Estimating Relative Change in Ventricular
Stroke Work from Aortic Pressure
Shun Kamoi1, CG Pretty1, YS Chiew1, A Pironet2, T Desaive2
GM Shaw3, JG Chase1
1Department
of Mechanical Engineering, University of Canterbury, New Zealand
2GIGA Cardiovascular Science, University of Liege, Belgium
3Intensive Care Unit, Christchurch Hospital, New Zealand
Introduction
Cardiac and circulatory disease are the largest cause of death in
the western world, and are the leading cause of ICU admission
and mortality (WHO Global report)
• Expected to increase with increasing elderly population
• 1 in every 3 deaths are related to cardiovascular disease
• Accounts for 30% of all ICU admissions (and mortality)
Patients with cardiovascular
disease require hemodynamic
monitors to obtain patient
information for diagnosis and
treatment
Hemodynamic Monitors
Pressure catheter
Blood pressure displayed on monitor
Blood Pressure Value?
Main determinants of blood pressure
• Blood volume
• Arterial wall stiffness
• Stroke volume
• Peripheral Resistance
Ventricular Stroke Work
Considerations
• Adding extra measurements are
clinically not feasible
• “Humans are horribly variable”
(J.L Dickson et al)
Method
A model-based analysis of blood pressure
waveform to estimate Stroke Work.
Analyse
Pressure
Contour
Estimate
Aortic Pressure Model
Reservoir pressure concept
Aortic pressure (Pao) can be represented
as the sum of two pressure components
1. Reservoir pressure (Pres) accounts
for the energy stored/released by
the arterial wall
2. Excess pressure (Pex) which is extra
work done by the heart to produce
blood flow into aorta
𝑃𝑎𝑜 𝑡 = 𝑃𝑟𝑒𝑠 𝑡 + 𝑃𝑒𝑥 (𝑡)
𝑃𝑒𝑥 𝑡 ∝ 𝑄𝑖𝑛 𝑡
Three Element Windkessel
Z0
R
C
- Characteristic impedance
- Peripheral resistance
- Aortic compliance
Parameter Relationships
Reservoir Pressure
𝑑𝑃𝑟𝑒𝑠 (𝑡) 𝑄𝑖𝑛 𝑡 − 𝑄𝑜𝑢𝑡 (𝑡)
=
𝑑𝑡
𝐶
Flow Leaving Aorta
𝑄𝑜𝑢𝑡
𝑃𝑟𝑒𝑠 𝑡 − 𝑃𝑚𝑠𝑓
𝑡 =
𝑅
Combine
𝑑𝑃𝑟𝑒𝑠 (𝑡) 𝑃𝑎𝑜 (𝑡) − 𝑃𝑟𝑒𝑠 (𝑡) 𝑃𝑟𝑒𝑠 (𝑡) − 𝑃𝑚𝑠𝑓
=
−
𝑑𝑡
𝑍0 𝐶
𝑅𝐶
Pulse Wave Velocity
Distensibility
∆𝑉𝑎𝑜
=
𝑉𝑎𝑜
𝑡𝑓
𝑃
𝑡𝑑 𝑟𝑒𝑠
𝑡𝑑
𝑃
𝑡0 𝑟𝑒𝑠
𝑡 − 𝑃𝑚𝑠𝑓 𝑑𝑡
𝑡 − 𝑃𝑚𝑠𝑓 𝑑𝑡
∆𝑉𝑎𝑜
𝐷=
𝑉𝑎𝑜 ∆𝑃𝑒𝑥
Bramwell-Hill equation
𝑃𝑊𝑉 = (𝜌𝐷)
1
−
2
Ventricular Stroke Work
α
𝑣𝑙𝑣
𝑉𝑆𝑊 =
𝑃𝑙𝑣 ( 𝑣𝑙𝑣 )𝑑𝑣𝑙𝑣
Experiment
To validate VSW estimation via aortic pressure model, data from
porcine experiment were used.
