A Mathematical Model of the Cardiac Chronotropic Response to Exercise

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Abstract
A mathematical model was developed from data collected from 410 normal subjects in order to describe the normal cardiac Chronotropic response to exercise. Subjects were examined by treadmill testing on either the Bruce protocol (189 patients) or the Chronotropic Assessment Exercise Protocol (CAEP) (221 patients), The CAEP, designed specifically for chronotropic assessment, is structured to collect heart rate data at submaximal as well as peak exercise intensities. Analysis of these subjects, without evidence of medical illness or cardiac medications, found the heart rate response to be a function of exercise intensity, age, resting heart rate, and maximal functional capacity. Heart rate reserve (HRR) was defined as the difference betii'een maximal predicted heart rate (MPHR) and resting heart (HRrest). Metabolic reserve was defined as the difference between the maximally achieved workload (METSpeak) and the workload at rest (METSrest). The Bruce and CAEP data provided a statistically linear and identical response of the form y = mx + b. The Bruce equation was %HRR = 0.95 ×%MR + 3.4 and the CAEP equation is %HRR = 0.94 ×%MR + 4.55. The following formula describes the normal predicted heart rate for an individual at some submaximal stage of exercise: HRstage= [(220 ‐ age ‐HRrest) × (METSstage ‐ 1)/(METSpeak ‐ 1)] + HRrest. We conclude that the cardiac chronotropic response can be modeled as a simple linear mathematical function of exercise intensity, age, resting heart rate, and maximal functional capacity, and is independent of type of treadmill exercise protocol in normal subjects.

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