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Computational modeling of orthostatic intolerance for travel to Mars

Computational modeling of orthostatic intolerance for travel to Mars www.nature.com/npjmgrav ARTICLE OPEN Computational modeling of orthostatic intolerance for travel to Mars 1✉ 1 1 1 1 Lex M. van Loon , Anne Steins , Klaus-Martin Schulte , Russell Gruen and Emma M. Tucker Astronauts in a microgravity environment will experience significant changes in their cardiopulmonary system. Up until now, there has always been the reassurance that they have real-time contact with experts on Earth. Mars crew however will have gaps in their communication of 20 min or more. In silico experiments are therefore needed to assess fitness to fly for those on future space flights to Mars. In this study, we present an open-source controlled lumped mathematical model of the cardiopulmonary system that is able simulate the short-term adaptations of key hemodynamic parameters to an active stand test after being exposed to microgravity. The presented model is capable of adequately simulating key cardiovascular hemodynamic changes—over a short time frame—during a stand test after prolonged spaceflight under different gravitational conditions and fluid loading conditions. This model can form the basis for further exploration of the ability of the human cardiovascular system to withstand long-duration space flight and life on Mars. npj Microgravity (2022) 8:34 ; https://doi.org/10.1038/s41526-022-00219-2 INTRODUCTION loss of consciousness and postural tone due to global cerebral hypoperfusion followed by complete recovery) or POTS (experi- Microgravity defines an environment where gravitational forces enced as lightheadedness, palpitations, tremulousness and on the human body are significantly less than those experienced on planet Earth. The fluid compartments of the human body are weakness) . expectedly most prone to immediate and mid-term effects, whilst Twenty to thirty percent of astronauts returning from short 8–10 duration space flights and ~80% of astronauts returning after solid organ composition may adapt to altered feedback loops as most evident in the musculoskeletal system. Exposure to long-duration space flight experience symptomatic orthostatic 11,12 microgravity profoundly changes cardiovascular hemodynamics. intolerance , compared with only 5% of the unexposed general Compared to upright posture on Earth, fluid rapidly redistributes population under 50 years of age . from the bottom half to the top half of the body. Reduced venous Symptoms can be prevented or managed with inflight lower pooling in the copious lower extremity territory is followed by a body negative pressure (LBNP) , fluid loading, compression rapid contraction of plasma volume. This is primarily due to garments, and pharmacological therapy on re-entry into Earth’s transcapillary fluid filtration into upper-body interstitial spaces, gravitational field. In absence of a specialist ground support team, exacerbated by any reduction of fluid intake, and leads to a as would be the case in early missions to Mars, post-flight 1–3 10–15% reduction of the extracellular fluid volume . orthostatic intolerance after such long-duration spaceflight con- Alongside fluid maldistribution, autonomic dysfunction occurs stitutes a significant risk to astronaut safety and mission success . within a few days of microgravity exposure. Whilst inapparent in Management algorithms suited to all possible scenarios are space, it causes inadequate vasoconstriction and lack of respon- needed. siveness and adaptability of total peripheral resistance on Modelling the cardiovascular system engages productive cycles 4,5 14,15 standing following return to Earth . In addition, cardiac atrophy of insight into the underlying physiological processes .It isa occurs rapidly in microgravity, likely due to the reduced safe, cost-effective and feasible way to predict changes and contractility required to maintain adequate arterial pressure . responses to treatment in space travelers. The approach has been Convergent lines of deconditioning cause an inability of the 16,17 used to simulate post flight orthostatic intolerance , short-term cardiovascular system to adapt to gravitational exposure upon a adaptations to low gravity and the effectiveness of the LBNP return to Earth and maintain adequate blood pressure in an countermeasure , and cardiovascular deconditioning during upright position . This is known as post (space) flight orthostatic long-term space flight . However, the effect of a prolonged intolerance. (>6 months) exposure to microgravity on orthostatic intolerance Orthostatic intolerance can be due to orthostatic hypotension, has never been modelled. Neither is there any modelling available neurally mediated (reflex) syncope, and postural tachycardia showing the response of the cardiovascular system to travelling to syndrome (POTS). Where orthostatic hypotension is defined as a Mars and performing an active stand test there. The primary sustained reduction of systolic blood pressure of at least 20 mmHg objective of the here presented model is to predict if humans can or diastolic blood pressure of 10 mmHg within 3 mins of standing withstand orthostatic stress on arrival on Mars after prolonged or head up tilt to at least 60 degrees and POTS is defined as a space travel. We aimed to develop a model suitable for short- and sustained heart rate of >30 beats/min within 10 mins of standing long-duration spaceflight, simulate re-entry to Earth’s and Mars’ or head up tilt in the absence of orthostatic hypotension. It is experienced as presyncope (symptoms of global cerebral hypo- gravity, and validate the model using previous orthostatic stress 8,20–22 perfusion without loss of consciousness) or syncope (a transient experiments in astronauts . College of Health and Medicine, Australian National University, Canberra, ACT, Australia. email: lexmaxim.vanloon@anu.edu.au Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; L.M. van Loon et al. RESULTS Long-duration spaceflight The key simulation results and available relevant physiological Table 2 and Fig. 2 show the hemodynamic responses to a stand data from astronauts pre-flight and on landing day are compared test after a long-duration (>6 months) spaceflight with or without fluid loading, and under either Earth’s or Mars’ gravitational in Figs. 1, 2 and Tables 1, 2. The effect of the stand test was conditions. The simulation results from the scenario in which assessed by observing the mean arterial pressure (pressure in orthostatic stress was tested in an astronaut on landing day with compartment 0), the central venous pressure (pressure in fluid loading prior to returning to Earth show to be within the compartment 15), cardiac output (flow into compartment 0), reported limits from experimental data. and heart rate. Results for in supine position were taken at Fluid loading in our simulations had minor positive effect on t = −50 s and for the standing position were taken at t = 100 s. MAP (< + 2 mmHg) but did prevent a major dip in MAP during a stand test (Fig. 2). This was mainly achieved by decreasing heart Pre-flight conditions rate (−5 bpm), increasing the cardiac output (+.4 l), and stroke Representative simulated pressure-volume loops of the left volume (+ 6 ml) prior to the stand test. Last, Table 2 and Fig. 2 also show results of simulating a stand ventricle during supine and standing position are shown in test on Mars after a prolonged spaceflight. The resulting Fig. 1. Table 1 and Fig. 2 panel A demonstrates that all key hemodynamic changes to this orthostatic stress test on Mars are physiological variables generated by the model are within the less pronounced compared to when performed on Earth, even if range of what is considered physiologically normal for our target one on Earth is preceded by fluid loading. Even more so, the stand population - i.e. well trained, healthy, adult males – for a steady test on Mars shows similar results to the pre-flight condition state supine position as well as for the dynamic response to a on Earth. 