In a resting adult the mean arterial pressure is and the cardiac output is

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Bioelectricity, the senses and the physics of the body · Bioelectricity, the senses and the physics of the body

Forces, Machines and Signals, Ch Bones, blood and body size

Problem

In a resting adult the mean arterial pressure is 100 mmHg100\,\mathrm{mmHg} and the cardiac output is 4.5 L min−14.5\,\mathrm{L\,min^{-1}}. Model the arterial tree as a windkessel: a compliance CaC_{\rm a} in parallel with a peripheral resistance RpR_{\rm p}, discharging exponentially during diastole according to p(t)=p0 e−t/RpCap(t) = p_0\,e^{-t/R_{\rm p}C_{\rm a}}, where p0p_0 is the pressure at the start of diastole. A pressure trace shows the pressure falling from p0=120 mmHgp_0 = 120\,\mathrm{mmHg} at aortic valve closure (t=0t=0) to 80 mmHg80\,\mathrm{mmHg} at the end of a diastole lasting 0.50 s0.50\,\mathrm{s}. Use 1 mmHg=133.3 Pa1\,\mathrm{mmHg} = 133.3\,\mathrm{Pa}. ((a)) Find the peripheral resistance RpR_{\rm p} in Pa s m−3\mathrm{Pa\,s\,m^{-3}}. ((b)) Find the windkessel time constant τ=RpCa\tau = R_{\rm p}C_{\rm a} from the pressure trace, in seconds. ((c)) Infer the arterial compliance CaC_{\rm a}, in mL mmHg−1\mathrm{mL\,mmHg^{-1}}.

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