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Sung Hoon (Steven) Yoon
Problem: blood
pressure = MAP
“Mean” Arterial
Pressure
Static value
Solution: blood
circulation dynamic
model
MAP(t)
Dynamic value
Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene.
Science 321.5887 (2008)
Closed-Loop
Control System
Circulation
Loop
Dynamic System Vasculature
Control System
Input
Arterial
blood pressure
Controller Central
Nervous System
Sensor Baroreceptors
Actuator Aorta
Dynamic System
Input
Blood
Flow
Dynamic System
Output
Blood
Pressure
𝑄 𝑎𝑜 𝑡 is the flow
source for the left
ventricle
Stroke Volume
70.5 mL
Basal Heart Rate
80 beats per minute
Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene.
Science 321.5887 (2008)
Duration of heartbeat (s) 𝑇 0.75
Duration of systole (s) 𝑇𝑠 0.4𝑇
Time @ Maximum Flow (s) 𝑇 𝑚𝑎𝑥 0.16𝑇
Flow @ Maximum flow (L/s) 𝑄 𝑚𝑎𝑥 0.47
function [Qao,tt] = genQao(t)
T = 0.75; % duration of heartbeat (s)
tt = mod(t,T); % tt cycle from 0 to T
Ts = 0.4*T; % duration of systole (s)
Tmx = 0.16*T; % time @maximum flow (s)
Qmx = 0.47*10^3; % flow @maximum (L/s)
if tt >=0 && tt < Tmx,
Qao = Qmx*tt/Tmx;
elseif tt >= Tmx && tt < Ts,
Qao = Qmx*(Ts-tt)/(Ts-Tmx);
else
Qao = 0; % third section
end
Dynamic modeling
using linear graph:
Pressure Output
Flow Input
Defined 5 nodes,
including:
Systemic artery
Splanchnic vein
Right atrial
Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene.
Science 321.5887 (2008)
Derived equations
from linear graph
Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene.
Science 321.5887 (2008)
𝐹𝑠𝑎 =
𝑃𝑠𝑎 − 𝑃𝑠𝑝
𝐿 𝑠𝑎
−
𝑅 𝑠𝑎
𝐿 𝑠𝑎
𝐹𝑠𝑎
𝑃𝑠𝑎 =
1
𝐶𝑠𝑎
(𝑄 𝑎𝑜 − 𝐹𝑠𝑎)
𝑃𝑠𝑝 =
1
𝐶𝑠𝑎 + 𝐶𝑒𝑝
(𝐹𝑠𝑎 −
𝑃𝑠𝑝 − 𝑃𝑠𝑣
𝑅 𝑠𝑝
−
𝑃𝑠𝑝 − 𝑃𝑒𝑣
𝑅 𝑒𝑝
)
𝑃𝑠𝑣 =
1
𝐶𝑠𝑣
(
𝑃𝑠𝑝 − 𝑃𝑠𝑣
𝑅 𝑠𝑝
−
𝑃𝑠𝑣 − 𝑃𝑟𝑎
𝑅 𝑠𝑣
)
𝑃𝑒𝑣 =
1
𝐶𝑒𝑣
(
𝑃𝑠𝑝 − 𝑃𝑒𝑣
𝑅 𝑒𝑝
−
𝑃𝑒𝑣 − 𝑃𝑟𝑎
𝑅 𝑒𝑣
)
Compliance and
Resistance of veins
and arteries
Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene.
Science 321.5887 (2008)
Signal Profile
Aortic Valve Highly compliant
Systemic Artery Compliant
Splanchnic Vein Non-compliant (constant) ; 3.45 – 3.55 mmHg
Right Atrium Slightly compliant (nearly constant); 1.5 – 3 mmHg
No breathing
effects
Closed-Loop
System
heart rate (bpm)
arterial blood
pressure (mmHg)
Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene.
Science 321.5887 (2008)
Heart Rate
Mean Arterial
Pressure Regulation
Delayed Signals from
Pressure Receptors
Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene.