11,23,24 stand test . This pressure-volume loops show physiological correct values for systolic blood pressure (~122 mmHg), diastolic blood pressure (~81 mmHg), diastolic filling pressure (~8 mmHg), DISCUSSION and stroke volume (~71 ml) . Exposure of the human body to orthostatic stress evokes prominent short-term physiological responses that aim at main- Short-duration spaceflight taining blood pressure. We here provide a physiological model capable of simulating these responses. Modelling outcomes The hemodynamic responses to a stand test of an astronaut on adequately reflect on real-life physiology, as exemplified by landing day on Earth, after being in space for a maximum of model predictions of key physiological parameters following 10 days, are shown in Table 1, Fig. 2 panel B. All values are within variations of parameters such as fluid loading, i.e. circulatory blood normal ranges of published experimental data from real astro- volume, or the length of exposure to microgravity. For such nauts performing a stand test on landing day post short-duration scenarios, model predictions are in line with real-life observations 11,23 spaceflight . Although the experimental data varies and obtained in astronauts following space flight. include both presyncopal and nonpresyncopal subjects, the trend Simulation results confirm the observed impact of prolonged and the relative changes of the key hemodynamic variables space travel on haemodynamic resilience to a stand test, and the 17,19 simulated by our model match well with experimental data . crucial importance of fluid loading to avert adverse outcomes in Table 1 shows that mean and diastolic blood pressure during terms of significant drops of mean arterial pressure and excessive supine and standing position are equal to each other and to the tachycardia, at least in the short term. The differences between baseline simulation despite a significant decrease in stroke key hemodynamic variables during standing and supine position volume. The unchanged blood pressure during a stand test is in in this study are all within the physiological limits that have been 9,11,26 accordance with literature and can be attributed to the reflexes as reported . Our model also affords a reasonable prediction of indicated by the markedly increased heart rate. The significant the major impact of gravity on haemodynamic outcomes. Whilst increase in heart rate in even more pronounced on landing day return to Earth following prolonged space travel requires compared to pre-flight conditions (ratio = 1.3) in order to counter adherence to fluid loading protocols, the same person will exhibit hemodynamic resilience to the much lesser gravitational chal- the spaceflight induced changes to the cardiovascular system. lenge caused on the surface of Mars, a planet with merely 10.7% of Earth’s mass. A stand test is a significant challenge for human physiology, as: gravity shifts half a litre of blood from the upper body to venous capacitance vessels of the lower limbs and splanchnic circulation within seconds . The ability of the human body, and here the mathematical model, to maintain blood pressure while standing relies on adequate autonomic function, the key driver of peripheral resistance, on adequate blood volume and on the elastance of heart and vessels. The pronounced orthostatic intolerance after long-duration spaceflight cannot primarily be attributed to abnormalities in the nervous system, since this reflex system is not significantly affected after a long-duration space-flight compared to shorter- duration missions. In fact, following prolonged space flight a stand test is answered by an increase of systemic vascular resistance by 71%, as opposed to merely 50% following short-term flight. Only Fig. 1 Pressure-volume loop: effect of stand test on the left severe impairment of this reflex system of sympathetic vasomotor ventricle before and after a short duration spaceflight. Pressure- activity will lead to hypotension associated with orthostatic volume loop of the left ventricle pre-flight (black) and on landing 21,28,29 syncope . A key literature based input assumption of our day after a short duration space flight (orange), with solid lines modelling approach is that the autonomic function affecting representing the supine position and the dashed lines after standing up. orthostatic tolerance is intact after prolonged exposure to npj Microgravity (2022) 34 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; L.M. van Loon et al. Fig. 2 Hemodynamic responses to stand test pre-flight and on landing day under different conditions. a Is pre-flight, b Landing day after short-duration space flight (<10 days), c Long-duration spaceflight, no fluid loading, and Earth’s gravity, d Long-duration space flight, fluid loading prior to return to Earth, and Earth’s gravity, and e Long-duration space flight, no fluid loading, and Mars’ gravity. Line colours: dashed line = start stand test, red = mean arterial pressure, dashed green = heart rate, black = cardiac output, and blue = central venous pressure. microgravity . With that, our observed orthostatic intolerance after spaceflights. Some individuals have severe symptoms, would result from other factors namely less circulating fluid and despite fluid loading, whereas others are less affected . The structural changes to the cardiovascular system. The role of the individual characterization of adrenergic responses to orthostatic autonomic nerves system on orthostatic intolerance would require stress may therefore be used to predict susceptible individuals 20,21 a dedicated experimental modelling approach. before launch and who could benefit from fluid loading . The Rather, sizable inter-individual variation in baseline function and reflex model is therefore not only quintessential for valid efficacy of the autonomic reflex system may explain the observed simulation results, but also offers opportunities to personalize wide range of individual susceptibility to orthostatic intolerance the model and with that its outcome. Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 34 L.M. van Loon et al. Table 1. Hemodynamic changes to a stand test pre-flight and after a short-duration spaceflight. Setting: Pre-flight Pre-flight Short Short Earth Earth Earth Earth Simulation Literature Simulation Literature Hemodynamic variable Standing-supine Standing-supine [limits] Standing-supine Standing-supine [limits] Ratio SAP (mmHg) −10 (−11%) −11.5 to 4 −12 (−12%) −44.8 to −6 1.2 DAP (mmHg) 3 (0%) 0 to 9 2 (+2%) 1.5 to 7 – MAP (mmHg) −2(−2%) −2to 5 −3(−3%) −30 to 2 2.2 CVP (mmHg) −3(−85%) −5to 2 −2(−102%) n.a. 1.2 HR (bpm) 12 (+16%) 6 to 20.6 16 (+21%) 23.5 to 41 1.3 CO (l/min) −1.8 (−31%) −2.5 to −1 −1.5 (−30%) −1.5 to −1.2 0.8 SV (ml) −32 (−40%) −50.5 to −9 −38 (−46%) −46 to −21.6 0.9 SVR (mmHg*l-1*min) 7 (+46%) 4.3 to 13.6 6 (+32%) 2.1 to 11.3 0.7 Values for supine were taken at t = −50 s. and for standing at t = 100 s of the simulation. All values are differences between standing and supines, except those with brackets -they indicate the percentual changes- and the ratio. The ratio shows the percentual change caused by a stand test after a short-duration space flight divided by percentual change caused by a stand test before a space flight. SAP systolic arterial pressure, DAP diastolic arterial pressure, MAP mean arterial pressure, CVP central venous pressure, HR heart rate, CO cardiac output, SV stroke volume, SVR systemic vascular resistance., n.a. not available. Table 2. Hemodynamic changes to an orthostatic stress test on Earth and Mars after a long-duration spaceflight. Setting: Long Long Long Long Long Long Earth Earth Earth Earth Mars Mars No FL No FL FL + FL + No FL No FL Simulation Literature Simulation Literature Simulation Literature Hemodynamic variable standing-supine standing-supine Standing-supine standing-supine Ratio 1 standing-supine standing-supine Ratio 2 [limits] [limits] SAP (mmHg) −11 (−11%) n.a. −14 (−13%) −42.4 to −5 1.2 −4(−4%) n.a. 0.3 DAP (mmHg) −2(−2%) n.a. 0 (0%) −21.8 to 0 0 1 (+1%) n.a. 0 MAP (mmHg) −6(−7%) n.a. −7(−8%) −28.6 to −5.7 1.1 −1(−1%) n.a. 0.1 CVP (mmHg) −3(−153%) n.a. −3(−124%) n.a. 0.8 −2.0 (−92%) n.a. 0.6 HR (bpm) 39 (+41%) n.a. 29 (+33%) 21.6 to 45 0.8 7 (+7%) n.a. 0.2 CO (l/min) −1.1 (−28%) n.a. −1.5 (−34%) −6.6 to −1.4 1.2 −0.4 (−10%) n.a. 0.3 SV (ml) −20 (−49%) n.a. −23 (−49%) −63.7 to −31.9 1 −6(−16%) n.a. 0.3 SVR (mmHg*l-1*min) 7 (+33%) n.a. 7 (+34%) 9.3 to 19.7 1 3 (+12%) n.a. 0.4 Values for supine were taken at t = −50 s. and for standing at t = 100 s of the simulation. All values are differences between standing and supines, except those with brackets -they indicate the percentual changes- and the ratios. Ratio 1 shows the effect of fluid loading by dividing the percentual change of a stand test with by one without fluid loading. Ratio 2 shows the effect of performing a stand test on Mars versus on Earth by dividing the percentual change caused by a stand test performed on Mars by the same stand test when returning to Earth after a long-duration spaceflight (without fluid loading). SAP systolic arterial pressure, DAP diastolic arterial pressure, MAP mean arterial pressure, CVP central venous pressure, HR heart rate, CO cardiac output, SV stroke volume, SVR systemic vascular resistance, FL fluid loading, n.a. not available. Mars exploration presents a number of challenges, not least as a simulation results showing that performing a stand test after a result of its distance from Earth. NASA currently estimates a travel long-duration space flight in 3/8 G will not induce significant time of seven months , a time essentially spent in microgravity. orthostatic intolerance, even in the absence of a fluid loading The duration of a human Mars mission is determined a long protocol. The simulated stand test with Mars conditions showed a interplanetary travel time of ~7–9 months, plus the duration the drop in cardiac output of 10% despites a compensatory rise in crew must remain on Mars waiting for optimal planetary heart rate of 7%, while the mean arterial pressure was maintained. alignment for return travel . There is limited