Download Right Heart Pumping

Right Heart Pumping
This module calculates right ventricular cardiac output from right atrial pressure (preload) and from pulmonary
arterial pressure (afterload).
INPUTS:
PRA – right atrial pressure (at normal level of autonomic stimulation) [torr]
PPA - pulmonary arterial pressure [torr]
AUHA – atrial autonomic stimulation [ratio to normal]
AUH - autonomic stimulation of heart ventricles [ratio to normal]
OSA – arterial oxygen hemoglobin saturation [ratio to full saturation]
HSR - basic strength or right ventricle [ratio to normal]
HPR - hypertrophy effect of heart [ratio to normal]
HMD - cardiac depressant effect of hypoxia, shock and other factors [ratio to normal]
QLO - output of left ventricle [l/min]
QLN - normalized output of the left heart [l/min]
OUTPUTS:
QRO - actual right ventricular output [l/min]
PRA1 - effective right atrial pressure (at actual level of autonomic stimulation) [torr]
QRN - normalized right ventricular output [l/min]
RVM - depressing effect on right ventricle of pulmonary arterial pressure [ratio to normal]
Outputs that are not used as inputs to other modules are printed by italics.
Calculation of Starling law for right heart
Calculation of the effective right pressure (PRA1) considering of autonomic atrial stimulation from the right atrial
pressure (PRA) which was calculated for normal level of autonomic stimulation. Atrial autonomic stimulation
(AUHA) influences on atrial pressures - it determines the slope of changing of right atrial pressures due to autonomic
stimulation of atrial heart muscle strength.
PRA1 = (PRA + 8)*AUHA - 8
(RH 01)
Function curve of Starling law that gives the output from the right heart (QRN) for any given level of right atrial
pressure (PRA1) when all conditions of the right heart are normal is calculated using interpolation of the following
values:
PRA1
<-8
-8
-6
-2
4
12
>12
QRN
0
0
0.75
2.6
9.8
13.5
13.5
QRN = function StarlingRNorm(PRA)
(RH 02)
Function StarlingRNorm interpolates data from the hereinbefore table. Guyton use linear interpolation, however it
will be better to use cubic spline interpolation1.
Starling law for right heart
14
12
QRN [torr]
10
8
6
4
2
0
-10
-5
0
5
10
15
PRA1 [torr]
Fig. 1 Linear and cubic spline approximation of QRN as a function of PRA1
Calculation of the pumping effectiveness of the right heart
Calculation of a multiplier factor (PP2) from three factors that affect the ability of the right heart to withstand
increasing output loads: The effect of the pulmonary arterial pressure itself (PPA), the effect of changes in heart
arterial oxygen saturation in the coronary blood flow (OSA), and the effect of sympathetic stimulation (AUH) – the
value of AUH is expressed as ratio to normal:
PP2 = PPA/(AUH*OSA)
(RH 03)
Function curve relating the multiplier factor from RH 04 (PP2) to a multiplier factor for pumping strength of the
right heart musculature (RVM). Function rightHeartLoading interpolates data from the hereinafter table. Guyton use
linear interpolation, however it will be better to use cubic spline interpolation 2.
1
In the case of spline interpolation, we use following coordinates of knot points: PRA1=[-8,-7, -6,-2,0, 4, 12,15];
QRN=[0, 0.375,0.75, 2.6,5, 9.8,13.5,13.5] with clipping QRN=0 if PRA1<-8, and QRN=13.5 if PRA1>15
2
In the case of spline interpolation, we use following coordinates of knot points: PP2=[0.0, 10,20, 32.0, 38.4,
48.0,60.8,72.0] ; RVM=[1.06,1.032,1.004, 0.97,0.93,0.8,0.46,0.0] with clipping RVM=1.06 if PA2<0 and RVM=0 if
PA2>70
RVM=function rightHeartLoading(PP2)
PA2
<0
0
32
38.4
48
60.8
72
>72
(RH 04)
RVM
1.06
1.06
0.97
0.93
0.8
0.46
0
0
Factor for pumping strength of the right heart musculature
1
RVM
0.8
0.6
0.4
0.2
0
0
10
20
30
40
PP2 [torr]
50
60
70
Fig. 2 Linear and cubic spline approximation of RVM as a function of PP2
Calculation of the proportion of the pumping effectiveness of the right heart (HPEF2) that is caused by left heart
contraction. This is determined by the normal proportion (QRF) times the instantaneous output of the left heart
(QLO) and divided by the normalized output of the left heart (QLN) when all factors affecting left heart strength are
normal.