Science 321.5887 (2008)

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Cardiac signals

  • 2. Problem: blood pressure = MAP “Mean” Arterial Pressure Static value Solution: blood circulation dynamic model MAP(t) Dynamic value Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene. Science 321.5887 (2008) Closed-Loop Control System Circulation Loop Dynamic System Vasculature Control System Input Arterial blood pressure Controller Central Nervous System Sensor Baroreceptors Actuator Aorta Dynamic System Input Blood Flow Dynamic System Output Blood Pressure
  • 3. 𝑄 𝑎𝑜 𝑡 is the flow source for the left ventricle Stroke Volume 70.5 mL Basal Heart Rate 80 beats per minute Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene. Science 321.5887 (2008) Duration of heartbeat (s) 𝑇 0.75 Duration of systole (s) 𝑇𝑠 0.4𝑇 Time @ Maximum Flow (s) 𝑇 𝑚𝑎𝑥 0.16𝑇 Flow @ Maximum flow (L/s) 𝑄 𝑚𝑎𝑥 0.47 function [Qao,tt] = genQao(t) T = 0.75; % duration of heartbeat (s) tt = mod(t,T); % tt cycle from 0 to T Ts = 0.4*T; % duration of systole (s) Tmx = 0.16*T; % time @maximum flow (s) Qmx = 0.47*10^3; % flow @maximum (L/s) if tt >=0 && tt < Tmx, Qao = Qmx*tt/Tmx; elseif tt >= Tmx && tt < Ts, Qao = Qmx*(Ts-tt)/(Ts-Tmx); else Qao = 0; % third section end
  • 4. Dynamic modeling using linear graph: Pressure Output Flow Input Defined 5 nodes, including: Systemic artery Splanchnic vein Right atrial Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene. Science 321.5887 (2008)
  • 5. Derived equations from linear graph Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene. Science 321.5887 (2008) 𝐹𝑠𝑎 = 𝑃𝑠𝑎 − 𝑃𝑠𝑝 𝐿 𝑠𝑎 − 𝑅 𝑠𝑎 𝐿 𝑠𝑎 𝐹𝑠𝑎 𝑃𝑠𝑎 = 1 𝐶𝑠𝑎 (𝑄 𝑎𝑜 − 𝐹𝑠𝑎) 𝑃𝑠𝑝 = 1 𝐶𝑠𝑎 + 𝐶𝑒𝑝 (𝐹𝑠𝑎 − 𝑃𝑠𝑝 − 𝑃𝑠𝑣 𝑅 𝑠𝑝 − 𝑃𝑠𝑝 − 𝑃𝑒𝑣 𝑅 𝑒𝑝 ) 𝑃𝑠𝑣 = 1 𝐶𝑠𝑣 ( 𝑃𝑠𝑝 − 𝑃𝑠𝑣 𝑅 𝑠𝑝 − 𝑃𝑠𝑣 − 𝑃𝑟𝑎 𝑅 𝑠𝑣 ) 𝑃𝑒𝑣 = 1 𝐶𝑒𝑣 ( 𝑃𝑠𝑝 − 𝑃𝑒𝑣 𝑅 𝑒𝑝 − 𝑃𝑒𝑣 − 𝑃𝑟𝑎 𝑅 𝑒𝑣 )
  • 6. Compliance and Resistance of veins and arteries Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene. Science 321.5887 (2008) Signal Profile Aortic Valve Highly compliant Systemic Artery Compliant Splanchnic Vein Non-compliant (constant) ; 3.45 – 3.55 mmHg Right Atrium Slightly compliant (nearly constant); 1.5 – 3 mmHg
  • 7. No breathing effects Closed-Loop System heart rate (bpm) arterial blood pressure (mmHg) Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene. Science 321.5887 (2008)
  • 8. Heart Rate Mean Arterial Pressure Regulation Delayed Signals from Pressure Receptors Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene. Science 321.5887 (2008)