# Arterial Blood Pressure During Diastole (Draft)

Abstract

Three models of arterial pressure during diastole; a single exponential with zero asymptote, a single exponential with a non-zero asymptote, and a double exponential with a zero asymptote; are fitted to measurements of pressure in the ascending aorta. The results indicate that the single exponential with zero asymptote fits the data relatively poorly. Both the single exponent with a non-zero asymptote and the double exponent fit the measured pressure during diastole remarkably well. These two models, however, diverge significantly at longer times commensurate with extended diastole due to missing or ectopic beats. We conclude that the best choice of model can only be ascertained by looking at the arterial pressure during abnormal extended diastoles.

## Introduction

Arterial pressure waveforms are routinely measured clinically and they contain a significant amount of information about the cardiovascular system. Of prime importance, clinically, are the systolic pressure $$P_{s}$$ (the maximum measured pressure), the diastolic pressure $$P_{d}$$, (the minimum pressure) and the pulse pressure, defined as the difference between these two values $$P_{s}-P_{d}$$. Secondly, the complex structure known as the dicrotic notch is identified and associated with the closure of the aortic valve, giving the approximate times of systole and diastole based on the pressure waveform. Thirdly, various features of the blood pressure waveform during systole have been identified and associated with various cardiovascular phenomena. Finally, the decrease in pressure during diastole is generally described as a falling exponential and its time constant $$\tau$$ is commonly measured to characterise the diastolic behaviour of the arterial system.

We believe that a fuller understanding of the mechanics of the cardiovascular system, particularly the pressure waveform, would be beneficial. The clinical use of the various waveform parameters is historically long and rich. One of the most prevalent cardiovascular diseases, hypertension, is defined and diagnosed almost exclusively from measurements of the systolic and diastolic pressure. Other features of the arterial blood pressure waveform depend upon models of the circulation whose bases are more or less established. Some features of the arterial pressure waveform, particularly the dicrotic notch, are very poorly understood mechanically and could provide a fruitful area of future research. The arterial pressure waveform during systole is particularly difficult to analyse, experiementally or theoretically, because it is affected by the complex interactions between the heart and the arteries which communicate through the open aortic valve. During diastole the aortic valve is closed and the arterial pressure should be easier to analyse because the left ventricle and the arterial system are uncoupled, although the history of previous cardiac output must be considered. It is this pressure that we consider in this work.