data assessing the The simulation results that the cardiovascular system is not risk of orthostatic intolerance on exposure to Mars’ gravity and strongly dependant on fluid loading to withstand orthostatic experiments that have attempted to quantify this risk using stress in Mars gravity is comforting, especially since the efficacy of approaches based on lower body negative pressure and 36,37 the NASA fluid loading protocol is questionable . parabolic flight use subjects without cardiovascular decondition- Re-exposure to Earth gravity, after being exposed to Mars and ing from the long-duration spaceflight of interplanetary travel. microgravity of more than 3 years, is expected to cause an Despite post-spaceflight orthostatic intolerance being promi- extremely high rates of orthostatic intolerance from adrenergic nent after return to Earth gravity from long-duration spaceflight, dysfunction and significant cardiac atrophy . It is not known if the consequences are usually minor due to mature counter- 11,12,26 exposure to Mars gravity will provide mitigating/protective effects measures, ground crew support and quick recovery . There- on orthostatic intolerance upon return to 1 G . We speculate that fore, risk assessment for human exploration is paramount at the given the cardiovascular stress induced by Mars gravity in our Mars side, as astronauts will re-enter (albeit reduced) gravity simulation is minimal, and it will be followed by the long-duration without medical and support infrastructure, no option for medical evacuation, and transmission delays from Earth based physicians of microgravity during interplanetary travel back to Earth, any of up to twenty minutes . We are not aware of any other protective effect will be negligible. npj Microgravity (2022) 34 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA L.M. van Loon et al. Previous parabolic flight data on subjects without cardiovas- future space flights should be able to perform autonomous care, cular deconditioning of long duration spaceflight shows that the handling medical conditions and emergencies without immediate magnitude of blood pressure reduction and heart rate response real-time support from Earth. during a stand test is dependent on gravitational loading [57] In conclusion, the presented mathematical model is capable of which is consistent with our results. Validation of a stand test in adequately simulating key cardiovascular hemodynamic changes - Mars gravity after prolonged spaceflight is not possible, but over a short time frame - during a stand test after prolonged knowing that the model is capable of simulating return to Earth spaceflight under different gravitational conditions and fluid after a long-duration spaceflight does reassure that model loading conditions. This model can form the basis for further responses to a change of a single model parameter (from 1 G to exploration of the ability of the human cardiovascular system to 3/8 G) is trustworthy. withstand long-duration space flight and life on Mars. To achieve our objective of simulating the response of the hemodynamic system to orthostatic stress after exposure to space 18,38 travel in different gravitational conditions, like others ,we METHODS chose to model the hemodynamic system by a finite set of Model requirements representative compartments, each of which captures the physical The main focus of this mathematical model is to simulate the properties of a segment of the vascular system. In doing so, we response of the hemodynamic system to orthostatic stress under implicitly assume that the dynamics of the system can be different gravitational conditions after exposure to space travel of simulated by restricting our analysis to relatively few representa- short and long-duration. This response will be simulated on a tive points within the cardiovascular system. Although this short-term time scale (2–250 s). Output requirements are a approach is incapable of simulating pulse wave propagation, for number of key physiological variables that can characterize example, it does reproduce realistic values of beat-by-beat orthostatic stress and that are routinely monitored clinically, in hemodynamic parameters . particular pulsative arterial and venous blood pressure (both It is well established that there is a gender difference in systemic and pulmonary), cardiac output, heart rate, and orthostatic tolerance both for Earth bound subjects and for respiratory rate .A final qualitative requirement is that this 41,42 astronauts with women having significantly higher incidence model represents the cardiorespiratory system of an averagely of presyncope during stand tests than men. This is thought to be trained, healthy, adult male astronaut; a population for which we due to low vascular resistance , decreased arterial baroreflex have explicit target data . 44 45,46 compensation and smaller stroke volumes . The model 18,50,51 In this paper, currently available models are extended and presented here represents a healthy adult male astronaut and adapted using parameters for short- and long-duration space does not include any gender effects. With increasing numbers of 17,19,22 flights . The orthostatic stress test will be simulated with female astronauts experiencing long-duration spaceflight, a logical Earth’s and Mars’ gravity. Model parameters will be based on extension of this work would be to include a gendered analysis literature values as much as possible. Newly introduced para- which may provide further insights into cardiovascular decondi- meters will be chosen to target available experimental data in the tioning of spaceflight as well other disorders of orthostatic 47 best way possible. The simulation results will be validated with intolerance such as postural tachycardia syndrome . 8,20–22 available orthostatic stress experiments in astronauts . Current space travels, especially the long ones, have shown that exercise is key to maintain muscle strength, bone health, and Conceptual model cardiac performance . Our model is limited in the sense that is assumes the presence of a strict exercise program during the The base model used here was built upon the work of Beneken , 39 18 space travel. Heldt and Gerber , who provide a controlled 21-compartment Last, an inherent limitation to any modelling effort is the degree of model of human cardiovascular system. The here presented uncertainty with which numerical values can be assigned to the conceptual model mimics the one described by Gerber at al. various parameters of the model. The origin of the parameter values (Fig. 3). we chose to assign has been provided where possible. The degree to which the model reproduces steady-state and transient hemody- Mathematical model namic data suggests that the present model architecture includes all This controlled cardiovascular response to gravity model (Fig. 3)is the major features that contribute significantly to the transient and 15,38 for the largest part described by two fundamental laws of physics. steady-state hemodynamic responses to orthostatic stress . We employed the classic definition of compliance/elastance to Travelling to Mars will challenge human health and well-being. calculate the pressure in a particular compartment based on the We here provide a first-layer reductionist approach assessing that volume. We applied Ohm’s law to fluid mechanics to calculate it is safe to travel to Mars under the perspective of hemodynamic flow by dividing a pressure difference by resistance, and resilience to orthostatic stress. Future models should focus on subsequently updates the volume based on this flow. Therefore, combining modelling results of multiple organs. Especially each of the 21 compartments were characterized with an inflow/ relevant for predicting syncope in astronauts would be to extend outflow resistance, elastance and unstressed volume. The volume our model with a lung and brain perfusion model. These that stretches the walls is called stressed volume and the rest is additional organ models would also allow further insight into called unstressed volume . The elastance governs relationship the effect of an inhaled gas mixture and cerebral vascular between stressed volume (total blood volume in a given response . Furthermore, adapting mathematical models of compartment minus its unstressed volume) and pressure . The physiology from healthy subject to groups or even individuals, heart compartments have both a minimum and maximum could enable healthcare providers to safely model and assess the elastance in order to generate pressure. Furthermore, the impacts of space travel. It also enables providers to remotely test elastances of the lower body venous compartments (compart- potential interventions to simulate their efficacy on individuals or ment no 10, 12, and 13) were made non-linear . identify adverse impacts to provide an informed and best-case The heart was treated as a pressure source - together with the treatment for a passenger or an astronaut patient. The future of presence of valves - where the elastances of the four heart medical care in space will be enabled by increasing autonomy and support from clinical decision-support systems to assess a much compartments (compartments; 15, 16, 19 and 20) switch between broader variety of prospective travellers. Healthcare providers will minimum (diastole) and maximum (systole) elastance .Asmooth need greater capabilities to assess fitness to fly and for those on transition between these two values was modelled by an out-of-sync Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 34 L.M. van Loon et al. Fig. 3 Diagram and conceptual model of the 21-compartment cardiovascular model. 