A Digital-Twin and Machine-Learning Framework for Ventilation System Optimization for Capturing Infectious Disease Respiratory Emissions.

The pandemic of 2019 has led to an enormous interest in all aspects of modeling and simulation of infectious diseases. One central issue is the redesign and deployment of ventilation systems to mitigate the transmission of infectious diseases, produced by respiratory emissions such as coughs. This work seeks to develop a combined Digital-Twin and Machine-Learning framework to optimize ventilation systems by building on rapidly computable respiratory emission models developed in Zohdi (Comput Mech 64:1025-1034, 2020). This framework ascertains the placement and flow rates of multiple ventilation units, in order to optimally sequester particles released from respiratory emissions such as coughs, sneezes, etc. Numerical examples are provided to illustrate the framework.

Rapid simulation of viral decontamination efficacy with UV irradiation.

This paper focuses on viral decontamination by ultraviolet (UV) irradiation technologies. This work develops an efficient and rapid computational method to simulate a UV pulse in order to ascertain the decontamination efficacy of UV irradiation for a surface. It is based on decomposition of a pulse into a group of rays, which are then tracked as they progress towards the target contact surface. The algorithm computes the absorption at the point of contact and color codes it relative to the incoming irradiation. This allows one to quickly quantify the decontamination efficacy across the topology of a structure.

Modeling and simulation of the infection zone from a cough.

The pandemic of 2020 has led to a huge interest of modeling and simulation of infectious diseases. One of the central questions is the potential infection zone produced by a cough. In this paper, mathematical models are developed to simulate the progressive time-evolution of the distribution of locations of particles produced by a cough. Analytical and numerical studies are undertaken. The models ascertain the range, distribution and settling time of the particles under the influence of gravity and drag from the surrounding air. Beyond qualitative trends that illustrate that large particles travel far and settle quickly, while small particles do not travel far and settle slowly, the models provide quantitative results for distances travelled and settling times, which are needed for constructing social distancing policies and workplace protocols.

An agent-based computational framework for simulation of global pandemic and social response on planet X.

The increase in readily available computational power raises the possibility that direct agent-based modeling can play a key role in the analysis of epidemiological population dynamics. Specifically, the objective of this work is to develop a robust agent-based computational framework to investigate the emergent structure of Susceptible-Infected-Removed/Recovered (SIR)-type populations and variants thereof, on a global planetary scale. To accomplish this objective, we develop a planet-wide model based on interaction between discrete entities (agents), where each agent on the surface of the planet is initially uninfected. Infections are then seeded on the planet in localized regions. Contracting an infection depends on the characteristics of each agent-i.e. their susceptibility and contact with the seeded, infected agents. Agent mobility on the planet is dictated by social policies, for example such as "shelter in place", "complete lockdown", etc. The global population is then allowed to evolve according to infected states of agents, over many time periods, leading to an SIR population. The work illustrates the construction of the computational framework and the relatively straightforward application with direct, non-phenomenological, input data. Numerical examples are provided to illustrate the model construction and the results of such an approach.

Estimates for the acoustical stimulation and heating of multiphase biotissue.

Low-intensity, unfocused, ultrasound-induced diathermy can produce undesired temperature increases at the interface of adjacent tissues within the body; particularly, at the interface of soft tissue and bone. This study provides a computational framework for predicting an upper bound on the temperature profile within a multiphase system composed of gel pad (water), tissue and bone from an input of acoustic energy, at frequencies and power levels consistent with applications of therapeutic hyperthermia. The model consists of solving a (one-dimensional) spatially discretized bioheat transfer equation via finite-difference method and updating the solution in time with a forward-Euler scheme. Simulations are then compared to experimental data to determine the energy-to-heat conversion factors within each constituent material using thermocouple-embedded, tissue-mimicking phantom material, with and without bone. Viscous heating artifacts from the presence of the thermocouples in the experimental phantom tissue are accounted for via additional experimental methods similar to those described by Morris et al. (Phys Med Biol 53:4759, 2008). Finally, an example application of the model is presented via prediction of the maximum temperature at the tissue-bone interface, as well as the peak temperatures in the composite structure at the end of a prescribed 2-min sonication, of blood-perfused, human soft-tissue at 1, 2 and 3 MHz frequencies and a spatial peak temporally averaged intensity of [Formula: see text]. The results of this simulation are then related to comparable experimental studies in the literature.

