Figure 1 Uncontrolled state where ZPFV is increased by 500 ml.

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1 Question 1 Part I Description The initial venous zero pressure filling volume was 2500 ml. The heart rate was fixed at 72 beats/min. The systemic arterial pressure (SAP) was 114/75 mmhg (average = 94 mmhg). After increasing the venous zero pressure filling volume to 3000 ml, we see a drop in SAP while the heart rate stays fixed at 72 beats/min. The systemic pressure is then 76/50 mmhg (average = 63 mmhg). Figure 1 Uncontrolled state where ZPFV is increased by 500 ml. Analysis We know that the veins are elastic. Increasing the venous zero pressure filling volume means that we increase the volume of blood in the veins present before any stretch in the wall of the veins (and any pressure) appears. Assuming that the volume of blood in the body doesn't change, there is less blood in the other parts of the cardiovascular system (including in the systemic arteries) and therefore, the pressure is dropping in the systemic arteries. With the baroreflex switched off, the cardiovascular system acts with a lack of control system. The heart rate doesn't change because the control system is not activated.

2 Part II Description The initial conditions are very similar to the ones in Part I. The SAP was initially 114/75 mmhg (average = 94 mmhg). This time, the heart rate calculated was oscillating as well between 67 and 77 beats/min (average at 72 beats/min, like in Part I). When the venous zero pressure filling volume went from 2500 ml to 3000 ml, simulating the standing test, the SAP began to drop as expected (to an average of 74 mmhg). The heart rate increased to around 91 beats/min to compensate for this pressure drop. The SAP then started to rise again, and with that pressure rise detected, the heart rate decreased, making the SAP decrease again. The SAP stabilized after 2 cycles (low frequency cycles on the graph) at 102/72 mmhg (average = 87 mmhg). The heart rate was oscillating between 78 and 90 beats/min (average = 84 beats/min). Analysis The general response makes sense. The increased heart rate to maintain the SAP and the transition as explained in the description (with the cycles) make sense. However, if we look closer, the high frequency oscillations of the heart rate don't make sense. They seem to be due to numerical calculations varying with the SAP (like if the heart rate would change proportionally with the SAP while the SAP is changing during 1 heart beat). It would be unrealistic to have the heart rate changing during the same heart beat. Figure 2 Controlled state, where baroreflex is activated, and ZPFV is increased by 500 ml.

3 Part III On the astronaut pre-flight stand up test data, we can see the initial heart rise from 72 to 136 beats/min, a decrease to 86 beats/min, and a stabilization after 2 cycles at an average of 104 beats/min. The pressure originally at 114/60 mmhg (at an average of 87 mmhg) decreased to an average of 48 mmhg and stabilized after 1 cycle (low frequency cycle on the graph) at 108/60 mmhg (at an average of 84 mmhg). The magnitude of values is in general similar to the ones in the simulation, except that the drop of pressure following the astronaut standing seems to be too smoothly approximated in the simulation. The real pressure drop was more important. However, the general dynamic of the response is similar, meaning that the instantaneous translocation of 500 ml of blood to the veins is a decent simulation of the data. The main differences are: The real system seems to be more critically damped than the simulated one. In the real data set, there is a greater initial transient peak in heart rate. Astronaut s SAP overshoots its pre-stress values upon standing and then oscillates around and settles on a mean SAP very close to the pre-stress SAP. In the model, SAP does not overshoot its initial values and settles on a lower baseline. In the pre-flight stand up test data, the heart rate reaches its maximum few seconds before the SAP drops to its minimum level. In the simulation, the SAP reaches its minimum level few seconds before the heart rate reaches its maximum. This might be due to the fact that the heart rate is not only proportional to the SAP, but also to the rate of change of the SAP. The model doesn t include the effects of respiration, which can clearly be seen in the astronaut s heart rate and SAP data as cyclical variations of those parameters with a period of about 5 sec.

