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Computational model of cardiovascular response to centrifugation and lower body cycling exercise

: 48 Short-radius centrifugation combined with exercise has been suggested as a potential countermeasure 49 against spaceflight deconditioning. Both the long-term and acute physiological responses to such 50 combination are incompletely understood. We developed and validated a computational model to study 51 the acute cardiovascular response to centrifugation combined with lower-body ergometer exercise. The 52 model consisted of 21 compartments, including the upper body, renal, splanchnic, and leg circulation, as 53 well as a four-chamber heart and pulmonary circulation. It also included the effects of gravity gradient 54 and ergometer exercise. Centrifugation and exercise profiles were simulated and compared to 55 experimental data gathered on twelve subjects exposed to a range of gravitational levels (1G and 1.4G 56 measured at the feet) and workload intensities (25-100W). The model was capable of reproducing 57 cardiovascular changes (within ±1SD from the group-averaged behavior) due to both centrifugation and 58 exercise, including dynamic responses during transitions between the different phases of the protocol. 59 The model was then used to simulate the hemodynamic response of hypovolemic subjects (blood 60 volume reduced by 5-15%) subjected to similar gravitational stress and exercise profiles, providing 61 insights into the physiological responses of experimental conditions not tested before. Hypovolemic 62 results are in agreement with the limited available data and the expected responses based on 63 physiological principles, although additional experimental data are warranted to further validate our 64 predictions, especially during the exercise phases. The model captures the cardiovascular response for a 65 range of centrifugation and exercise profiles, and it shows promise in simulating additional conditions 66 where data collection is difficult, expensive, or infeasible. 67


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Artificial gravity (AG) generated by centrifugation is a promising countermeasure to mitigate 82 the detrimental effects of weightlessness during space missions (7). Previous ground-based studies have 83 shown that exposure to centrifugation can improve cardiovascular responses to orthostatic stress (18, 35, 84 44, 55), especially if centrifugation is combined with exercise (20,(27)(28)(29)(30)(51)(52)(53). Artificial gravity has 85 also been proposed as a potential countermeasure to mitigate the recently discovered Spaceflight 86 Associated Neuro-Ocular Syndrome (SANS) (6). Before implementing AG in space, however, 87 additional research efforts are needed to determine the parameters that are most effective, including the 88 angular velocity and radius of the centrifuge, and to characterize the cardiovascular response to these 89 stressors under varying physiological baseline conditions (6). The expensive and time-consuming nature 90 of these experimental studies with human subjects makes the use of computational tools a very 91 attractive approach to systematically study human responses under these conditions.

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Computational cardiovascular models can be used to describe and, more importantly, to predict, 94 human responses in cases where data collection is difficult, expensive, or infeasible. Despite the 95 complexity of the human body, computational approaches of various kinds and anatomical resolution 96 have been successfully applied to a variety of applications, from very detailed three-dimensional models 97 of selected regions, to low-dimensional models representing more aggregate system behavior (i.e. 98 lumped-parameter models). The selection of the type of model is primarily driven by the objectives of 99 the analysis as well as the availability of computational resources (46) and data to specify model 100 parameters and validate the model behavior. In the present work we are interested in the overall, short-101 term, cardiovascular response to centrifugation combined with exercise and thus, the implementation of 102 a lumped-parameter model seems the appropriate approach.

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One of the first systematic approaches of quantitative, system-level modeling of cardiovascular 105 regulation was developed by Guyton (21,22). He was one of the first to apply a system engineering 106 approach to quantify and analyze various aspects of cardiovascular function using mathematical and 107 graphical techniques before computers became widely available. Since then, multiple models have been 108 developed to study cardiovascular responses to gravitational stress, including head up tilt (HUT) (25, Figure 2 shows the architecture of a generic compartment (25,50). The lumped physical 142 characteristics of each compartment are defined by a resistance and a capacitive element that 143 relates the distending volume , stored in the segment to transmural pressure ∆ = − , . The associated with each compartment (not shown in Figure 2) include zero-pressure filling volume , , 148 and the anatomical vertical length , (superior-to-inferior extension of the vascular segment).

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The flow in each compartment is calculated using the following constitutive relation: where , are the compartment pressures,   Exercise causes circulatory adjustments that are essential to satisfy the metabolic needs of 229 exercising muscles. These adjustments include local vasodilation in exercising muscle groups, 230 sympathetic nervous system activation, an increase in cardiac output, and an increase in arterial blood 231 pressure above the baseline level. In our modeling effort the effects of exercise are represented using the 232 following four mechanisms:

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Decrease in leg arterial resistance. Due to the higher metabolic demand during exercise, arterial 235 resistance decreases locally in the exercising muscles to increase local blood flow to satisfy the local 236 metabolic demand, and remove metabolic end products. In our modeling effort, we simulate lower-body 237 cycling exercise by disconnecting the leg resistance from the control systems at the onset of exercise 238 and manually adjusting it to match previously gathered experimental data (10) according to the 239 following expression: where is the leg vascular resistance immediately before the onset of an exercise phase, is the 241 final leg vascular resistance for a given exercise intensity, and is the time constant governing the 242 changes in local vascular resistance.

