Session X09: Biofluids: Physiological II

A mathematical model of drug delivery via a contact lens during wear

Contact lenses have been studied as a potential method of ophthalmic drug delivery since at least the 1970s, but no therapeutic option has been marketed to date. Barriers to commercial implementation include lack of in vivo and in vitro studies, and the absence of a complete understanding of the underlying fluid dynamics. To join theoretical and experimental information, we design a compartmental model of contact lens drug delivery to align with an in vitro model eye system. The model couples a partial differential equation for linear diffusion of drug inside the contact lens with ordinary differential equations governing the dynamics of the pre- and post-lens tear films and the eyelid region. The model simulates tear film dynamics during blinking over multiple hours. We compute the cumulative amount of drug released from the contact lens and compare our results to experimental model eye data. By isolating certain mechanisms or combinations of mechanisms in our model during this comparison, we attempt to better understand the mechanics of contact lens drug delivery.   

Predicting human red blood cell damage using experiments and machine learning

Circulating human red blood cells (erythrocytes) are exposed to fluid stressors. If the stressors are large enough, these erythrocytes can be damaged or even destroyed (hemolysis). In particular, hemolysis can cause organ injury, negatively affecting a person's health. While prior studies have shown an increase in hemolysis with the fluid shear rate, they contain large uncertainties in the experimental results—too large to offer insight on a per-person basis. Here, we predict hemolysis of human erythrocytes using a combination of experimental measurements and machine learning (ML). We conduct microfluidic experiments to directly measure the degree of hemolysis after the erythrocytes are exposed to a known stressor. We then combine experimental measurements with patient demographics and ML-modeling. Additionally, we demonstrate the use of active learning to guide experiment selection. We anticipate these results will offer insights on how to combine human biology-focused experiments and ML. Specifically, these results may drive the development of new devices and procedures designed to reduce hemolysis on a per-patient basis.   

Modelling the wall deformation of fluid conveying elastic-walled tubes

We investigate the small-amplitude deformations of a long, thin-walled elastic tube that is initially axially uniform with an arbitrary cross-sectional shape. The tube is deformed by a (possibly non-uniform) transmural pressure. For an initially elliptical tube, the leading-order deformations are shown to be governed by a single partial differential equation (PDE) for the azimuthal displacement as a function of the axial and azimuthal co-ordinates and time. Previous authors have obtained solutions of this PDE by making ad-hoc approximations based on truncating an approximate Fourier representation. In this new work, we present a generalised governing PDE, which permits arbitrary initial cross-sectional shapes, and describe a new solution method in which we instead write the azimuthal displacement as a sum over the azimuthal eigenfunctions of a generalised eigenvalue problem. We show that we are able to derive an uncoupled system of linear PDEs with constant coefficients for the amplitude of the azimuthal modes as a function of the axial co-ordinate and time. This results in a formal series solution of the whole system being found as a sum over the azimuthal modes. We show that the nth mode's contribution to the tube's relative area change is governed by a simplified second-order PDE. For the case in which wall deformation is driven by a uniform transmural pressure, we determine a family of initial cross-sectional shapes that have the property that only the first azimuthal mode is excited, which results in a semi-analytical solution of this three-dimensional problem.   

Biot Theory-Based FEM Simulations of Continuous Ultrasound Propagation through Microscale Articular Cartilage

Low-intensity ultrasound has shown promise in promoting the healing and regeneration of articular cartilage degraded by osteoarthritis. In this study, a 2-D finite element method (FEM) model was developed for solving the Biot theory equations governing the propagation of continuous ultrasound through the cartilage. Specifically, we computed the ultrasound-induced dilatations and displacements in the microscale cartilage that is represented as consisting of four zones, namely the chondrocyte cell and its nucleus, the pericellular matrix (PCM) that forms a layer around the chondrocyte, and the extracellular matrix (ECM). The chondrocyte--PCM complex, referred to as the chondron, is embedded in the ECM. We model multiple cartilage configurations wherein the ECM layer contains chondrons along the depth, as well as laterally. The top surface of the ECM layer is subjected to specified amplitude and frequency of continuous ultrasound. The resulting wave propagation is modeled by numerically solving the 2-D Biot equations for seven frequencies in the 0.5 MHz to 5 MHz range. It is seen that ultrasound is attenuated in the ECM and the attenuation increases monotonically with frequency. In contrast, manyfold augmentation of the ultrasound amplitude is observed inside the cytoplasm and the nucleus of the chondrocyte. Chondrocytes act as a major sink of ultrasound energy, thereby reducing the depthwise propagation of ultrasound fluctuations. Regions of high dilatations and displacements were found at the ECM--PCM interface, PCM--chondrocyte interace, as well as in the cytoplasm and nucleus of the chondrocyte. We observe that the ultrasound field around a chondron interacts with that around a neighboring chondron located at the same depth in the ECM layer. The qualitative and quantitative insights gained from our study may be relevant to designing ultrasound-based therapies for osteoarthritis.   

