Download Left Heart Pumping

Left Heart Pumping
This module calculates left ventricular cardiac output from right atrial pressure (preload) and from pulmonary arterial
pressure (afterload).
INPUTS:
PLA - left atrial pressure (at normal level of autonomic stimulation) [torr]
PA - systemic arterial pressure [torr]
AUHA – atrial autonomic stimulation [ratio to normal]
AUH - autonomic stimulation of heart [ratio to normal]
OSA - oxygen hemoglobin saturation
HSL - basic strenght or left ventricle [ratio to normal]
HPL - hypertrophy effect of left heart [ratio to normal]
HMD - cardiac depressant effect of hypoxia, shock \n and other factors [ratio to normal]
OUTPUTS:
QLO - actual left ventricular output [l/min]
QLN - normalized lwft ventricular output [l/min]
LVM – aortic pressure load effect on left ventricular output [ratio to normal]
Outputs that are not used as inputs to other modules are printed by italics.
Calculation of Starling law for left heart
Calculation of the effective left pressure (PLA1) considering of autonomic atrial stimulation from the left atrial
pressure (PLA) which was calculated for normal level of autonomic stimulation. Atrial autonomic stimulation
(AUHA) influences on atrial pressures - it determines the slope of changing of left atrial pressures due to autonomic
stimulation of atrial heart muscle strength.
PLA1 = (PLA+4)*AUHA – 4
(LH 01)
Function curve of Starling law that gives the output from the left heart (QLN) for any given level of left atrial
pressure (PLA1) when all conditions of the left heart are normal is calculated using interpolation of the following
values:
PLA1
<-2
-2
1
5
8
12
>12
QLN
0.01
0.01
3.6
9.4
11,6
13.5
13.5
QLN = function StarlingLNorm(PLA)
(LH 02)
Function StarlingLNorm interpolates data from the hereinbefore table. Guyton use linear interpolation, however it
will be better to use cubic spline interpolation1.
1
In the case of spline interpolation, we use following coordinates of knot points: PLA1=[-2.0,1.0,2,5.0,8.0,12.0,15],
QLN=[-0.01,3.6,5,9.4,11.6,13.5,13.5] with clipping QLN=0.01 if PLA1<-2, and QRN=13.5 if PRA1>15 .
Starling law for left heart
14
12
10
QLN [torr]
8
6
4
2
0
-2
-10
-5
0
5
10
15
PLA1 [torr]
Fig. 1 Linear and cubic spline approximation of QLN as a function of PLA1
Calculation of the pumping effectiveness of the left heart
A temporary multiplier function (PA2) for the effectiveness of left heart pumping is calculated from three factors:
Stimulation of the left heart by the autonomic nervous system (AUH), effect on heart pumping caused by changes in
arterial oxygen saturation (OSA), effect on heart pumping caused by the loading effect of systemic arterial pressure
(PA):
PA2 = PA/(AUH*OSA)
(LH 03)
Function curve relating the pumping effectiveness of the left heart (LVM) to the multiplier function calculated in the
equation LH 03 (PA2). Function rightHeartLoading interpolates data from the hereinafter table. Guyton use linear
interpolation, however it will be better to use cubic spline interpolation
LVM=function rightHeartLoading(PA2)
(LH 04)
PA2
<0
0
60
125
160
200
240
>240
RVM
1.04
1.04
1.025
0.97
0.88
0.50
0
0
Factor for pumping strength of the left heart musculature
1.4
1.2
1
LVM
0.8
0.6
0.4
0.2
0
0
50
100
150
200
250
PA2 [torr]
Fig. 2 Linear and cubic spline approximation of LVM as a function of PA2
Multiplication factor that represents the pumping effectivnetes of the left heart (HLPEF) is calculated by
multiplication of various factors that alter pumping effectivnetess of the heart: a multiplier that reduces the
effectiveness because of pressure load on the heart (LVM), a factor that changes the effectiveness of the heart
because of abnormal left heart strength (HSL), a factor that increases the effectiveness of the heart because of
hypertrophy (HPL), a factor that decreases the strength of the heart because of deterioration of the heart in low blood
flow states (HMD), and a factor that alters the strength of the heart by increases or decreases in autonomic
stimulation (AUH).
HLPEF=LVM*HSL*HPL*HMD*AUH
(LH 05)
Calculation of the actual output from left heart
Calculation of the passive rate of blood flow through the left ventricle into the aorta (QLO1) when the left atrial
pressure (PLA) is greater than the aortic pressure (PA). Condition prevents any backflow because of closure of the
aortic value when aortic pressure is higher than atrial pressure.
if (PLA>PA) then QLO1 = (PLA-PA)/3 else QLO1=0
(HL 06)
Calculation of the actual output from the left heart (QRLO) by multiplying the normalized value for the output (QLN)
times a value that represents the instantaneous pumping effectiveness of the left heart (HLPEF) plus additional
passive rate of blood flow through the left ventricle into the aorta (QLO1) when the left atrial pressure is greater than
the aortic pressure:
QLO = QLN*HLPEF+QLO1
2
PLA
LEFT HEART PUMPING
PLA
100
PA
PA
1
AUHA
AUHA
1
AUH
AUH
0.97
OSA
OSA
1
HPL
HPL
1
INTPUTS:
PLA - left atrial pressure [torr]
PA - systemic arterial pressure [torr]
AUHA - atrial autonomic stimulation [ratio to normal]
AUH - autonomic stimulation of heart ventricles
[ratio to normal]
OSA - oxygen hemoglobin saturation
HSL - basic strenght or left ventricle (ratio to normal)
HPL - hypertrophy effect of left heart [ratio to normal]
HMD - cardiac depressant effect of hypoxia, shock
and other factors [ratio to normal]
QLO
4.996
QLN
5
LVM
0.9992
HSL
HSL
1
(LH 07)
HMD
OUTPUTS:
QLO - actual left ventricular output [l/min]
QLN - normalized left ventricular output [l/min]
LVM - aortic pressure load effect
on left ventricular output [ratio to normal]
HMD1
Left Heart Pumping
LEFT HEART PUMPING
4
LH 01
1-D T(u)
1
PLA
LH 02
PLA1
QLN
2
QLN
function StarlingLNorm(PLA)
cubic spline interpolation
x=[-2.0,1.0,2,5.0,8.0,12.0,15]
y=[-0.01,3.6,5,9.4,11.6,13.5,13.5]
3
AUHA
LH 07
QLN
HLPEF
LH 03
2
PA
PA2
5
OSA
LH 04
1-D T(u)
LVM
3
LVM
function leftHeartLoading(PA2)
cubic spline interpolation
x=[0,100, 125, 160, 200, 240]
y=[1.04, 1.0,0.97,0.88,0.59,0]
LH 05
4
AUH
HLPEF
6
HSL
7
HPL
8
HMD
LH 06
QLO1
QLO1
lower limit 0
3
QLO0
1
QLO