0: Ascending aorta. 1: Brachiocephalic arteries. 2: Upperbody arteries. 3: Upper body veins. 4: Superior vena cava. 5: Thoracic aorta. 6: Abdominal aorta. 7: Renal arteries. 8: Renal veins. 9: Splanchnic arteries. 10: Splanchnic veins. 11: Lower body arteries. 12: Lower body veins. 13: Abdominalveins. 14: Thoracic inferior vena cava. 15: Right atrium. 16: Right ventricle. 17: Pulmonary arteries. 18: Pulmonary veins. 19: Left atrium. 20: Left ventricle. a Anatomic model. Dashed square indicated the intrathoracic pressure. b Hydraulic circuit model. The orange circles with numbers are elastic elements with a pre and post resistance in blue and annotated with Roman numbers. The cardiac compartments are illustrated with red circles and represent time- variant elastances, together with their valves (green single triangles). The dashed rectangle outlines the intrathoracic compartments, and the brown wide-dashed line with round arrowheads indicates the lymphatic flow from the lower and upper body to the super vena cava. The 18,39 green and red apple indicate gravity and its direction (green = added, red = subtracted) . sinusoidal curve , with one curve representing the atria, while the other was used for the ventricles (Fig. 4). For timing of these curves, the maximum atrial elastance was placed at 0.2 s and the maximum of the ventricular elastance at 0.3 s with an offset of 0.12 .These timing constants were dynamically adjusted to the heart rate by multiplying them by the square root of the heart rate period . The base model is controlled by arterial baroreflex (ABR) and cardiopulmonary reflex (CPR) as short-term blood pressure regulation, mimicking the sympathetic and parasympathetic nervous signals . Figure 5 shows the steps that are involved in adjusting multiple cardiovascular effector sides in order to bring the two measured blood pressures (arterial and venous) close to their predefined static set-point. The reflex mechanisms are set- point controllers that aim at minimizing an error signal (see Supplementary Table 2 for reflex parameters). In short: Step I; pressure and pulse pressure of compartment 0 (aortic Fig. 4 Time-varying heart elastances. Red lines indicate the left arch) and pressure of compartment 15 (right atrium) were heart, and blue lines the right heart. Dashed lines indicate the atria, integrated over 250 data points. Step II; an error signal was and solid lines the ventricles. created by subtracting predefined static set-points − 95 mmHg for arterial, 35 mmHg for pulse pressure and 3 mmHg for venous pressure - from this integrated signal. This error signal was Transcapillary fluid exchange in the extremities (compartment 3 subsequently scaled, as described by deBoer et al. , using an and 12) was incorporated by using Starling forces (hydrostatic and inverse tangent together with scale limits of 18 and 5 for the ABR oncotic pressure) in accordance with Heldt’s and Gerber’s and CPR respectively. Step III; the scaled error signals were 18,51,61,62 models (see Supplementary Table 1 for the parameters). thereafter convolved with 6 different unit-area impulse response This allows fluid to move from the intravascular space into the functions in order to describe the different reflex components of interstitial space in the upper and lower half of the body. In the autonomic nerves system. In the last step, step IV, the resulting addition, a pathway was used to move excessive interstitial fluid vector from the convolution is multiplied by effector mechanism- specific static gain values to produce the 6 different effector via a lymphatic pump back to the superior vena cava (compart- pathways that eventually influence the heart rate, contractility, ment 4). This pathway is shown with a thick brown dashed line on peripheral resistance, and unstressed volume . the left side of the conceptual model (Fig. 3). npj Microgravity (2022) 34 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA L.M. van Loon et al. Fig. 5 Schematic overview of the baro- and cardiopulmonary reflex control model. Step I; create a mean blood pressure, Step II; create an error signal, Step III convolute the error signal with 6 different impulse responses, and step IV; influence hemodynamic effector sides. See text section 2.3.2, ref. , and model code for more information. or subtracting (red apples in Fig. 3) a hydrostatic pressure to driving pressure of blood flow between two adjacent compart- ments. The hydrostatic pressures are the result of the vessel length times a gravity pressure, and was calculated using below equation. Hydrostatic pressure ¼ ρ  g  vessel length  sinðaÞ (1) where ρ is density of the blood (1060 kg/m^3), g is either Earth’s gravitational acceleration (9.81 m/s^2) or Mars’ (3.721 m/s^2), and the vessel length in meter (see Supplementary Table 1) is under consideration of its angle (α) with respect to the horizontal plane . A smooth transition of gravity from zero to maximum gravity was parameterized by using a sinusoidal curve to parameterize the tilt angle alpha from 0 to 90 degrees over 5 s . Finally, muscle contraction preceding the changes in posture were incorporated by reducing the effect of the hydrostatic pressure on the intravascular pressure by a factor 2 and 3 for the Fig. 6 Ventilation. Simulated intra-thoracic pressure curve with a legs and abdominal compartment, respectively. This reflects on respiratory rate of 12/min. the higher pressure produced by muscle contraction in the latter compartment . The result of respiration induced changes in intrathoracic Oral fluid loading is often used with the intent of increasing pressure is implemented by forcing the intrathoracic pressure on plasma volume and maintaining mean arterial pressure during specific (intrathoracic) compartments (see Fig. 3, compartments orthostatic stress . The NASA fluid loading countermeasure that sits within the dashed line). The intrathoracic pressure was protocol uses 15 ml/kg of body weight of water with 1 g of NaCl parameterization-based on the average profile of the respiratory per 125 ml of water several hours before re-entry . We assumed 63,64 muscle activity as proposed by Mecklenburgh and Mapleson , this protocol to be effective in the sense that it is able to increase see Fig. 6.A fixed respiratory rate of 12/min was used, with an plasma fluid by ~8% . This was implemented by increasing the inspiration to expiration ratio of 0.6 . Intrathoracic pressure is intravascular total blood volume with 5% at t = 0, since plasma influenced by the effect of gravity on the abdomen and chest wall, volume is ~60% of the total blood volume . and is posture dependent, therefore we used the angle of the subject with respect to the horizontal plane to adjust the Parameter estimation intrathoracic pressure . In upright postures the intrathoracic Initial model parameters, including the reflex parameters and the pressure decreases with increased gravity as the abdominal mass resistance, elastance, unstressed volumes, vascular lengths of each and diaphragm are pulled downwards, while this increase in cardiovascular unit were obtained from Heldt’s thesis on gravity will increase the intrathoracic pressure in recumbent 67 51 cardiovascular response to orthostatic stress . This set of postures as the abdominal mass moves head ward . parameters describes a healthy adult male under unstressed Gravitational tolerance is assessed by simulating a stand test, an active supine-to-stand task, because it is the most clinically condition in Earth’s gravity. Parameters were then adjusted to relevant test and experimental data from astronauts post mimic both short- and long-duration space flight and different spaceflights are available for model validation . The effect of levels of gravity. No changes to the conceptual model of the standing is incorporated by either adding (green apples in Fig. 5) cardiovascular system (i.e. vessel length or connection between Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 34 L.M. van Loon et al. compartments) when simulating the effect of microgravity. Using CODE AVAILABILITY existing (clinical) literature, primarily following Gallo et al. and The model code and all model parameters are available from the corresponding author on reasonable request. Mohammadyari et al. who did a comprehensive review of this literature for long- and short-duration space flight respectively. The rational for the long-duration setting can be found in the Received: 17 January 2022; Accepted: 15 July 2022; supplementary information of Gallo et al.’s work . 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A., van Meurs, W. L., Sá Couto, C. D., Beneken, J. E. W. & Graves, S. A. A L.M.vL. and E.T. build the model and designed the experiments. L.M.vL., E.T., and A.S. model for educational simulation of infant cardiovascular physiology. Anesth. analyzed the data. All authors validated the results. L.M.vL. wrote the paper. All Analg. 99, 1655–1664, table of contents (2004). authors reviewed and approved the final version of the manuscript. Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 34 L.M. van Loon et al. 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Computational modeling of orthostatic intolerance for travel to Mars

