this is repost!!! This is one question with many part to it so please try best a

Question

this is repost!!! This is one question with many part to it so please try best and let me know what you answer in detail. Please clear handwriting, type if possible. show all step and logic okay. quick resonse

Model of heart and peripheral blood vesels show below

Heart model as current source and switch. Heart pumps during systole -> switch is on, current I(t) = I0. Heart is not pumping during diastole, switch is off, current I(t) =0.

Signal I(t) shown above as funct of time. ts­ and td represent time at end of systole and diastole.process repeat every cardiac cycle.

Rest of model shown as RC circuit. Resistance R represents peripheral resistance and C-capacitance represents compliance of blood vessel. (pressure same as votlage). systemic blood pressure, P(t) can represented as voltage across periphral resistance.

Now answer the follow question:

1) Write down differential equation for P(t) during diastole,(an example between t=ts and t=td). During this time heart not pumping blood, i.e., I(t) =0. Assume that val of P(t) at the end of systole is 120 mmHg.

Next do this,

2) Solve equation to write equation for P as func. of time during diastole. You can choose to use Laplace transforms to solve equation. Draw schematic plot of this function P(t) as funct of time. What is time constant of system?

3) If model were realistic representation of cardio system, blood pressure should decayto 80 mmHg at end of diastole, example at t = td. Assume diastolic interval last 640 ms (example., td-ts = 0.64 s). Calculate in seconds what suitable value of time constant should be to observe this type o f behavior.

4) Now, consider systolic time interval, when 0<t<ts. During this time, heart pumping with current I(t) = I0u(t). Write down differential equation for P(t) during this time interval. now solve by assuming that P(0) = 80 mmHg, I­0=10. Write down expression for P(t) in terms of unknown resstance R.

5) Calculate appropriate value of R in 4 above so that pressure rises 80 mmHg to 120 mmHg within 160 ms systolic time interval (example ts= 0.16 s).

6) Now with result estimate value of compliance C.

7) Lastly what can you said about relationship b/w systolic and diastolic pressure and peripheral resistance and also compliance? How would systolic and diastolic pressure change if peripheral resistance R increased? and what would happen if resistance decreased?

8) In model, we had resistor and capacitor in parallel. Comment on if this a proper configuration based on underlying cardiovascular model that we trying to approximate. What would happen if two elements were in series instead?

Explanation / Answer

T[K] = T(°C) + 273

P[t] = P(273)

R = 458mmhg

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