Abstract
The techniques of optimal control are applied to a validated blood circulation model of cardiopulmonary resuscitation (CPR), consisting of a system of seven difference equations. In this system, the nonhomogeneous forcing term is the externally applied chest pressure acting as the "control". We seek to maximize the blood flow, as measured by the pressure differences between the thoracic aorta and the superior vena cava. The new aspect in this application is that the control values from the two previous time steps are used to calculate the pressures (state variables) at the current time step. We prove the existence and uniqueness of the optimal control and provide a new CPR strategy, with increased blood flow. The characterization of the optimal control is given in terms of the solutions of the circulation model and of the corresponding adjoint system. The numerical results show a significant increase in the blood flow as compared with standard CPR.
| Original language | English |
|---|---|
| Pages (from-to) | 1519-1531 |
| Number of pages | 13 |
| Journal | Mathematical Models and Methods in Applied Sciences |
| Volume | 15 |
| Issue number | 10 |
| DOIs | |
| State | Published - Oct 2005 |
Funding
This work was partially supported by an ORNL seed money grant. We also acknowledge partial support of Lenhart and Protopopescu by the Division of Material Sciences of the U.S. Department of Energy, under contract No. DE-AC05-00OR22725 with UT-Battelle, LLC. The work of Jung was partially supported by grant No. R08-2003-000-11093-0 from the Basic Research Program of the Korea Science and Engineering Foundation.
Keywords
- Cardiopulmonary resuscitation
- Cardiopump
- Difference equation
- Mechanical CPR
- Optimal control