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