HPEF2=QRF*QLO/QLN
(RH 05)
Calculation of the proportion of the right heart pumping effectiveness that is caused by right heart musculature
contraction itself (HPEF1), calculated from multiple factors that affect right heart pumping including the normal
proportion of right heart pumping that is caused by left heart pumping (QRF), the strength of the right heart (HSR)
relative to its normal strength, the loading effect of pulmonary arterial pressure on the right heart (RVM), the effect
of autonomic stimulation on right heart strength (AUH), the effect of possible deterioration of the right heart from
shock and other factors (HMD), and the effect on right heart strength caused by hypertrophy of the right heart (HPR).
HPEF1=(1-QRF)*AUH*RVM*HSR*HMD*HPR
(RH 06)
Calculation of the pumping effectiveness of the right heart (HPEF) by adding the proportion of the pumping
effectiveness caused by left heart function (HPEF2) as calculated from RH 06 plus the proportion caused by
pumping by the right heart (HPEF2) as calculated from HR 07:
HPEF=HPEF1+HPEF2
(RH 07)
Calculation of the actual output from right heart
Calculation of the actual output from the right heart (QRO) by multiplying the normalized value for the output
(QRN) times a value that represents the instantaneous pumping effectiveness of the right heart (HPEF):
QRO = QRN*HPEF
0
PRA
15
PRA
RIGHT HEART PUMPING
INTPUTS:
QRO
PRA - right atrial pressure [torr]
PPA - pulmonary arterial pressure [torr]
AUHA - atrial autonomic stimulation [ratio to normal]
AUHA
AUH - autonomic stimulation of heart ventricles
[ratio to normal]
AUH
OSA - oxygen hemoglobin saturation
QRN
HSR - basic strength or right ventricle [ratio to normal]
OSA
HPR - hypertrophy effect of heart [ratio to normal]
HMD - cardiac depressant effect of hypoxia. shock
and other factors [ratio to normal]
HSR
QLO - output of left ventricle [l/min]
QLN - normalized output of the left heart [l/min]
PRA1
HPR
5.032
PPA
PPA
1
AU
1
AUH
0.97287
OSA
1
HSR
1
HPR
1
HMD
HMD
5
QLO
QLO
5
(RH 08)
QLN
OUTPUTS:
QRO - actual right ventricular output [l/min]
QRN - normalized right ventricular output [l/min]
PRA1 - effective right atrial pressure
(at actual level of autonomic stimulation) [torr]
RVM
RVM - depressing effect on right ventricle of pulmonary
arterial pressure [ratio to normal]
QLN
Right Heart Pumping
5
0
1.016
3
PRA1
8
RH 01
1-D T(u)
1
PRA
RH 02
PRA1
PRA1
2
QRN
QRN
function QRN=StarlingRNorm(PRA)
cubic spline interpolation
x=[-8,-7, -6,-2,0, 4, 12,15]
y=[0, 0.375,0.75, 2.6,5, 9.8,13.5,13.5]
3
AUHA
2
PPA
RH 04
RH 03
1-D T(u)
RVM
PP2
5
OSA
4
RVM
function RVM=rightHeartLoading(PP2)
cubic spline interpolation
PP2=[0.0, 10,20, 32.0, 38.4, 48.0,60.8,72.0]
RVM=[1.06,1.032,1.004, 0.97,0.93,0.8,0.46,0.0]
1
RH 06
0.6
4
AUH
QRN
QRF
6
HSR
7
HPR
8
HMD
9
QLO
10
QLN
HPEF
HPEF1
RH 05
HPEF2
RIGHT HEART PUMPING
RH 07
HPEF
HPEF2
RH 08
1
QRO