AH drainage and if IOP-lowering medications are administrated to patients that exhibit a high initial level of IOP. Thus, the effectiveness of IOP-lowering medications depend on a patient’s value of IOP. In conclusion, the results of this thesis demonstrate that the insight provided by mathematical modeling alongside clinical studies can improve the understanding of diseases and potentially contribute to the clinical development of new treatments.
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    Combining Theoretical and Experimental Techniques to Study Murine Heart Transplant Rejection
    (Frontiers Media SA, 2016) Arciero, Julia C.; Maturo, Andrew; Arun, Anirudh; Oh, Byoung Chol; Brandacher, Gerald; Raimondi, Giorgio; Department of Mathematical Sciences, School of Science
    The quality of life of organ transplant recipients is compromised by complications associated with life-long immunosuppression, such as hypertension, diabetes, opportunistic infections, and cancer. Moreover, the absence of established tolerance to the transplanted tissues causes limited long-term graft survival rates. Thus, there is a great medical need to understand the complex immune system interactions that lead to transplant rejection so that novel and effective strategies of intervention that redirect the system toward transplant acceptance (while preserving overall immune competence) can be identified. This study implements a systems biology approach in which an experimentally based mathematical model is used to predict how alterations in the immune response influence the rejection of mouse heart transplants. Five stages of conventional mouse heart transplantation are modeled using a system of 13 ordinary differential equations that tracks populations of both innate and adaptive immunity as well as proxies for pro- and anti-inflammatory factors within the graft and a representative draining lymph node. The model correctly reproduces known experimental outcomes, such as indefinite survival of the graft in the absence of CD4(+) T cells and quick rejection in the absence of CD8(+) T cells. The model predicts that decreasing the translocation rate of effector cells from the lymph node to the graft delays transplant rejection. Increasing the starting number of quiescent regulatory T cells in the model yields a significant but somewhat limited protective effect on graft survival. Surprisingly, the model shows that a delayed appearance of alloreactive T cells has an impact on graft survival that does not correlate linearly with the time delay. This computational model represents one of the first comprehensive approaches toward simulating the many interacting components of the immune system. Despite some limitations, the model provides important suggestions of experimental investigations that could improve the understanding of rejection. Overall, the systems biology approach used here is a first step in predicting treatments and interventions that can induce transplant tolerance while preserving the capacity of the immune system to protect against legitimate pathogens.
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    The Controversy of Myopia as a Risk Factor for Glaucoma: a Mathematical Approach
    (Office of the Vice Chancellor for Research, 2012-04-13) Guidoboni, G.; Cassani, S.; Carichino, L.; Arieli, Y.; Siesky, B.A.; Harris, A.
    Purpose: to quantify how individual variations in anatomical parameters often associated with myopia (e.g. longer ocular axial length (OAL), reduced scleral thickness (ST), lamina cribrosa diameter (LCD) and thickness (LCT)) affect retinal blood flow (RBF) and its sensitivity to ocular perfusion pressure (OPP). Methods: A mathematical model is used to calculate RBF through central retinal artery (CRA), arterioles, capillaries, venules, and central retinal vein (CRV). The flow is time-dependent, driven by systemic pressure and regulated by variable resistances to account for nonlinear effects due to (1) autoregulation (AR), and (2) lamina cribrosa effect on CRA and CRV. The latter is a nonlinear function of intraocular pressure (IOP), cerebrospinal fluid pressure (CSF) and OAL, ST, LCD, and LCT. RBF is computed as the solution of a system of five non-linear ordinary differential equations. The system is solved for different OPP values, obtained by varying independently IOP and mean arterial pressure (MAP), with and without AR. Results: Four representative eyes are compared: Eye 1 (OAL=24mm, ST=1mm, LCD=3mm, LCT=0.4mm), Eye 2 (OAL=28mm, ST=1mm, LCD=3mm, LCT=0.4mm), Eye 3 (OAL=24mm, ST=0.7mm, LCD=2mm, LCT=0.2mm), Eye 4 (OAL=28mm, ST=0.7mm, LCD=2mm, LCT=0.2mm). The model predicts that the cardiac cycle RBF average (RBFav) for eyes with smaller LCD and LCT is notably less than in normal eyes when IOP is elevated and without AR (c). Without AR and reduced MAP, the four eyes show similar RBFav reductions (d). With AR, anatomical changes do not induce notable changes in RBFav, (a) and (b). Conclusions: Reduced LCD and LCT, often associated with myopia, seem to affect RBFav more than elevated OAL. RBFav reductions magnify when AR is impaired, and this might reduce IOP safe levels for eyes with reduced LCD and LCT. These findings suggest that a combination of anatomical and vascular factors might cause certain myopic eyes to be at higher risk for glaucomatous damage than others.