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Leg muscle pump effect. During exercise, muscles exert a pump effect by squeezing the veins while contracting, thus facilitating the return of blood to the heart. In our model, muscle pump effects are 246 simulated by varying the external pressure at the venous leg compartment periodically, following a 247 cycling cadence of 1 rev/sec (similar to the subjects' experimental data). The leg external pressure due to the muscle pump effect, , is represented according to: (1 + cos(4 ( − 1 2 ⁄ ))) 1 2 ⁄ ≤ < 3 4 ⁄ 0 3 4 ⁄ ≤ < 1 where is the maximal leg external pressure and depends on the exercise intensity. In addition to the periodic muscle pump effect during cycling, an external muscle pump pressure , proportional to 251 the centrifugal force, was added to the venous leg compartment when subjects were not cycling while 252 they were being centrifuged (i.e. spin-up phase, AG-alone phases, and spin-down phase, see Figure 3).

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This pressure models the effects of continuous leg muscle activation when subjects are pushed against 254 the pedals by centrifugal force (similar to the muscle pump caused by "active" standing).

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Increase in intra-abdominal pressure. Abdominal pressure increases during exercise due to the 257 contraction of abdominal muscles. This effect is represented as an increase in external pressure in the 258 abdominal compartments (7, 8, 9, 10, 11, and 14), according to the following exponential function: where ̂ is a time constant on the order of a few seconds and is the maximal external pressure that 260 depends on the intensity of the exercise.

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A comparatively small set of physiologically plausible parameters from our model were 304 adjusted to simulate the centrifugation and exercise profiles described above. First, total blood volume 305 was set to V = 5175 ml to closely represent our study population. This choice was based on an 306 average of 75 ml of blood per kg of body mass (17, 25, 42) and our experimental subjects' average 307 weight (± standard deviation) of 69.3 ± 11.6 kg.

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Additional details about flow and volume distributions among the compartments are given in Table 5  348 external pressure , and leg arterial resistance were selected for each exercise level (see Table   349 2). The top graphs in Figure 4 and Figure 5 show that our matching approach captures MAP and TPR

461
To explore the physiological consequences of centrifugation we further studied quantitative 462 responses to centrifugation and exercise in hypovolemic subjects, with reduction of 5, 10, and 15% of 463 total blood volume. There is limited experimental data in the literature to perform a direct comparison 464 between our simulations and hemodynamic responses from hypovolemic subjects subjected to short-465 radius centrifugation an exercise. Thus, we base our comparison to a similar study that used tilt tests 466 maneuvers to study orthostatic stress. Linnarsson and his colleagues (35) investigated orthostatic volume during the 5-day bed rest, and their short-term, post-bedrest HR, SYS, and DIA responses 469 during a tilt test (80º upright) changed approximately +29%, −15%, and −5% respectively, with respect 470 to pre-bed rest. Our data indicate that hypovolemic subjects presenting blood volume losses between 10-471 15% will also experience increases in HR (+14 to 17%) and decreases in SYS (−10.5 to −15.6%) and 472 DIA (−2.8 to −5.7%). We expect to see less significant changes in a short-radius centrifuge due to the 473 presence of a strong gravity gradient that makes the gravitational stress less intense than being exposed

489
(within a cardiac cycle), which is not the case in the present study. Inertial effects have been estimated 490 to account for less than 1% of stroke volume and mean arterial pressure (9) and therefore they have been 491 neglected.

492
We have also not taken into account possible non-linear cardiac effects. Both systolic and 493 diastolic pressure-volume relationships were assumed to be linear, which is reasonable at normal filling 494 pressures, but these relationships become non-linear at higher filling pressures. Simulations of 495 pathologically high pressures were beyond of the scope of this work, and for the purpose of the 496 simulations presented here, the pressure-volume relationships were assumed linear. Additionally, the 497 unstressed volume was assumed to be static throughout the cardiac cycle and the same for the diastolic 498 and systolic pressure-volume relationships. Typically, the end-systolic unstressed volume is between 499 25-40% lower than its diastolic counterpart (2, 32), indicating a small but potentially significant 500 contribution to stroke volume, thus decreasing the underestimation seen in our simulations.
Viscoelastic stress-relaxation effects of the systemic veins were also not included in our modeling effort. This phenomenon refers to the intrinsic ability of the vascular walls to stretch slowly passive head-up tilt, due to the altering of the time-course of venous pooling to the lower body and thus,

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limiting the blood pressure dip typically seen during active standing (26). In our work we focused on 507 steady-state cardiovascular responses during active exposure to centrifugation and therefore these 508 effects were also neglected. We have also not taken into account breathing-related changes in 509 intrathoracic pressure. As the depth of breathing increases with increasing exercise, the lowering of 510 intrathoracic pressure aids in venous return at higher exercise levels. We have also assumed that the 511 resistance changes due to exercise are largely determined by the arteriolar vasodilation and that the 512 muscle pump primarily affects the filling state of the leg veins.
Region III: Gradual decline in gravitational stress over a period of length ∆ .

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Region IV: Post-orthostatic stress recovery of unspecified length.

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The following 23 non-linear algebraic equations are used to find the initial conditions, and they 604 describe the blood flow in the compartments assuming that the system is in steady state (54)

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The right heart and left heart include variable capacitors and diodes representing the heart valves that