## General

Airflow through bronchi during natural, spontaneous breathing may be characterized with the following statement: the airflow is proportional to the difference between the pressure in lungs and ambient pressure; it depends also on properties of the bronchi

. The same can be described with mathematics: the above, relatively long statement would have the following short form:

airflow = (lungs_pressure – ambient_pressure) / resistance

where ‘resistance’ means bronchi properties connecting the airflow with pressures.

Theoretically, each other statement related to respiratory system physiology may be expressed with some mathematical formula. A mathematical model of the respiratory system is a set of such formulas. However, the two following features differ the knowledge expressed with mathematical models from the knowledge expressed with words:

- mathematical formulas can be transformed automatically with mathematical rules which results in ‘new physiological laws’ (e.g. a new, not yet observed phenomenon may be predicted),
- the formulas can be described as a computer program (computer model) which makes the knowledge alive.

Constantly improving technology in computers has made possible to build computer models so complex that they may be treated as *virtual organs*. A virtual organ means that physiological or anatomical knowledge is expressed with mathematical formulas so precisely that it is not easy to decide whether a result relates to a virtual or real patient. Such precision means that a *virtual patient* has to be a set of formulas much more complex than simple mathematical expression of some fundamental physiological phenomenon. For example, the above simple formula describing dependence of the airflow on pressures and bronchi resistance is correct only for normal breathing. When the expiration is forced, the airflow does not depend on those pressures; it depends on the lungs volume. Thus, a complex formula is necessary to describe both the airflow dependence on the pressures for normal breathing and appearing of dependence on the lungs volume when the expiration starts to be more forced.

Application of *virtual patients* in medical education is of special meaning because:

- such a patient is easy to duplicate, and thus each student may have own patient,
- there are no ethical, financial or legal problems when a student makes a mistake, even if he/she ‘kills’ such patient,
- a student can choose a convenient place and time for learning.

The main features of the virtual respiratory system that is utilized in the Tgol.e-spirometry™ system are:

- Division of the lungs into lobes and separation of them and the chest wall which enables us to observe the intrathoracic pressure crushing intermediate bronchi during forced expirations;
- Division of the airway resistance into:
- resistances of the upper airways and main bronchi;
- the resistance of intermediate bronchi that depends on the transmural pressure, i.e. the resistance of the bronchi that may collapse;
- the resistance that depends on the lung volume, i.e. the resistance of the smallest bronchi that are a component of the lung tissue.

Many others properties such as: influence of gravity, air compressibility, viscosity of the chest wall and lungs tissue, air inertance, or mediastinum compliance are not ‘visible’ in the Tgol.e-spirometry™ system (mediastinum compliance will be ‘visible’ in the next version of the Tgol.e-spirometry™ Advanced because it influences spirometry in the case of lobe resection or scoliosis).