On the biomechanical analysis of the calories expended in a straight boxing jab.

Boxing and related sports activities have become a standard workout regime at many fitness studios worldwide. Oftentimes, people are interested in the calories expended during these workouts. This note focuses on determining the calories in a boxer's jab, using kinematic vector-loop relations and basic work-energy principles. Numerical simulations are undertaken to illustrate the basic model. Multi-limb extensions of the model are also discussed.

On firework blasts and qualitative parameter dependency.

In this paper, a mathematical model is developed to qualitatively simulate the progressive time-evolution of a blast from a simple firework. Estimates are made for the blast radius that one can expect for a given amount of detonation energy and pyrotechnic display material. The model balances the released energy from the initial blast pulse with the subsequent kinetic energy and then computes the trajectory of the material under the influence of the drag from the surrounding air, gravity and possible buoyancy. Under certain simplifying assumptions, the model can be solved for analytically. The solution serves as a guide to identifying key parameters that control the evolving blast envelope. Three-dimensional examples are given.

Modeling and Simulation of Coupled Cell Proliferation and Regulation in Heterogeneous Tissue.

The primary objective of this work is to develop a computational framework that efficiently simulates the time-transient proliferation of cellular tissue, with heterogeneous microstructure, utilizing two strongly-coupled conservation laws: Conservation Law 1: comprises (a) rate of change of cells, (b) cellular migration, (c) cellular proliferation controlled by a cell mitosis regulating chemical, (d) cell apoptosis and Conservation Law 2: comprises (a) rate of change of the cell mitosis chemical regulator, (b) regulator diffusion, (c) regulator production by cells and (d) regulator decay. Specifically, a straightforward approach is developed that researchers in the field can easily implement and use as a computationally-efficient tool to study such biological systems. Because multifield coupling is present, a recursive, staggered, temporally-adaptive, Finite Difference Time Domain scheme is developed to resolve the interacting fields. The time-step adaptation allows the numerical scheme to iteratively resolve the changing physical fields by reducing the time-steps during phases of the process when the system is undergoing changes on relatively small time-scales or enlarging the time-steps when the processes are relatively slow. The spatial discretization grids are uniform and dense, and the heterogeneous microstructure, is embedded into the spatial discretization. The regular grid allows one to generate a matrix-free iterative formulation which is amenable to rapid computation and minimal memory requirements, making it ideal for laptop computation. Numerical examples are provided to illustrate the approach.

Modeling electrical power absorption and thermally-induced biological tissue damage.

This work develops a model for thermally induced damage from high current flow through biological tissue. Using the first law of thermodynamics, the balance of energy produced by the current and the energy absorbed by the tissue are investigated. The tissue damage is correlated with an evolution law that is activated upon exceeding a temperature threshold. As an example, the Fung material model is used. For certain parameter choices, the Fung material law has the ability to absorb relatively significant amounts of energy, due to its inherent exponential response character, thus, to some extent, mitigating possible tissue damage. Numerical examples are provided to illustrate the model's behavior.

Mechanically driven accumulation of microscale material at coupled solid-fluid interfaces in biological channels.

The accumulation of microscale materials at solid-fluid interfaces in biological channels is often the initial stage of certain growth processes, which are present in some forms of atherosclerosis. The objective of this work is to develop a relatively simple model for such accumulation, which researchers can use to qualitatively guide their analyses. Specifically, the approach is to construct rate equations for the accumulation at the solid-fluid interface as a function of the intensity of the shear stress. The accumulation of material subsequently reduces the cross-sectional area of the channel until the fluid-induced shear stress at the solid-fluid interface reaches a critical value, which terminates the accumulation rate. Characteristics of the model are explored analytically and numerically.

Modelling and rapid simulation of multiple red blood cell light scattering.

The goal of this work is to develop a computational framework to rapidly simulate the light scattering response of multiple red blood cells. Because the wavelength of visible light (3.8 x 10(-7) m < or = lambda < or = 7.2 x 10(-7) m) is approximately an order of magnitude smaller than the diameter of a typical red blood cell scatterer (d approximately 8 x 10(-6) m), geometric ray-tracing theory is applicable, and can be used to quickly ascertain the amount of optical energy, characterized by the Poynting vector, that is reflected and absorbed by multiple red blood cells. The overall objective is to provide a straightforward approach that can be easily implemented by researchers in the field, using standard desktop computers. Three-dimensional examples are given to illustrate the approach and the results compare quite closely to experiments on blood samples conducted at the Children's Hospital Oakland Research Institute (CHORI).

