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Hemodynamic Theory

Field: Cardiology

Sequence of Expressions

Let P(V)P(V) be the pressure-volume curve, where PP is the ventricular pressure and VV is the ventricular volume. The mechanical work done by the ventricle per cycle, WcycleW_{cycle}, is defined by the area enclosed by the closed path C\mathcal{C} in the P-V plane: Wcycle=∮CP⋅dVW_{cycle} = \oint_{\mathcal{C}} P \cdot dV
For a systemic or pulmonary circuit modeled as an electrical circuit, the pressure gradient ΔP\Delta P driving the flow QQ is related to the total vascular resistance RR by the linear relationship: ΔP=Q⋅R\Delta P = Q \cdot R
The resistance RR to laminar flow of a Newtonian fluid with viscosity η\eta through a cylindrical tube of length LL and radius rr is given by: R=8ηLπr4R = \frac{8 \eta L}{\pi r^4}
The stroke volume SVSV is functionally dependent on the end-diastolic volume EDVEDV via a proportionality relationship, assuming constant afterload: SV∝EDVSV \propto EDV
Define the Cardiac Output (COCO) as the product of the Heart Rate (HRHR) and the Stroke Volume (SVSV): CO=HR⋅SVCO = HR \cdot SV
The Mean Arterial Pressure (MAPMAP) is calculated as the weighted average of the systolic (SBPSBP) and diastolic (DBPDBP) pressures over the cardiac cycle: MAP=DBP+13(SBP−DBP)MAP = DBP + \frac{1}{3}(SBP - DBP)
The Windkessel model describes the arterial pressure P(t)P(t) using a lumped-parameter circuit involving compliance CC and peripheral resistance RR: CdPdt+P(t)R=Qin(t)C \frac{dP}{dt} + \frac{P(t)}{R} = Q_{in}(t) where Qin(t)Q_{in}(t) is the flow rate into the arterial system.
The intrinsic contractility of the myocardium, represented by the force of contraction FcontractF_{contract}, increases with the degree of ventricular stretch λ\lambda (related to EDVEDV), such that the resulting stroke volume SVSV satisfies: SV=f(λ)SV = f(\lambda) where ff is a monotonically increasing function.
Let PLVEDPP_{LVEDP} be the Left Ventricular End-Diastolic Pressure and PAortaP_{Aorta} be the mean aortic pressure. Preload is defined by PLVEDPP_{LVEDP} and EDVEDV. Afterload is defined by the systemic vascular resistance RsysR_{sys} and the mean aortic pressure: Afterload≈Rsys⋅PAortaAfterload \approx R_{sys} \cdot P_{Aorta}
The Systemic Vascular Resistance (SVRSVR) is defined as the ratio of the mean arterial pressure (MAPMAP) minus the central venous pressure (CVPCVP), to the cardiac output (QQ): SVR=MAP−CVPQSVR = \frac{MAP - CVP}{Q}