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www.nature.com/npjmgrav ARTICLE OPEN Computational modeling of orthostatic intolerance for travel to Mars 1✉ 1 1 1 1 Lex M. van Loon , Anne Steins , Klaus-Martin Schulte , Russell Gruen and Emma M. Tucker Astronauts in a microgravity environment will experience significant changes in their cardiopulmonary system. Up until now, there has always been the reassurance that they have real-time contact with experts on Earth. Mars crew however will have gaps in their communication of 20 min or more. In silico experiments are therefore needed to assess fitness to fly for those on future space flights to Mars. In this study, we present an open-source controlled lumped mathematical model of the cardiopulmonary system that is able simulate the short-term adaptations of key hemodynamic parameters to an active stand test after being exposed to microgravity. The presented model is capable of adequately simulating key cardiovascular hemodynamic changes—over a short time frame—during a stand test after prolonged spaceflight under different gravitational conditions and fluid loading conditions. This model can form the basis for further exploration of the ability of the human cardiovascular system to withstand long-duration space flight and life on Mars. npj Microgravity (2022) 8:34 ; https://doi.org/10.1038/s41526-022-00219-2 INTRODUCTION loss of consciousness and postural tone due to global cerebral hypoperfusion followed by complete recovery) or POTS (experi- Microgravity defines an environment where gravitational forces enced as lightheadedness, palpitations, tremulousness and on the human body are significantly less than those experienced on planet Earth. The fluid compartments of the human body are weakness) . expectedly most prone to immediate and mid-term effects, whilst Twenty to thirty percent of astronauts returning from short 8–10 duration space flights and ~80% of astronauts returning after solid organ composition may adapt to altered feedback loops as most evident in the musculoskeletal system. Exposure to long-duration space flight experience symptomatic orthostatic 11,12 microgravity profoundly changes cardiovascular hemodynamics. intolerance , compared with only 5% of the unexposed general Compared to upright posture on Earth, fluid rapidly redistributes population under 50 years of age . from the bottom half to the top half of the body. Reduced venous Symptoms can be prevented or managed with inflight lower pooling in the copious lower extremity territory is followed by a body negative pressure (LBNP) , fluid loading, compression rapid contraction of plasma volume. This is primarily due to garments, and pharmacological therapy on re-entry into Earth’s transcapillary fluid filtration into upper-body interstitial spaces, gravitational field. In absence of a specialist ground support team, exacerbated by any reduction of fluid intake, and leads to a as would be the case in early missions to Mars, post-flight 1–3 10–15% reduction of the extracellular fluid volume . orthostatic intolerance after such long-duration spaceflight con- Alongside fluid maldistribution, autonomic dysfunction occurs stitutes a significant risk to astronaut safety and mission success . within a few days of microgravity exposure. Whilst inapparent in Management algorithms suited to all possible scenarios are space, it causes inadequate vasoconstriction and lack of respon- needed. siveness and adaptability of total peripheral resistance on Modelling the cardiovascular system engages productive cycles 4,5 14,15 standing following return to Earth . In addition, cardiac atrophy of insight into the underlying physiological processes .It isa occurs rapidly in microgravity, likely due to the reduced safe, cost-effective and feasible way to predict changes and contractility required to maintain adequate arterial pressure . responses to treatment in space travelers. The approach has been Convergent lines of deconditioning cause an inability of the 16,17 used to simulate post flight orthostatic intolerance , short-term cardiovascular system to adapt to gravitational exposure upon a adaptations to low gravity and the effectiveness of the LBNP return to Earth and maintain adequate blood pressure in an countermeasure , and cardiovascular deconditioning during upright position . This is known as post (space) flight orthostatic long-term space flight . However, the effect of a prolonged intolerance. (>6 months) exposure to microgravity on orthostatic intolerance Orthostatic intolerance can be due to orthostatic hypotension, has never been modelled. Neither is there any modelling available neurally mediated (reflex) syncope, and postural tachycardia showing the response of the cardiovascular system to travelling to syndrome (POTS). Where orthostatic hypotension is defined as a Mars and performing an active stand test there. The primary sustained reduction of systolic blood pressure of at least 20 mmHg objective of the here presented model is to predict if humans can or diastolic blood pressure of 10 mmHg within 3 mins of standing withstand orthostatic stress on arrival on Mars after prolonged or head up tilt to at least 60 degrees and POTS is defined as a space travel. We aimed to develop a model suitable for short- and sustained heart rate of >30 beats/min within 10 mins of standing long-duration spaceflight, simulate re-entry to Earth’s and Mars’ or head up tilt in the absence of orthostatic hypotension. It is experienced as presyncope (symptoms of global cerebral hypo- gravity, and validate the model using previous orthostatic stress 8,20–22 perfusion without loss of consciousness) or syncope (a transient experiments in astronauts . College of Health and Medicine, Australian National University, Canberra, ACT, Australia. email: lexmaxim.vanloon@anu.edu.au Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; L.M. van Loon et al. RESULTS Long-duration spaceflight The key simulation results and available relevant physiological Table 2 and Fig. 2 show the hemodynamic responses to a stand data from astronauts pre-flight and on landing day are compared test after a long-duration (>6 months) spaceflight with or without fluid loading, and under either Earth’s or Mars’ gravitational in Figs. 1, 2 and Tables 1, 2. The effect of the stand test was conditions. The simulation results from the scenario in which assessed by observing the mean arterial pressure (pressure in orthostatic stress was tested in an astronaut on landing day with compartment 0), the central venous pressure (pressure in fluid loading prior to returning to Earth show to be within the compartment 15), cardiac output (flow into compartment 0), reported limits from experimental data. and heart rate. Results for in supine position were taken at Fluid loading in our simulations had minor positive effect on t = −50 s and for the standing position were taken at t = 100 s. MAP (< + 2 mmHg) but did prevent a major dip in MAP during a stand test (Fig. 2). This was mainly achieved by decreasing heart Pre-flight conditions rate (−5 bpm), increasing the cardiac output (+.4 l), and stroke Representative simulated pressure-volume loops of the left volume (+ 6 ml) prior to the stand test. Last, Table 2 and Fig. 2 also show results of simulating a stand ventricle during supine and standing position are shown in test on Mars after a prolonged spaceflight. The resulting Fig. 1. Table 1 and Fig. 2 panel A demonstrates that all key hemodynamic changes to this orthostatic stress test on Mars are physiological variables generated by the model are within the less pronounced compared to when performed on Earth, even if range of what is considered physiologically normal for our target one on Earth is preceded by fluid loading. Even more so, the stand population - i.e. well trained, healthy, adult males – for a steady test on Mars shows similar results to the pre-flight condition state supine position as well as for the dynamic response to a on Earth. 