High-Fidelity Simulation of Collapsible Vessels Using a Novel Immersed Boundary Method

The dynamic interactions between the blood flow and collapsible vessels give rise to intricate, non-linear, and fluctuating behaviors, including self-excited oscillations and internal flow instabilities. In this study, high-fidelity simulations using a novel sharp-interface immersed boundary method are employed to study such complex dynamic interactions. Both steady and pulsatile flow conditions are predicted by controlling the internal pressure gradient and transmural pressure. The study finds strong agreement between simulations and experimental data, suggesting vessel deformation follows Shapiro's tube law under steady conditions. Additionally, pulsatile cases show self-oscillation within a critical transmural pressure range. These findings shed light on the mechanisms behind self-excited oscillations and provide valuable insights into the behavior of physiological systems with collapsible vessels subject to pulsatile flow.   

Hydrodynamics of passive environmental DNA (eDNA) detection

Passive detection of environmental DNA (eDNA) in aquatic environments is a promising, low-cost alternative biomonitoring tool for studies of species abundance and distribution in the ocean. The effectiveness of passive detection depends on the interplay between the fluid transport (advection and diffusion), the state (particulate vs. dissolved) and fate (shedding, decay, and settling rates) of the eDNA molecules, and the sampling protocol (filter type, position, submergence times, etc.). A simplified numerical model of the passive detection process was developed to simulate the time-dependent eDNA concentration at the surface of porous membrane filters of varying geometry, orientation, and translational speed in the water. The predictions of the numerical model were tested in controlled laboratory experiments using known concentrations of eDNA collected from 2 different invertebrates and 1 vertebrate. In addition to studying purely diffusive detection of eDNA by stationary samplers, the effect of flow advection was studied with a combination of translating samplers in quiescent flow and stationary samplers exposed to uniform flow. Understanding the mechanisms that control the transport and retention of eDNA on passive samplers will be critical for designing future sampling protocols and subsequently relating detected eDNA to species presence in space and time.  

Characteristics of catheter injection for predictive particle transport modeling in Y-90 transarterial radioembolization procedures

Hepatic cellular carcinoma is one of the most common forms of liver cancer. Depending on the cancer's progression, treatment can include a combination of external radiation therapy, chemotherapy, or surgery. Radioembolization using microspheres loaded with a radioactive isotope such as yttrium-90 (Y-90) has shown promise increasing patient outcomes but requires personalized and complex planning due to sensitivity of liver tissue to radiation and the need to reach a certain threshold of radiation dose in the tumors. Our modeling framework, CFDose, incorporates clinical patient cone-beam Computed Tomography images to predict microsphere transport in the patient liver vasculature using computational fluid dynamics (CFD). For this work, we consider a finite-thickness catheter wall at injection points that are at least one generation downstream of either the left or right hepatic arteries (considered a super selective injection). These considerations are important when super selective injections are used since the catheter obstructs the vessel lumen significantly. We also consider the effects of the local injection curvature on the injection profile by considering increasing levels of tortuosity. The model geometry we employ is an idealized structure where the surface mesh is truncated following two bifurcations from the right hepatic arteries. Preliminary results indicate increased particle asymmetries downstream of a tortuous injection segment when compared to an idealized extrusion or considering only an idealized parabolic flow profile. The injection location geometries are motivated by a particular patient case where the microsphere injection occurred directly downstream of a curved vascular segment, requiring a second injection further downstream the hepatic arterial tree. In such cases, we recommend carefully considering the segment tortuosity on modeling Y-90 injection.   

Hemodynamics analysis for advancing risk assessment of coronary artery aneurysm caused by Kawasaki disease using patient-specific cardiovascular simulation

Kawasaki disease (KD) is a systemic vasculitis primarily affecting children, which can lead to coronary artery aneurysms (CAA). Large CAA can cause thrombosis, coronary artery stenosis, occlusion, and even sudden death. However, the current KD guidelines primarily focus on the size of the aneurysm, without considering hemodynamics associated with the thrombus formation. Previous small-scale pilot studies have shown evidence of associations between thrombus formation and hemodynamic metrics derived from computational fluid dynamics in KD patients with CAA. This study aimed to investigate the risk assessment capability of hemodynamic metrics using a large number of patient cohort. We conducted a retrospective analysis of 45 computed tomography scans from 30 patients diagnosed with KD and CAA with the thrombosis group comprising 9 patients. CAAs were divided into two groups based on the presence of thrombosis, and the hemodynamic factors were compared between the groups. The Wilcox Rank test revealed significant differences in hemodynamic parameters between the two groups of vessels with and without thrombus formation, specifically Residence time (RT) and Time-averaged wall shear stress. The Receiver-Operating-Characteristics analysis demonstrated the superior predictive performance of hemodynamic parameters over geometry-based metrics in identifying thrombus formation. 