Fatigue of kidney stones with heterogeneous microstructure subjected to shock-wave lithotripsy.

In this article a theoretical framework is developed for the mechanics of kidney stones with an isotropic, random microstructure--such as those comprised of cystine or struvite. The approach is based on a micromechanical description of kidney stones comprised of crystals in a binding matrix. Stress concentration functions are developed to determine load sharing of the particle phase and the binding matrix phase. Measurements have shown the inclusions to be considerably harder than the binder; consequently, loading of a stone leads to higher stresses in the inclusions than in the binder. As an illustration of the theory, the fatigue of kidney stones subject to shock-wave lithotripsy is considered. Stress concentration functions are used to construct fatigue-life estimates for each phase, as a function of the volume fraction and of the mechanical properties of the constituents, as well as the loading from SWL. The failure of the binding matrix, or of the particulate phase, is determined explicitly in a model for the accumulation of distributed damage. The theory can be used to assess the importance of microscale heterogeneity on the comminution of renal calculi, and to estimate the number of cycles to failure in terms of measurable material properties.

A simple model for shear stress mediated lumen reduction in blood vessels.

The goal of this paper is to qualitatively describe the dominant flow characteristics associated with shear stress mediated lumen reduction due to atherosclerotic plaque growth. The approach is to develop rate equations for the reduction of the lumen as a function of the shear stress near the intima wall. Elementary, qualitative, models for fully developed laminar and turbulent flows are employed, leading to nonlinear ordinary differential equations. The model provides a qualitative description of one aspect of the long-term reduction, perhaps taking years, of the lumen due to wall growth. This is useful because of the extreme complexity of long-term experiments.

A phenomenological model for atherosclerotic plaque growth and rupture.

The objective of this communication is to develop a computer-based framework for the overall coupled phenomena leading to growth and rupture of atherosclerotic plaques. The modeling is purposely simplified to expose the dominant phenomenological controlling mechanisms, and their coupled interaction. The main ingredients of the present simplified modeling approach, describing the events that occur due to the presence and oxidation of excess low-density lipoprotein (LDL) in the intima, are: (i) adhesion of monocytes to the endothelial surface, which is controlled by the intensity of the blood flow and the adhesion molecules stimulated by the excess LDL, (ii) penetration of the monocytes into the intima and subsequent inflammation of the tissue, and (iii) rupture of the plaque accompanied with some degree of thrombus formation or even subsequent occlusive thrombosis. The set of resulting coupled equations, each modeling entirely different physical events, is solved using an iterative staggering scheme, which allows the equations to be solved in a computationally convenient decoupled fashion. Theoretical convergence properties of the scheme are given as a function of physical parameters involved. A numerical example is given to illustrate the modeling approach and an a priori prediction for time to rupture as a function of arterial geometry, diameter of the monocyte, adhesion stress, bulk modulus of the ruptured wall material, blood viscosity, flow rate and mass density of the monocytes.

Genetic design of solids possessing a random-particulate microstructure.

There exists a variety of difficulties in the computational design of macroscopic solid material properties formed by doping a homogeneous base matrix material with randomly distributed particles having different properties. Three primary problems are (1) the wide array of free microdesign variables, such as particle topology, property phase contrasts and volume fraction, which render the associated objective functions to be highly non-convex; (2) that the associated objective functions are not differentiable with respect to design variables, primarily due to prescribed constraints, such as prespecified restrictions on the microscale stress-field behaviour; and (3) the effective responses of various finite-sized samples, of equal volume but of different random particle distributions, exhibit mutual fluctuations, leading to amplified noise in optimization strategies where objective function sensitivities or comparisons are needed. The focus of this paper is the development of a statistical genetic algorithm which can handle difficulties due to non-convexity, lack of regularity and size effects. Theoretical properties of the overall approach are investigated. Semi-analytical and large-scale numerical examples, involving finite-element type discretizations, are given to illustrate its practical application.