11,23,24 stand test . This pressure-volume loops show physiological correct values for systolic blood pressure (~122 mmHg), diastolic blood pressure (~81 mmHg), diastolic filling pressure (~8 mmHg), DISCUSSION and stroke volume (~71 ml) . Exposure of the human body to orthostatic stress evokes prominent short-term physiological responses that aim at main- Short-duration spaceflight taining blood pressure. We here provide a physiological model capable of simulating these responses. Modelling outcomes The hemodynamic responses to a stand test of an astronaut on adequately reflect on real-life physiology, as exemplified by landing day on Earth, after being in space for a maximum of model predictions of key physiological parameters following 10 days, are shown in Table 1, Fig. 2 panel B. All values are within variations of parameters such as fluid loading, i.e. circulatory blood normal ranges of published experimental data from real astro- volume, or the length of exposure to microgravity. For such nauts performing a stand test on landing day post short-duration scenarios, model predictions are in line with real-life observations 11,23 spaceflight . Although the experimental data varies and obtained in astronauts following space flight. include both presyncopal and nonpresyncopal subjects, the trend Simulation results confirm the observed impact of prolonged and the relative changes of the key hemodynamic variables space travel on haemodynamic resilience to a stand test, and the 17,19 simulated by our model match well with experimental data . crucial importance of fluid loading to avert adverse outcomes in Table 1 shows that mean and diastolic blood pressure during terms of significant drops of mean arterial pressure and excessive supine and standing position are equal to each other and to the tachycardia, at least in the short term. The differences between baseline simulation despite a significant decrease in stroke key hemodynamic variables during standing and supine position volume. The unchanged blood pressure during a stand test is in in this study are all within the physiological limits that have been 9,11,26 accordance with literature and can be attributed to the reflexes as reported . Our model also affords a reasonable prediction of indicated by the markedly increased heart rate. The significant the major impact of gravity on haemodynamic outcomes. Whilst increase in heart rate in even more pronounced on landing day return to Earth following prolonged space travel requires compared to pre-flight conditions (ratio = 1.3) in order to counter adherence to fluid loading protocols, the same person will exhibit hemodynamic resilience to the much lesser gravitational chal- the spaceflight induced changes to the cardiovascular system. lenge caused on the surface of Mars, a planet with merely 10.7% of Earth’s mass. A stand test is a significant challenge for human physiology, as: gravity shifts half a litre of blood from the upper body to venous capacitance vessels of the lower limbs and splanchnic circulation within seconds . The ability of the human body, and here the mathematical model, to maintain blood pressure while standing relies on adequate autonomic function, the key driver of peripheral resistance, on adequate blood volume and on the elastance of heart and vessels. The pronounced orthostatic intolerance after long-duration spaceflight cannot primarily be attributed to abnormalities in the nervous system, since this reflex system is not significantly affected after a long-duration space-flight compared to shorter- duration missions. In fact, following prolonged space flight a stand test is answered by an increase of systemic vascular resistance by 71%, as opposed to merely 50% following short-term flight. Only Fig. 1 Pressure-volume loop: effect of stand test on the left severe impairment of this reflex system of sympathetic vasomotor ventricle before and after a short duration spaceflight. Pressure- activity will lead to hypotension associated with orthostatic volume loop of the left ventricle pre-flight (black) and on landing 21,28,29 syncope . A key literature based input assumption of our day after a short duration space flight (orange), with solid lines modelling approach is that the autonomic function affecting representing the supine position and the dashed lines after standing up. orthostatic tolerance is intact after prolonged exposure to npj Microgravity (2022) 34 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; L.M. van Loon et al. Fig. 2 Hemodynamic responses to stand test pre-flight and on landing day under different conditions. a Is pre-flight, b Landing day after short-duration space flight (<10 days), c Long-duration spaceflight, no fluid loading, and Earth’s gravity, d Long-duration space flight, fluid loading prior to return to Earth, and Earth’s gravity, and e Long-duration space flight, no fluid loading, and Mars’ gravity. Line colours: dashed line = start stand test, red = mean arterial pressure, dashed green = heart rate, black = cardiac output, and blue = central venous pressure. microgravity . With that, our observed orthostatic intolerance after spaceflights. Some individuals have severe symptoms, would result from other factors namely less circulating fluid and despite fluid loading, whereas others are less affected . The structural changes to the cardiovascular system. The role of the individual characterization of adrenergic responses to orthostatic autonomic nerves system on orthostatic intolerance would require stress may therefore be used to predict susceptible individuals 20,21 a dedicated experimental modelling approach. before launch and who could benefit from fluid loading . The Rather, sizable inter-individual variation in baseline function and reflex model is therefore not only quintessential for valid efficacy of the autonomic reflex system may explain the observed simulation results, but also offers opportunities to personalize wide range of individual susceptibility to orthostatic intolerance the model and with that its outcome. Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 34 L.M. van Loon et al. Table 1. Hemodynamic changes to a stand test pre-flight and after a short-duration spaceflight. Setting: Pre-flight Pre-flight Short Short Earth Earth Earth Earth Simulation Literature Simulation Literature Hemodynamic variable Standing-supine Standing-supine [limits] Standing-supine Standing-supine [limits] Ratio SAP (mmHg) −10 (−11%) −11.5 to 4 −12 (−12%) −44.8 to −6 1.2 DAP (mmHg) 3 (0%) 0 to 9 2 (+2%) 1.5 to 7 – MAP (mmHg) −2(−2%) −2to 5 −3(−3%) −30 to 2 2.2 CVP (mmHg) −3(−85%) −5to 2 −2(−102%) n.a. 1.2 HR (bpm) 12 (+16%) 6 to 20.6 16 (+21%) 23.5 to 41 1.3 CO (l/min) −1.8 (−31%) −2.5 to −1 −1.5 (−30%) −1.5 to −1.2 0.8 SV (ml) −32 (−40%) −50.5 to −9 −38 (−46%) −46 to −21.6 0.9 SVR (mmHg*l-1*min) 7 (+46%) 4.3 to 13.6 6 (+32%) 2.1 to 11.3 0.7 Values for supine were taken at t = −50 s. and for standing at t = 100 s of the simulation. All values are differences between standing and supines, except those with brackets -they indicate the percentual changes- and the ratio. The ratio shows the percentual change caused by a stand test after a short-duration space flight divided by percentual change caused by a stand test before a space flight. SAP systolic arterial pressure, DAP diastolic arterial pressure, MAP mean arterial pressure, CVP central venous pressure, HR heart rate, CO cardiac output, SV stroke volume, SVR systemic vascular resistance., n.a. not available. Table 2. Hemodynamic changes to an orthostatic stress test on Earth and Mars after a long-duration spaceflight. Setting: Long Long Long Long Long Long Earth Earth Earth Earth Mars Mars No FL No FL FL + FL + No FL No FL Simulation Literature Simulation Literature Simulation Literature Hemodynamic variable standing-supine standing-supine Standing-supine standing-supine Ratio 1 standing-supine standing-supine Ratio 2 [limits] [limits] SAP (mmHg) −11 (−11%) n.a. −14 (−13%) −42.4 to −5 1.2 −4(−4%) n.a. 0.3 DAP (mmHg) −2(−2%) n.a. 0 (0%) −21.8 to 0 0 1 (+1%) n.a. 0 MAP (mmHg) −6(−7%) n.a. −7(−8%) −28.6 to −5.7 1.1 −1(−1%) n.a. 0.1 CVP (mmHg) −3(−153%) n.a. −3(−124%) n.a. 0.8 −2.0 (−92%) n.a. 0.6 HR (bpm) 39 (+41%) n.a. 29 (+33%) 21.6 to 45 0.8 7 (+7%) n.a. 0.2 CO (l/min) −1.1 (−28%) n.a. −1.5 (−34%) −6.6 to −1.4 1.2 −0.4 (−10%) n.a. 0.3 SV (ml) −20 (−49%) n.a. −23 (−49%) −63.7 to −31.9 1 −6(−16%) n.a. 0.3 SVR (mmHg*l-1*min) 7 (+33%) n.a. 7 (+34%) 9.3 to 19.7 1 3 (+12%) n.a. 0.4 Values for supine were taken at t = −50 s. and for standing at t = 100 s of the simulation. All values are differences between standing and supines, except those with brackets -they indicate the percentual changes- and the ratios. Ratio 1 shows the effect of fluid loading by dividing the percentual change of a stand test with by one without fluid loading. Ratio 2 shows the effect of performing a stand test on Mars versus on Earth by dividing the percentual change caused by a stand test performed on Mars by the same stand test when returning to Earth after a long-duration spaceflight (without fluid loading). SAP systolic arterial pressure, DAP diastolic arterial pressure, MAP mean arterial pressure, CVP central venous pressure, HR heart rate, CO cardiac output, SV stroke volume, SVR systemic vascular resistance, FL fluid loading, n.a. not available. Mars exploration presents a number of challenges, not least as a simulation results showing that performing a stand test after a result of its distance from Earth. NASA currently estimates a travel long-duration space flight in 3/8 G will not induce significant time of seven months , a time essentially spent