8 research outputs found
Energy-based operator splitting approach for the time discretization of coupled systems of partial and ordinary differential equations for fluid flows: The Stokes case
The goal of this work is to develop a novel splitting approach for the
numerical solution of multiscale problems involving the coupling between Stokes
equations and ODE systems, as often encountered in blood flow modeling
applications. The proposed algorithm is based on a semi-discretization in time
based on operator splitting, whose design is guided by the rationale of
ensuring that the physical energy balance is maintained at the discrete level.
As a result, unconditional stability with respect to the time step choice is
ensured by the implicit treatment of interface conditions within the Stokes
substeps, whereas the coupling between Stokes and ODE substeps is enforced via
appropriate initial conditions for each substep. Notably, unconditional
stability is attained without the need of subiterating between Stokes and ODE
substeps. Stability and convergence properties of the proposed algorithm are
tested on three specific examples for which analytical solutions are derived
A Multiscale Thermo-Fluid Computational Model for a Two-Phase Cooling System
In this paper, we describe a mathematical model and a numerical simulation
method for the condenser component of a novel two-phase thermosyphon cooling
system for power electronics applications. The condenser consists of a set of
roll-bonded vertically mounted fins among which air flows by either natural or
forced convection. In order to deepen the understanding of the mechanisms that
determine the performance of the condenser and to facilitate the further
optimization of its industrial design, a multiscale approach is developed to
reduce as much as possible the complexity of the simulation code while
maintaining reasonable predictive accuracy. To this end, heat diffusion in the
fins and its convective transport in air are modeled as 2D processes while the
flow of the two-phase coolant within the fins is modeled as a 1D network of
pipes. For the numerical solution of the resulting equations, a Dual
Mixed-Finite Volume scheme with Exponential Fitting stabilization is used for
2D heat diffusion and convection while a Primal Mixed Finite Element
discretization method with upwind stabilization is used for the 1D coolant
flow. The mathematical model and the numerical method are validated through
extensive simulations of realistic device structures which prove to be in
excellent agreement with available experimental data
Multiscale mathematical modeling of ocular blood flow and oxygenation and their relevance to glaucoma
Glaucoma is a multifactorial ocular disease progressively leading to irreversible blindness. There is clear evidence of correlations between alterations in ocular hemodynamics and glaucoma; however, the mechanisms giving rise to these correlations are still elusive. The objective of this thesis is to develop mathematical models and methods to help elucidate these mechanisms. First, we develop a mathematical model that describes the deformation of ocular structures and ocular blood flow using a reduced-order fluid-structure interaction model. This model is used to investigate the relevance of mechanical and vascular factors in glaucoma. As a first step in expanding this model to higher dimensions, we propose a novel energy-based technique for coupling partial and ordinary differential equations in blood flow, using operator splitting. Next, we combine clinical data and model predictions to propose possible explanations for the increase in venous oxygen saturation in advanced glaucoma patients. We develop a computer-aided manipulation process of color Doppler images to extract novel waveform parameters to distinguish between healthy and glaucomatous individuals. The results obtained in this work suggest that: 1) the increase in resistance of the retinal microcirculation contributes to the influence of intraocular pressure on retinal hemodynamics; 2) the influence of cerebrospinal fluid pressure on retinal hemodynamics is mediated by associated changes in blood pressure; 3) the increase in venous oxygen saturation levels observed among advanced glaucoma patients depends on the value of the patients’ intraocular pressure; 4) the normalized distance between the ascending and descending limb of the ophthalmic artery velocity profile is significantly higher in glaucoma patients than in healthy individuals
Physiology-Enhanced Data Analytics to Evaluate the Effect of Altitude on Intraocular Pressure and Ocular Hemodynamics
Altitude affects intraocular pressure (IOP); however, the underlying mechanisms involved and its relationship with ocular hemodynamics remain unknown. Herein, a validated mathematical modeling approach was used for a physiology-enhanced (pe-) analysis of the Mont Blanc study (MBS), estimating the effects of altitude on IOP, blood pressure (BP), and retinal hemodynamics. In the MBS, IOP and BP were measured in 33 healthy volunteers at 77 and 3466 m above sea level. Pe-retinal hemodynamics analysis predicted a statistically significant increase (p < 0.001) in the model predicted blood flow and pressure within the retinal vasculature following increases in systemic BP with altitude measured in the MBS. Decreased IOP with altitude led to a non-monotonic behavior of the model predicted retinal vascular resistances, with significant decreases in the resistance of the central retinal artery (p < 0.001) and retinal venules (p = 0.003) and a non-significant increase in the resistance in the central retinal vein (p = 0.253). Pe-aqueous humor analysis showed that a decrease in osmotic pressure difference (OPD) may underlie the difference in IOP measured at different altitudes in the MBS. Our analysis suggests that venules bear the significant portion of the IOP pressure load within the ocular vasculature, and that OPD plays an important role in regulating IOP with changes in altitude
Computer-aided ophthalmic artery waveform analysis in healthy individuals and glaucoma patients
Purpose: Arterial waveform parameters (WPs) are commonly used to monitor and
diagnose systemic diseases. Color Doppler Imaging (CDI) is a consolidated technique
to measure blood velocity profile in some of the major ocular vessels. This study
proposes a computer-aided manipulation process of ophthalmic artery (OA) CDI
images to classify and quantify WPs that might be significant in the assessment of
glaucoma.
Methods: Fifty CDI images acquired by four different operators on nine healthy
individuals and 38 CDI images of 38 open-angle glaucoma (OAG) patients were
considered. An ad-hoc semi-automated image processing code was implemented
to detect the digitalized OA velocity waveform and to extract the WPs. Concordance
correlation coefficient (CCC), two-sample t-test and Pearson\u2019s correlation coefficient
were used to test for similarities, differences and associations among variables
Computer-aided identification of novel ophthalmic artery waveform parameters in healthy subjects and glaucoma patients
Arterial waveform parameters (WPs) are commonly used to monitor and diagnose systemic diseases. Color Doppler Imaging (CDI) is a consolidated technique to measure blood velocity profile in some of the major ocular vessels. This study proposes a computer-aided manipulation process of ophthalmic artery (OA) CDI images to classify and quantify WPs that might be significant in the assessment of glaucom