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In end-stage kidney disease, kidneys no longer sufficiently perform their intended functions, for example, filtering blood of excess fluid and waste products. Without transplantation or chronic dialysis, this condition results in mortality. Dialysis is the process of artificially replacing some of the kidney’s functionality by passing blood from a patient through an external semi-permeable membrane to remove toxins and excess fluid. The rate of ultrafiltration – the rate of fluid removal from blood – is controlled by the hemodialysis machine per prescription by a nephrologist. While essential for survival, hemodialysis is fraught with clinical challenges. Too high a fluid removal rate could result in hypotensive events where the patient blood pressure drops significantly which is associated with adverse symptoms such as exhaustion, fainting, nausea, and cramps, leading to decreased patient quality of life. Too low a fluid removal rate, in contrast, could leave the patient fluid overloaded often leading to hypertension, which is associated with adverse clinical outcomes. Previous work in our lab demonstrated via simulations that it is possible to design an individualized, model-based ultrafiltration profile with the aim of minimizing hypotensive events during dialysis. The underlying model using in the design of the individualized ultrafiltration profile is a simplified, linearized, continuous-time model derived from a nonlinear model of the patient’s fluid dynamics system. The parameters of the linearized model are estimated from actual patient’s temporal hematocrit response to ultrafiltration. However, the parameter identification approach used in the above work was validated using limited clinical data and often failed to achieve accurate estimation. Against this backdrop, this thesis had three goals: (1) obtain a new, larger set of clinical data, (2) improve the linearized model to account for missing physiological aspects of fluid dynamics, and (3) develop and validate a new approach for identification of model parameters for use in the design of individualized ultrafiltration profiles. The first goal was accomplished by retrofitting an entire in-center, hemodialysis clinic in Holyoke, MA, with online hematocrit sensors (CliC devices), Wi-Fi boards, and a laptop with a radio receiver. Treatment data was wirelessly uploaded to a laptop and redacted files and manual treatment charts were made available for our research per approved study IRB. The second goal was accomplished by examining the nonlinear system of equations governing the relevant dynamics and simplifying the model to an identifiable case. Considerations of refill not accounted for fully in previous works were integrated into the Cardimino 7 linearized model, adding terms but making it generally more accurate to the underlying dynamics. The third goal was accomplished by developing an algorithm to identify major system parameters, using steady-state behavior to effectively reduce the number of parameters to identify. The system was subsequently simulated over an established range for all remaining parameters, compared to collected data, with the lowest RMS error case being taken as the set of identified parameters. While intra-patient identified individual model parameters were associated with a high degree of variability, the system’s steady-state gain and time constants exhibited more consistent estimations, though the time constants still had high variability overall. Parameter sensitivity analysis shows high sensitivity to small changes in individual model parameters. The addition of refill dynamics in the model constituted a significant improvement in the identifiability of the measured dynamics, with up to 70% of data sets resulting in successful estimates. Unmodelled dynamics, resulting from unmeasured input variables, resulted in about 30% of measured data sets unidentifiable. The updated model and associated parameter identification developed in this thesis can be readily integrated with the model-based design of individualized UFR profile.

Controlling infectious disease spread and preventing disease onset are ongoing challenges, especially in the presence of newly emerging diseases. While vaccines have successfully eradicated smallpox and reduced occurrence of many diseases, there still exists challenges such as fear of vaccination, the cost and difficulty of transporting vaccines, and the ability of attenuated viruses to evolve, leading to instances such as vaccine derived poliovirus. Antibiotic resistance due to mistreatment of antibiotics and quickly evolving bacteria contributes to the difficulty of eradicating diseases such as tuberculosis. Additionally, bacteria and fungi are able to produce an extracellular matrix in biofilms that protects them from antibiotics/antifungals. Mathematical models are an effective way of measuring the success of various control measures, allowing for cost savings and efficient implementation of those measures. While many models exist to investigate the dynamics on a human population scale, it is also beneficial to use models on a microbial scale to further capture the biology behind infectious diseases. In this dissertation, we develop mathematical models at several spatial scales to help improve disease control. At the scale of human populations, we develop differential equation models with quarantine control. We investigate how the distribution of exposed and infectious periods affects the control efficacy and suggest when it is important for models to include realistically narrow distributions. At the microbial scale, we use an agent-based stochastic spatial simulation to model the social interactions between two yeast strains in a biofilm. While cheater strains have been proposed as a control strategy to disrupt the harmful cooperative biofilm, some yeast strains cooperate only with other cooperators via kin recognition. We study under what circumstances kin recognition confers the greatest fitness benefit to a cooperative strain. Finally, we look at a multiscale, two-patch model for the dynamics between wild-type (WT) poliovirus and defective interfering particles (DIPs) as they travel between organs. DIPs are non-viable variants of the WT that lack essential elements needed for reproduction, causing them to steal these elements from the WT. We investigate when DIPs can lower the WT population in the host.

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