in microgravity. orthostatic intolerance, even in the absence of a fluid loading The duration of a human Mars mission is determined a long protocol. The simulated stand test with Mars conditions showed a interplanetary travel time of ~7–9 months, plus the duration the drop in cardiac output of 10% despites a compensatory rise in crew must remain on Mars waiting for optimal planetary heart rate of 7%, while the mean arterial pressure was maintained. alignment for return travel . There is limited data assessing the The simulation results that the cardiovascular system is not risk of orthostatic intolerance on exposure to Mars’ gravity and strongly dependant on fluid loading to withstand orthostatic experiments that have attempted to quantify this risk using stress in Mars gravity is comforting, especially since the efficacy of approaches based on lower body negative pressure and 36,37 the NASA fluid loading protocol is questionable . parabolic flight use subjects without cardiovascular decondition- Re-exposure to Earth gravity, after being exposed to Mars and ing from the long-duration spaceflight of interplanetary travel. microgravity of more than 3 years, is expected to cause an Despite post-spaceflight orthostatic intolerance being promi- extremely high rates of orthostatic intolerance from adrenergic nent after return to Earth gravity from long-duration spaceflight, dysfunction and significant cardiac atrophy . It is not known if the consequences are usually minor due to mature counter- 11,12,26 exposure to Mars gravity will provide mitigating/protective effects measures, ground crew support and quick recovery . There- on orthostatic intolerance upon return to 1 G . We speculate that fore, risk assessment for human exploration is paramount at the given the cardiovascular stress induced by Mars gravity in our Mars side, as astronauts will re-enter (albeit reduced) gravity simulation is minimal, and it will be followed by the long-duration without medical and support infrastructure, no option for medical evacuation, and transmission delays from Earth based physicians of microgravity during interplanetary travel back to Earth, any of up to twenty minutes . We are not aware of any other protective effect will be negligible. npj Microgravity (2022) 34 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA L.M. van Loon et al. Previous parabolic flight data on subjects without cardiovas- future space flights should be able to perform autonomous care, cular deconditioning of long duration spaceflight shows that the handling medical conditions and emergencies without immediate magnitude of blood pressure reduction and heart rate response real-time support from Earth. during a stand test is dependent on gravitational loading [57] In conclusion, the presented mathematical model is capable of which is consistent with our results. Validation of a stand test in adequately simulating key cardiovascular hemodynamic changes - Mars gravity after prolonged spaceflight is not possible, but over a short time frame - during a stand test after prolonged knowing that the model is capable of simulating return to Earth spaceflight under different gravitational conditions and fluid after a long-duration spaceflight does reassure that model loading conditions. This model can form the basis for further responses to a change of a single model parameter (from 1 G to exploration of the ability of the human cardiovascular system to 3/8 G) is trustworthy. withstand long-duration space flight and life on Mars. To achieve our objective of simulating the response of the hemodynamic system to orthostatic stress after exposure to space 18,38 travel in different gravitational conditions, like others ,we METHODS chose to model the hemodynamic system by a finite set of Model requirements representative compartments, each of which captures the physical The main focus of this mathematical model is to simulate the properties of a segment of the vascular system. In doing so, we response of the hemodynamic system to orthostatic stress under implicitly assume that the dynamics of the system can be different gravitational conditions after exposure to space travel of simulated by restricting our analysis to relatively few representa- short and long-duration. This response will be simulated on a tive points within the cardiovascular system. Although this short-term time scale (2–250 s). Output requirements are a approach is incapable of simulating pulse wave propagation, for number of key physiological variables that can characterize example, it does reproduce realistic values of beat-by-beat orthostatic stress and that are routinely monitored clinically, in hemodynamic parameters . particular pulsative arterial and venous blood pressure (both It is well established that there is a gender difference in systemic and pulmonary), cardiac output, heart rate, and orthostatic tolerance both for Earth bound subjects and for respiratory rate .A final qualitative requirement is that this 41,42 astronauts with women having significantly higher incidence model represents the cardiorespiratory system of an averagely of presyncope during stand tests than men. This is thought to be trained, healthy, adult male astronaut; a population for which we due to low vascular resistance , decreased arterial baroreflex have explicit target data . 44 45,46 compensation and smaller stroke volumes . The model 18,50,51 In this paper, currently available models are extended and presented here represents a healthy adult male astronaut and adapted using parameters for short- and long-duration space does not include any gender effects. With increasing numbers of 17,19,22 flights . The orthostatic stress test will be simulated with female astronauts experiencing long-duration spaceflight, a logical Earth’s and Mars’ gravity. Model parameters will be based on extension of this work would be to include a gendered analysis literature values as much as possible. Newly introduced para- which may provide further insights into cardiovascular decondi- meters will be chosen to target available experimental data in the tioning of spaceflight as well other disorders of orthostatic 47 best way possible. The simulation results will be validated with intolerance such as postural tachycardia syndrome . 8,20–22 available orthostatic stress experiments in astronauts . Current space travels, especially the long ones, have shown that exercise is key to maintain muscle strength, bone health, and Conceptual model cardiac performance . Our model is limited in the sense that is assumes the presence of a strict exercise program during the The base model used here was built upon the work of Beneken , 39 18 space travel. Heldt and Gerber , who provide a controlled 21-compartment Last, an inherent limitation to any modelling effort is the degree of model of human cardiovascular system. The here presented uncertainty with which numerical values can be assigned to the conceptual model mimics the one described by Gerber at al. various parameters of the model. The origin of the parameter values (Fig. 3). we chose to assign has been provided where possible. The degree to which the model reproduces steady-state and transient hemody- Mathematical model namic data suggests that the present model architecture includes all This controlled cardiovascular response to gravity model (Fig. 3)is the major features that contribute significantly to the transient and 15,38 for the largest part described by two fundamental laws of physics. steady-state hemodynamic responses to orthostatic stress . We employed the classic definition of compliance/elastance to Travelling to Mars will challenge human health and well-being. calculate the pressure in a particular compartment based on the We here provide a first-layer reductionist approach assessing that volume. We applied Ohm’s law to fluid mechanics to calculate it is safe to travel to Mars under the perspective of hemodynamic flow by dividing a pressure difference by resistance, and resilience to orthostatic stress. Future models should focus on subsequently updates the volume based on this flow. Therefore, combining modelling results of multiple organs. Especially each of the 21 compartments were characterized with an inflow/ relevant for predicting syncope in astronauts would be to extend outflow resistance, elastance and unstressed volume. The volume our model with a lung and brain perfusion model. These that stretches the walls is called stressed volume and the rest is additional organ models would also allow further insight into called unstressed volume . The elastance governs relationship the effect of an inhaled gas mixture and cerebral vascular between stressed volume (total blood volume in a given response . Furthermore, adapting mathematical models of compartment minus its unstressed volume) and pressure . The physiology from healthy subject to groups or even individuals, heart compartments have both a minimum and maximum could enable healthcare providers to safely model and assess the elastance in order to generate pressure. Furthermore, the impacts of space travel. It also enables providers to remotely test elastances of the lower body venous compartments (compart- potential interventions to simulate their efficacy on individuals or ment no 10, 12, and 13) were made non-linear . identify adverse impacts to provide an informed and best-case The heart was treated as a pressure source - together with the treatment for a passenger or an astronaut patient. The future of presence of valves - where the elastances of the four heart medical care in space will be enabled by increasing autonomy and support from clinical decision-support systems to assess a much compartments (compartments; 15, 16, 19 and 20) switch between broader variety of prospective travellers. Healthcare providers will minimum (diastole) and maximum (systole) elastance .Asmooth need greater capabilities to assess fitness to fly and for those on transition between these two values was modelled by an out-of-sync Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 34 L.M. van Loon et al. Fig. 3 Diagram and conceptual model of the 21-compartment cardiovascular model. 