GIGA Cardiovascular
Science
Stroke Work Changes
Mechanical ventilation settings
Airway pressure increase and decrease
changes the amount of blood flowing into
the ventricle during diastole.
Measured Stroke Work (Joule)
Preload
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1200
1400
1600
1800
2000
Time (s)
50
45
Pressure airway (cmH2O)
Step-wise changes in positive end
expiratory pressure were made
40
35
30
25
20
15
10
5
0
0
200
400
600
800
1000
Time (s)
Correlation Plot
Ventricular Stroke work (Jouls)
0.4
Ventricular Stroke Work (Joule)
0.35
0.3
0.25
0.2
0.15
0.1
1.8
0.4
2.4
0.35
2.3
0.3
2.2
0.25
2.1
0.2
0.15
0.1
0
1.9
2
2.1
2.2
2.3
2.4
2
1.9
500
1000
Time (s)
1500
Pressure-Velocity Gradient (kPas/m)
Results
2000
2.5
Pressure-Velocity Gradient (dP/dU)
VSW trend was accurately captured
Estimated pc versus calculated VSW showing relationship between the
two parameters. The plot indicates that there are high degree of
agreement with correlation coefficient of R=0.71.
Clinical Benefit
Patients cardiovascular performance can be analysed more
accurately than just Mean Arterial Pressure (MAP)
Stroke work trend can be used to guide treatment selection and
to titrate therapy
Does not require specialised
equipment and/or personnel
Clinical data
• Fluid resuscitation
• Use of inotrope and vasoactive drugs
model
raw
Cost/Invasiveness
Limitation & Future Work
Sample data still too small
• Does the theory hold in afterload changes
and/or different disease condition
• Could pulse wave velocity changes be validated using multiple
pressure measurements
Aortic pressure measurements (Highly Invasive?)
• How much information can be retrieved from less invasive arterial
pressure measurement
• Could the changes in transit time measured between ECG readings
and radial arterial pressure.
Acknowledgement
Supervisors
Bioengineering Centre
Medical Team at Liege
Questions?
Parameter Identification
Diastolic Condition: 𝑃𝑟𝑒𝑠 (𝑡) = 𝑃𝑎𝑜 (𝑡)
𝑆𝑖𝑛𝑐𝑒 𝑄𝑖𝑛 = 0
Diastolic Reservoir
𝑃𝑟𝑒𝑠 𝑡 =
𝑡−𝑡𝑑
−
𝑃𝑎𝑜 𝑡𝑑 − 𝑃𝑚𝑠𝑓 𝑒 𝑅𝐶
Pressure in mmHg
140
RC & Pmsf
+ 𝑃𝑚𝑠𝑓
Aortic Pressure
Diastolic Pressure Decay
Valve Closure Time (td)
130
120
110
100
90
0
0.1
0.2
0.3
0.4
Systole
0.6
Aortic compartment flow dynamics
Z0 C
300
𝑅𝐶𝑃𝑎𝑜 𝜏 + 𝑍0 𝐶𝑃𝑚𝑠𝑓
𝜏 =
𝑍0 𝐶 + 𝑅𝐶
250
90
200
Pressure in mmHgFlow in ml/s
Equilibrium Condition: 𝑑𝑃𝑟𝑒𝑠 (𝜏)
=0
𝑑𝑡
𝑃𝑟𝑒𝑠
0.5
Diastole
85
150
100
80
50
75 0
-50
70
0
0.1
0.2
0.3
Time in s
0.4
0.5
0.6
65
ODE
𝑑𝑃𝑟𝑒𝑠 (𝑡) 𝑃𝑎𝑜 (𝑡) − 𝑃𝑟𝑒𝑠 (𝑡) 𝑃𝑟𝑒𝑠 (𝑡) − 𝑃𝑚𝑠𝑓
=
−
𝑑𝑡
𝑍0 𝐶
𝑅𝐶
60
0
0.1
0.2
0.3
0.4
Time (s)
0.5
0.6
0.7
0.8