The cardiac physiome: foundations and future prospects for mathematical modelling of the heart

Physiological models in pharmacokinetics are instrumental in understanding the distribution and elimination of drugs within the body. These models describe the drug concentration within target organs, influenced by factors such as drug uptake, tissue volume, and blood flow. Drug uptake is governed by the partition coefficient, which signifies the drug concentration ratio in tissue to that in the blood. The blood flow rate to a specific tissue is expressed as Qt, and the rate of change in tissue...

Typical heart performance is influenced by heart rate, rhythm, myocardial contraction, and metabolism or blood flow. The cardiac muscle exhibits distinct electrophysiological features, including pacemaker activity and calcium channel control, which play a vital role in the heart's response to various drugs. The autonomic nervous system, comprising the sympathetic and parasympathetic branches, regulates heart rate. Sympathetic activation increases heart rate, while parasympathetic activation...

The cardiac cycle describes the events from one heartbeat to the next. It includes three main phases: diastole, atrial systole, and ventricular systole, all driven by changes in chamber pressures and the function of heart valves.
Diastole: The Relaxation Phase
During diastole, all four heart chambers relax. The atrioventricular (AV) valves open, and the semilunar valves close. This phase sees the lowest chamber pressures, promoting ventricular filling. Venous blood enters the heart through the...

Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...

Mechanistic models, a category encompassing both physiological and compartmental modeling, differ from empirical models' approaches to incorporating known factors about the systems being modeled. Empirical models describe data with minimal assumptions, while mechanistic models aim to provide a robust description of available data by specifying assumptions and integrating known factors about the system. Compartmental analysis is a key example of a mechanistic model in pharmacokinetics and...

Pharmacokinetic models utilize mathematical analysis to achieve a detailed quantitative understanding of a drug's life cycle within the body. They are instrumental in simulating a drug's pharmacokinetic parameters, predicting drug concentrations over time, optimizing dosage regimens, linking concentrations with pharmacologic activity, and estimating potential toxicity.
There are three primary types of models: empirical, compartment, and physiological. Empirical models, with minimal assumptions,...