    

Computational Fluid Dynamics-Based Stratification of Morbidity Risks in Hypoplastic Pulmonary Anatomy

Numerous attempts have been made to assess morbidity and mortality risks in conditions that create hypoplastic pulmonary arteries such as congenital diaphragmatic hernia (CDH) and congenital pulmonary airway malformation. Previous studies have utilized proxy measures, like the lung-to-head ratio and liver position, to assess pulmonary hypoplasia. However, these convenient but simplified metrics are inherently limited in providing a comprehensive description of lung vasculature and corresponding function [1]. Perinatal MRI-calculated lung volumes are sometimes used, but mainly for general predictions of postnatal survival and morbidity risks.

This study employs computational fluid dynamics (CFD) comprehensively characterize and stratify neonatal pulmonary vasculature. Neonate MRIs were reconstructed using 3D Slicer, and time of flight MRI data stacks were selectively filtered to isolate arterial structures. CFD was implemented using Star CCM+ to determine vascular wall resistance, utilizing approximated pressure gradients, velocities, and pulsatile flow rates as boundary conditions. Moreover, this model possesses significant prognostic utility as CFD-calculated pulmonary resistance enables the calculation of optimal blood viscosity as a function of hematocrit concentration, maximizing pulmonary flow and subsequent systemic oxygen delivery. By leveraging CFD, this study demonstrates a a more complete understanding of the intricate dynamics within the pulmonary system and provides improved risk assessment and treatment planning for neonates diagnosed with CDH.

 

Multiscale Computational Methods for Heat Transfer Simulation between Body Tissue and Blood Flow

Estimating heat transfer in the human body is challenging due to the complexity of its heterogeneous tissues and blood vessels at different scales. To address this challenge, many bioheat models have been developed but they often rely on simplistic approaches when modeling heat transfer between blood and tissues, limiting the realistic evaluation of heat flux between two and the interactions with blood flow. To overcome these limitations, we developed multiscale computational methods by considering the interactions between blood flow and nearby tissues. Blood flow and heat transfer are solved using one-dimensional (1D) flow and advection-diffusion equations. The advection-diffusion equation is modeled to have radial variations to estimate the heat flux occurring at the boundary between blood and nearby tissues. The computed temperature distribution is utilized as boundary conditions to a three-dimensional heat equation which is solved for the tissue. Heat flux at the boundary between blood and nearby tissues is updated and explicitly fed back to the 1D advection-diffusion equation. The interactions between blood and tissues with an explicit coupling will be demonstrated for idealized geometries and complex geometries with varying scales of blood vessels. The developed methods will be utilized to estimate the effects of thermal therapy on blood flow within body tissues using a commercial thermo-mechanical massage bed.   

The significance of non-Newtonian behavior in the Fontan circulation: a computational fluid dynamics study on pediatric patient-specific models

For univentricular heart patients, Fontan circulation presents a unique challenge due to its passive blood flow through the lungs, resulting in chronic non-pulsatile low-shear-rate pulmonary blood flow where non-Newtonian effects might be substantial. This study evaluates the influence of non-Newtonian behavior on fluid dynamics and energetic efficiency in pediatric patient-specific models with Fontan circulation. We employed Lattice Boltzmann Method-Immersed Boundary based computational fluid dynamics simulations on patient-specific Fontan pulmonary vascular geometries and compared Newtonian and non-Newtonian fluid models. The study involved twenty patients exhibiting a low cardiac output state. The flow and shear stress distribution are assessed with both local and total non-Newtonian importance factors evaluated. Several metrics of indexed flow energy loss are quantified. Results show significant differences in flow structure between Newtonian and non-Newtonian models. Specifically, the non-Newtonian simulations demonstrate significantly higher viscosity, corresponding to a high non-Newtonian importance factor and larger energy loss. These findings suggest that non-Newtonian behavior contributes to flow structure and energetic inefficiency in the low cardiac output state of Fontan circulation. Further investigation is needed to determine the extent of correlation between these and clinical outcomes.   

Investigating Self-Excited Oscillation in Pulsating Thin-Walled Elastic Vessels

Physiological fluid transport in thin-walled elastic vessels under pulsating conditions plays a crucial role in various processes like respiratory airflow, urinary, lymphatics, and blood flows. Self-excited oscillation can be triggered in such vessels under specific conditions of sufficiently negative transmural pressure and high Reynolds number, caused by vortex shedding and elastic wall inertia. However, the impact of pulsatile flow conditions on self-excited oscillation remains poorly understood. This study conducted experiments using a pulsatile flow loop to investigate self-excited wall oscillation under such conditions. By precisely controlling the transmural pressure with a pressure chamber and utilizing high-frequency pressure and flow sensors, along with high-speed cameras and PIV measurements, the complex fluid-structure interactions were examined. The results unveiled intricate periodic deformation patterns in the vessel wall as the pressure wave passed through it. Moreover, certain Reynolds and Womersley number conditions revealed a short period of self-excited oscillation, distinct from the pulsatile flow frequency. Notably, at a specific threshold, a transient and complete vessel collapse occurred, leading to abrupt flow closure and a sharp increase in pressure gradient. This study provides valuable insights into collapsible vessel-related diseases and serves as a benchmark for computational studies.