4 Question 2 Part I On the astronaut post-flight stand up test data, we can see the initial heart rise from 79 to 135 beats/min, a decrease to 108 beats/min, an increase and a stabilization at an average of 132 beats/min. The pressure originally was 126/78 mmhg (at an average of 102 mmhg) decreased to an average of 70 mmhg and stabilized after 1 cycle (low frequency cycle on the graph) at 138/84 (at an average of 111 mmhg). In the post-flight stand up test data, the heart rate reaches its first maximum few seconds after the SAP drops to its minimum level. It is the opposite in the pre-flight data. The control system have a reduced capability to sense the rate of change of the SAP. In general, the SAP curve has a similar shape in post-flight than in pre-flight, except that the pressure is higher during the original and transition state, and even higher during the steady state (84 mmhg for pre-flight steady state compared to 111 mmhg for post-flight steady state). To achieve that higher pressure, the heart rate increased a lot in the steady state, from an average of 104 beats/min (pre-flight) to an average of 132 beats/min (post-flight). That would mean that the other effector mechanisms increasing the cardiac output (venous tone, cardiac contractility and arteriolar resistance) would not be as effective after space flight. Part II With the baroreflex switched off, we can see that the main effect of removing blood (400 ml out of 5000 ml) is to drop the pressure, prior and after standing up, while the heart rate doesn t change at all. This result is expected. The effect is quite high. The average SAP is 94 mmhg with full blood before standing compared with 70 mmhg when blood is removed. On the other side, the average SAP is 63 mmhg with full blood after standing compared with 38 mmhg when blood is removed. A most realistic effect is obtained with the baroreflex switched on. With blood removed, the initial state involved a SAP averaging 89 mmhg (compared with 94 mmhg with full blood) and a heart rate averaging 80 beats/min (compared with 72 beats/min with full blood). The dynamics of the transition and steady state is very similar with blood removed than with full blood, except that the pressure is in general lower (averaging 81 mmhg compared to 87 mmhg), and the heart rate is in general higher (averaging 95 beats/min compared to 84 beats/min). Another difference with blood removed is that the difference between the end-diastolic and the end-systolic pressure seems a little bit smaller (22 mmhg compared to

5 30 mmhg with full blood in steady state). Figure 3 Uncontrolled state where 400 ml blood loss is incorporated into the original simulation. Figure 4 Controlled state where blood loss is incorporated into the model. The general dynamic of heart rate is not really realistic in the sense that the heart rate generated by the model in steady state is way too low (the model outputs an average heart rate of 95 beats/min in steady state compared with 132 beats/min with the real data. Part III In microgravity, fluids in the body are redistributed (fluid shift) due to the absence of gravity. The blood that is normally attracted by the gravity towards the legs gets now redistributed in the upper parts of the body. Volume sensors (used to measure pressure) located in the upper part of the body (at the atria) detects this

6 increase of pressure caused by the increase of blood volume in that area. To reduce the pressure in that area to a normal level, the control system acts to remove blood in the body, eliminating plasma through urine. Part IV Other simulations were made reducing the peripheral sympathetic gain by 20% (from 9 to 7.2). We know that sympathetic stimulation causes constriction of veins, decreased venous capacitance, increased peripheral resistance, increased contractility of the heart and increased heart rate. Reducing the peripheral sympathetic gain simulates the difficulty of the control system to compensate for the drop in the SAP while standing up post-flight. The curves obtained with the baroreflex turned off were exactly the same as in Part II. However, the curves when the baroreflex are turned on are slightly different. The Figure 5 Controlled state where both blood volume and peripheral sympathetic gain have been decreased. pressure curve is about the same, but we can see a slight increase in the heart rate when reducing the peripheral sympathetic gain by 20% (from about 95 beats/min before reducing the gain to about 99 beats/min after). Reducing the peripheral sympathetic gain by 20% slightly improves the dynamics of the heart rate data, but it is still far from the real data (132 beats/min in steady state). Overall, we can see that reducing the blood volume and the peripheral sympathetic gain improves the dynamics of the heart rate after a post-flight standing test simulation (compared to the real data). However, the parameters need to be better adjusted in order to more accurately represent the real data and the model of stand/tilt needs to be improved.

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