# Evolution of Hemodynamic Parameters Simulated by Means of Diffusion Models
###### Abstract  
Diffusion is a well-known physical phenomenon governing such processes as movement of particles or transportation of heat. In this paper, we prove that a close analogy to those processes exists in medical data behavior, and that changes in the values of medical parameters measured while treating patients may be described using diffusion models as well. The medical condition of a patient is usually described by a set of discrete values. The evolution of that condition and, consequently, of the disease has the form of a transition of that set of discrete values, which correspond to specific parameters. This is a typical medical diagnosis scheme. However, disease evolution is a phenomenon that is characterized by continuously varying, temporal characteristics. A mathematical disease evolution model is, in fact, a continuous diffusion process from one discrete slot of the diagnosed parameter value to another inside the mentioned set. The ability to predict such diffusion-related properties offer precious support in diagnostic decision-making. We have examined several hundred patients while conducting a medical research project. All patients were under treatment to stabilize their hemodynamic parameters. A diffusion model relied upon simulating the results of treatment is proposed here. Time evolution of thoracic fluid content (TFC) has been used as the illustrative example. The objective is to prove that diffusion models are a proper and convenient solution for predicting disease evolution processes. We applied the Fokker-Planck equation (FPE), considering it to be most adequate for examining the treatment results by means of diffusion. We confirmed that the phenomenon of diffusion explains the evolution of the heart disease parameters observed. The evolution of TFC has been chosen as an example of a hemodynamic parameter.  
Fokker-Planck equation; diffusion; heart failure; impedance cardiography; thoracic fluid content +
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predictive approaches are present in the literature. The results presented in there are organized in accordance with risk analysis, and such an approach does not allow us to simulate disease evolution. The following question arises: are we able to simulate the evolution of hemodynamic parameters during medical treatment? In this paper, we propose a model explaining the rules of hemodynamic parameter evolution in patients with heart failure. Simulation of the disease evolution seems to be possible with the presented approach.  
The activities undertaken may be divided into experimental and theoretical phases. In the experimental phase of the project, a multicenter, prospective, randomized, open-label, and controlled, parallel group trial was conducted (ClinicalTrials.gov Identifier: NCT03476590). Here, 605 patients suffering from heart failure were recruited to participate in the project. In the theoretical phase, we propose to describe the behavior of the hemodynamic parameters measured by relying on diffusion models.  
In Section 2, experimental observations and analyses are presented. Section 3 presents theoretical models describing the diffusion phenomena. Section 3 contains the results of confrontation theoretical models with experimental data. Finally, Section 4 contains a summary and a discussion.  
The achieved aim is the creation of a continuous, differential model for disease evolution.