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    Mathematical model of subthalamic nucleus neuron: Characteristic activity patterns and bifurcation analysis
    (AIP, 2021-11) Park, Choongseok; Rubchinsky, Leonid L.; Ahn, Sungwoo; Mathematical Sciences, School of Science
    The subthalamic nucleus (STN) has an important role in the pathophysiology of the basal ganglia in Parkinson's disease. The ability of STN cells to generate bursting rhythms under either transient or sustained hyperpolarization may underlie the excessively synchronous beta rhythms observed in Parkinson's disease. In this study, we developed a conductance-based single compartment model of an STN neuron, which is able to generate characteristic activity patterns observed in experiments including hyperpolarization-induced bursts and post-inhibitory rebound bursts. This study focused on the role of three currents in rhythm generation: T-type calcium (CaT) current, L-type calcium (CaL) current, and hyperpolarization-activated cyclic nucleotide-gated (HCN) current. To investigate the effects of these currents in rhythm generation, we performed a bifurcation analysis using slow variables in these currents. Bifurcation analysis showed that the HCN current promotes single-spike activity patterns rather than bursting in agreement with experimental results. It also showed that the CaT current is necessary for characteristic bursting activity patterns. In particular, the CaT current enables STN neurons to generate these activity patterns under hyperpolarizing stimuli. The CaL current enriches and reinforces these characteristic activity patterns. In hyperpolarization-induced bursts or post-inhibitory rebound bursts, the CaL current allows STN neurons to generate long bursting patterns. Thus, the bifurcation analysis explained the synergistic interaction of the CaT and CaL currents, which enables STN neurons to respond to hyperpolarizing stimuli in a salient way. The results of this study implicate the importance of CaT and CaL currents in the pathophysiology of the basal ganglia in Parkinson's disease.
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    Modeling acute and chronic vascular responses to a major arterial occlusion
    (Wiley, 2022-01) Zhao, Erin; Barber, Jared; Sen, Chandan K.; Arciero, Julia; Mathematical Sciences, School of Science
    Objective To incorporate chronic vascular adaptations into a mathematical model of the rat hindlimb to simulate flow restoration following total occlusion of the femoral artery. Methods A vascular wall mechanics model is used to simulate acute and chronic vascular adaptations in the collateral arteries and collateral-dependent arterioles of the rat hindlimb. On an acute timeframe, the vascular tone of collateral arteries and distal arterioles is determined by responses to pressure, shear stress, and metabolic demand. On a chronic timeframe, sustained dilation of arteries and arterioles induces outward vessel remodeling represented by increased passive vessel diameter (arteriogenesis), and low venous oxygen saturation levels induce the growth of new capillaries represented by increased capillary number (angiogenesis). Results The model predicts that flow compensation to an occlusion is enhanced primarily by arteriogenesis of the collateral arteries on a chronic time frame. Blood flow autoregulation is predicted to be disrupted and to occur for higher pressure values following femoral arterial occlusion. Conclusions Structural adaptation of the vasculature allows for increased blood flow to the collateral-dependent region after occlusion. Although flow is still below pre-occlusion levels, model predictions indicate that interventions which enhance collateral arteriogenesis would have the greatest potential for restoring flow.
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    Predicting retinal tissue oxygenation using an image-based theoretical model
    (Elsevier, 2018-11) Fry, Brendan C.; Coburn, Ehren Brant; Whiteman, Spencer; Harris, Alon; Siesky, Brent; Arciero, Julia; Mathematical Sciences, School of Science
    Impaired oxygen delivery and tissue perfusion have been identified as significant factors that contribute to the loss of retinal ganglion cells in glaucoma patients. This study predicts retinal blood and tissue oxygenation using a theoretical model of the retinal vasculature based on confocal microscopy images of the mouse retina. These images reveal a complex and heterogeneous geometry of vessels that are distributed non-uniformly into multiple distinct retinal layers at varying depths. Predicting oxygen delivery and distribution in this irregular arrangement of retinal microvessels requires the use of an efficient theoretical model. The model employed in this work utilizes numerical methods based on a Green's function approach to simulate the spatial distribution of oxygen levels in a network of retinal blood vessels and the tissue surrounding them. Model simulations also predict the blood flow rates and pressures in each of the microvessels throughout the entire network. As expected, the model predicts that average vessel PO2 decreases as oxygen demand is increased. However, the standard deviation of PO2 in the vessels nearly doubles as oxygen demand is increased from 1 to 8 cm3 O2/100 cm3/min, indicating a very wide spread in the predicted PO2 levels, suggesting that average PO2 is not a sufficient indicator of oxygenation in a heterogeneous vascular network. Ultimately, the development of this mathematical model will help to elucidate the important factors associated with blood flow and metabolism that contribute to the vision loss characteristic of glaucoma.