Currently we do not have active researchers in this area. Please contact the persons mentioned for further information.

*( R.P. Hämäläinen, A. Kettunen, M. Lindroos, J. Ylikarjula, V. Kaitala )*

The research carried out under this general title has two main areas of focus. One of them is the application of optimal control theory in the modelling of biomechanical systems, and the other is ecological wolley.

Physiological control systems have the ability to adapt to changing environmental conditions. There are many physiological processes the main task of which can be realized by a number of different ways. Often there are infinitely many feasible control alternatives. One approach to model and describe such processes is to use optimization criteria (such as the minimization of energy cost) to explain the adaptation process and choice of controls.

We have been working in the area for more than fifteen years. The first studies dealt with the control of breathing: Subsequently we applied the same approach to the control of the left ventricular function of the heart. The results obtained both in the control of breathing and in the analysis of cardiac ejection are well known and acknowledged.

Our optimization models for the control of the mechanics of breathing (P[HÄM84c, HÄM87, HÄM92e, HÄM93b], HÄM95b], R[HÄM95b]), for a review see R[HÄM87] are able to predict changes in the airflow pattern quite well when compared to average human data. Numerically the models are relatively difficult to solve and, so far, our large main frame code has been the only one available for the solution. We have also analyzed other mathematical methods for the description of breathing cycles (P[HÄM00c]).

An interface of the WBREPAT P[HÄM92e] software

Currently we continue the research on the development of interactive modelling softwares. The first product titled WBREPAT - **W**indows **bre**athing **pat**tern analyzer - runs in the Windows environment (P[HÄM92e]). It solves the optimal inspiratory airflow pattern and also has easy to use data visualization and parameter estimation features. The existence of such a software enables experimental physiologists to do testing of our models and to learn more about the respiratory systems. One of the most interesting possibilities is the diagnostic use of the models. This kind of softwares could be used to detect early changes in the control pattern of breathing.

*( R.P. Hämäläinen, J.J. Hämäläinen )*

Our comprehensive analysis of the validity of the minimum external work criterion for predicting the left ventricular ejection pattern (i.e. the root aortic pressure and flow curves during the contraction of the left ventricle of the heart) has been summarized in (R[HÄJ88b]). We compared different theoretical normalized ejection patterns and showed that for a constant mean ejection pressure the initial peak pattern, which is in qualitative accordance with experimental observations, is indeed optimal with respect to external work.

External work constitutes only part of the total energy consumption of the ventricle. A new model has been developed which is based on minimizing the total energy cost of ejection (R[HÄJ88b]). Stroke volume was fixed in the above studies. An optimization model for the prediction of stroke volume is presented in (P[HÄJ89]). The model predicts the effects of changes in the end-diastolic volume and arterial input impedance on stroke volume. The model for optimal stroke volume has been combined with the previous model for the optimal ejection pattern. The new three-leveloptimization model (R[HÄJ88a]) predicts the effects of changes in ventricular load on stroke volume, ejection time, and ejection pattern. Model predictions have been shown to quite accurately match experimental data from an isolated heart preparation.

*( M. Lindroos, J. Ylikarjula, V. Kaitala )*

The research work on theoretical and mathematical ecology develops and analyses dynamical models of population and animal behavior. The area of applications ranges from studies on behavior and life history of individual animals to population dynamics. The work attempts to combine genetic dynamics with dynamic ESS models of animal behavior and to study population consequences of behavior (e.g. ESS models of dispersal and migration polymorphism, ESS sex allocation in parasitoids, optimal maturation and reproduction in age structured populations). Currently the following topics are studied: 1) Population dynamics and conservation biology P[GET89, KAI89b, KAI90a, RAN95, KAI96a, KAI96b, KAI96c, KAI96d, HEI97b, KAI97c, KAI97d, RAN97e]; 2) Genetic aspects of populations dynamics in heterogeneous environments P[GET89]; 3) The theory of evolutionary stable strategies (ESS) P[KAI89b, KAI89f, KAI90a, KAI90d, GET93, KAI93b, HEI97a, HEI97c, KAI97a, KAI97b]; 4) Evolution of biased sex ratios in parasitoids and consequences on the interaction between host and parasitoid populations, P[GET92, KAI92e].