Title: Cardiac-fitness biomathematical model of HR response to VO2 during and after exercise stress-testing

Authors: G.H. Lim, D.N. Ghista, T.Y. Koo, J.C.C. Tan, P.C.T. Eng, C.M. Loo

Addresses: School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, 639798, Singapore. ' School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, 639798, Singapore. ' School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, 639798, Singapore. ' Physical Education and Sports Science, National Institute of Education, Nanyang Walk, 637616, Singapore ' Department of Respiratory and Critical Care Medicine, Singapore General Hospital, Outram Road, 169608, Singapore. ' Department of Respiratory and Critical Care Medicine, Singapore General Hospital, Outram Road, 169608, Singapore

Abstract: This study aims to improve on the single reading method that is normally used to detect heart condition in stress (or exercise)-testing on a treadmill or bicycle. The main objectives are to formulate a time-based heart performance model and to develop a non-dimensional parameter to assess a person|s stress and heart condition. Based on the stress testing results on a treadmill, biomathematical (or biomedical engineering) modelling for heart-rate versus oxygen-consumption was formulated, by the use of first-order differential equations (deq). The forcing function was represented by the oxygen consumption during the test. The final expressions representing heart-rate (HR) response for the entire test contain the deq-model parameters, which characterise the HR rate-of-change during and after the stress-testing. The application and validation of the HR-response models to differentially diagnose fit versus deconditioned subjects as well as normal versus patients with impaired heart function was achieved, by employing exercise data collected from 45 heterogeneous subjects with various varying fitness heart conditions. Using the cardiac stress-testing results of normal (student) subjects and patients from a local hospital, it is shown that a person|s HR increases exponentially due to exercise, and decreases exponentially back to its initial state after some time. However, the HR rate-of-increase and the HR rate-of-decrease varied from subject to subject, and particularly between fit and ill-conditioned group of subjects as well as between acutely myocardial-ischemic and rehabilitated patients. The model of HR response to oxygen consumption (or VO2) is novel in that it was able to exhibit clear demarcations between healthy and ill-conditioned subjects, in terms of the range of values of a new non-dimensional cardiac fitness index (CFI), formulated in terms of the model parameters. It is found that people with relatively poor heart condition would have relatively higher values of the CFI. Thus, the CFI can be employed as a reliable measure of the state of fitness and heart condition of a person.

Keywords: time-based; heart performance model; cardiac fitness index; differential equation; demarcation; stress testing; heart condition; biomedical engineering; biomathematical modelling; heart rate; exercise.

DOI: 10.1504/IJCAT.2004.005337

International Journal of Computer Applications in Technology, 2004 Vol.21 No.1/2, pp.38 - 45

Available online: 25 Sep 2004 *

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