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Cardiac Anatomy Circulatory System Physical Variables involved in Circulation • Flow (Q): Volume of blood per unit time passing a point in circulation (Liter/minute) • Pressure (P): The conventional unit for pressure in physiology is mmHg • Volume (V): Blood volume in each segment of the circulatory system. The conventional unit for pressure in physiology is liter Resistance and Compliance Vessels • Rigid Tube: R=8µL/πr V=constant; Q=(1/R)(P1-P2); 4 • Distensible Tube (no resistance to blood flow): P=constant; V=CP or V=CP+Vd Resistance and Compliance Vessels: Concerns • A real vessel must exhibit both resistance and compliance property simultaneously • We have assumed linear relationships that maybe too simple to describe real blood vessels Resistance and Compliance Vessels: Answers • The circulation has a clear separation between the resistance and compliance functions of its different vessels. The large arteries and veins are primary compliance vessels and the main site of resistance is in the tissues. • The approximation of linear relation between Q and ∆P is a good approximation when we allow for the changes in resistance Anatomy of Blood Vessels The Heart as a Pair of Pumps • Heart is a pair of pumps that can accept fluid at low pressure and transfer it to a region of high pressure • Each side of the heart, in normal condition, expels exactly the same volume of blood that enters into it • There is always a lag between the time blood enters the ventricle and expels Brief overview of mechanical events in cardiac cycle • Diastole (ventricular relaxation) – 60% of cardiac cycle • Isovolumic relaxation • Ventricular filling – Rapid inflow – Diastesis (Slow inflow) – Atrial systole • Systole (ventricular contraction) – 40% of cardiac cycle • Isovolumic contraction • Ventricular ejection Sagawa Model for Ventricle Considering ventricle as a compliance vessel whose compliance changes with time: V(t)=C(t)P(t)+Vd CHtL C(ts)=Min(C)=Cs C(td)=Max(C)=Cd 2 1.5 1 0.5 t 2 4 6 8 Model for the Pump VED=CdPv+Vd VES=CsPa+Vd Vstroke=VED-VES=CdPv-CsPa CO=VstrokexHR Q=FVstroke=(CdPv-CsPa)F Simplified Model Assumption: Cs≈0 Q=FCdPv Kr=FCrd; KL=FCLd ; K:Pump Coefficient Q=KPv Qr=KrPsv; QL=KLPpv ;Qr=QL Kr>KL ; Psv <Ppv Mathematical Model of the Uncontrolled Circulation • Equations for right and left heart: (2) Qr=KrPsv; QL=KLPpv • Equations for systemic and pulmonary arteries and veins: (4) Vsa=CsaPsa; Vsv=CsvPsv Vpa=CpaPpa; Vpv=CpvPpv • Equations for systemic and pulmonary tissues: (2) Qs=(1/Rs)(Psa-Psv); Qp=(1/Rp)(Ppa-Ppv) Known and Unknown • Known parameters: (8) Kr, KL, Rs, Rp, Csa, Csv, Cpa, Cpv • Unknowns: (12) Qr, QL, Qs, Qp, Psa, Psv, Ppa, Ppv, Vsa, Vsv, Vpa, Vpv • Equations: (8) Additional Equations • Vsa+Vsv+Vpa+Vpv=V0 • Qr=QL=Qs=Qp=Q • Unknows: (9) Q, Psa, Psv, Ppa, Ppv, Vsa, Vsv, Vpa, Vpv • Equations: (9) Model’s Solution • Combination of parameters: Tsv=Csv/Kr; Tpv=Cpv/KL; Tsa=(Csa/Kr)+CsaRs; Tpa=(Cpa/KL)+CpaRp • Solution: Q=V0/(Tsv+Tpv+ Tsa+ Tpa) Vi=TiV0/(Tsv+Tpv+ Tsa+ Tpa) Pi=(1/ci)(TiV0)/(Tsv+Tpv+ Tsa+ Tpa) i=sv,sa,pv,pa Normal Resting Parameters of the Model Circulation Systemic R (Resistance) C (Compliance) Rs=17.5 mmHg/(liter/min) Csa=0.01liters/mmHg Csv=1.75 K (Pump Coefficient) V (Volume) Pulmonary liters/mmHg Rp=1.79 mmHg/(liter/min) Cpa=0.0067liters/mmHg Cpv=0.08liters/mmHg Right Left Kr=2.8(liter/min)/mmHg KL=1.12(liter/min)/mmHg V0=5.0 Liters Example of Control Mechanism Kr Qr<QL Vp<Vs New Equilibrium with new parameters Qr=QL Ppv Psv