0: Ascending aorta. 1: Brachiocephalic arteries. 2: Upperbody arteries. 3: Upper body veins. 4: Superior vena cava. 5: Thoracic aorta. 6: Abdominal aorta. 7: Renal arteries. 8: Renal veins. 9: Splanchnic arteries. 10: Splanchnic veins. 11: Lower body arteries. 12: Lower body veins. 13: Abdominalveins. 14: Thoracic inferior vena cava. 15: Right atrium. 16: Right ventricle. 17: Pulmonary arteries. 18: Pulmonary veins. 19: Left atrium. 20: Left ventricle. a Anatomic model. Dashed square indicated the intrathoracic pressure. b Hydraulic circuit model. The orange circles with numbers are elastic elements with a pre and post resistance in blue and annotated with Roman numbers. The cardiac compartments are illustrated with red circles and represent time- variant elastances, together with their valves (green single triangles). The dashed rectangle outlines the intrathoracic compartments, and the brown wide-dashed line with round arrowheads indicates the lymphatic flow from the lower and upper body to the super vena cava. The 18,39 green and red apple indicate gravity and its direction (green = added, red = subtracted) . sinusoidal curve , with one curve representing the atria, while the other was used for the ventricles (Fig. 4). For timing of these curves, the maximum atrial elastance was placed at 0.2 s and the maximum of the ventricular elastance at 0.3 s with an offset of 0.12 .These timing constants were dynamically adjusted to the heart rate by multiplying them by the square root of the heart rate period . The base model is controlled by arterial baroreflex (ABR) and cardiopulmonary reflex (CPR) as short-term blood pressure regulation, mimicking the sympathetic and parasympathetic nervous signals . Figure 5 shows the steps that are involved in adjusting multiple cardiovascular effector sides in order to bring the two measured blood pressures (arterial and venous) close to their predefined static set-point. The reflex mechanisms are set- point controllers that aim at minimizing an error signal (see Supplementary Table 2 for reflex parameters). In short: Step I; pressure and pulse pressure of compartment 0 (aortic Fig. 4 Time-varying heart elastances. Red lines indicate the left arch) and pressure of compartment 15 (right atrium) were heart, and blue lines the right heart. Dashed lines indicate the atria, integrated over 250 data points. Step II; an error signal was and solid lines the ventricles. created by subtracting predefined static set-points − 95 mmHg for arterial, 35 mmHg for pulse pressure and 3 mmHg for venous pressure - from this integrated signal. This error signal was Transcapillary fluid exchange in the extremities (compartment 3 subsequently scaled, as described by deBoer et al. , using an and 12) was incorporated by using Starling forces (hydrostatic and inverse tangent together with scale limits of 18 and 5 for the ABR oncotic pressure) in accordance with Heldt’s and Gerber’s and CPR respectively. Step III; the scaled error signals were 18,51,61,62 models (see Supplementary Table 1 for the parameters). thereafter convolved with 6 different unit-area impulse response This allows fluid to move from the intravascular space into the functions in order to describe the different reflex components of interstitial space in the upper and lower half of the body. In the autonomic nerves system. In the last step, step IV, the resulting addition, a pathway was used to move excessive interstitial fluid vector from the convolution is multiplied by effector mechanism- specific static gain values to produce the 6 different effector via a lymphatic pump back to the superior vena cava (compart- pathways that eventually influence the heart rate, contractility, ment 4). This pathway is shown with a thick brown dashed line on peripheral resistance, and unstressed volume . the left side of the conceptual model (Fig. 3). npj Microgravity (2022) 34 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA L.M. van Loon et al. Fig. 5 Schematic overview of the baro- and cardiopulmonary reflex control model. Step I; create a mean blood pressure, Step II; create an error signal, Step III convolute the error signal with 6 different impulse responses, and step IV; influence hemodynamic effector sides. See text section 2.3.2, ref. , and model code for more information. or subtracting (red apples in Fig. 3) a hydrostatic pressure to driving pressure of blood flow between two adjacent compart- ments. The hydrostatic pressures are the result of the vessel length times a gravity pressure, and was calculated using below equation. Hydrostatic pressure ¼ ρ  g  vessel length  sinðaÞ (1) where ρ is density of the blood (1060 kg/m^3), g is either Earth’s gravitational acceleration (9.81 m/s^2) or Mars’ (3.721 m/s^2), and the vessel length in meter (see Supplementary Table 1) is under consideration of its angle (α) with respect to the horizontal plane . A smooth transition of gravity from zero to maximum gravity was parameterized by using a sinusoidal curve to parameterize the tilt angle alpha from 0 to 90 degrees over 5 s . Finally, muscle contraction preceding the changes in posture were incorporated by reducing the effect of the hydrostatic pressure on the intravascular pressure by a factor 2 and 3 for the Fig. 6 Ventilation. Simulated intra-thoracic pressure curve with a legs and abdominal compartment, respectively. This reflects on respiratory rate of 12/min. the higher pressure produced by muscle contraction in the latter compartment . The result of respiration induced changes in intrathoracic Oral fluid loading is often used with the intent of increasing pressure is implemented by forcing the intrathoracic pressure on plasma volume and maintaining mean arterial pressure during specific (intrathoracic) compartments (see Fig. 3, compartments orthostatic stress . The NASA fluid loading countermeasure that sits within the dashed line). The intrathoracic pressure was protocol uses 15 ml/kg of body weight of water with 1 g of NaCl parameterization-based on the average profile of the respiratory per 125 ml of water several hours before re-entry . We assumed 63,64 muscle activity as proposed by Mecklenburgh and Mapleson , this protocol to be effective in the sense that it is able to increase see Fig. 6.A fixed respiratory rate of 12/min was used, with an plasma fluid by ~8% . This was implemented by increasing the inspiration to expiration ratio of 0.6 . Intrathoracic pressure is intravascular total blood volume with 5% at t = 0, since plasma influenced by the effect of gravity on the abdomen and chest wall, volume is ~60% of the total blood volume . and is posture dependent, therefore we used the angle of the subject with respect to the horizontal plane to adjust the Parameter estimation intrathoracic pressure . In upright postures the intrathoracic Initial model parameters, including the reflex parameters and the pressure decreases with increased gravity as the abdominal mass resistance, elastance, unstressed volumes, vascular lengths of each and diaphragm are pulled downwards, while this increase in cardiovascular unit were obtained from Heldt’s thesis on gravity will increase the intrathoracic pressure in recumbent 67 51 cardiovascular response to orthostatic stress . This set of postures as the abdominal mass moves head ward . parameters describes a healthy adult male under unstressed Gravitational tolerance is assessed by simulating a stand test, an active supine-to-stand task, because it is the most clinically condition in Earth’s gravity. Parameters were then adjusted to relevant test and experimental data from astronauts post mimic both short- and long-duration space flight and different spaceflights are available for model validation . The effect of levels of gravity. No changes to the conceptual model of the standing is incorporated by either adding (green apples in Fig. 5) cardiovascular system (i.e. vessel length or connection between Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 34 L.M. van Loon et al. compartments) when simulating the effect of microgravity. Using CODE AVAILABILITY existing (clinical) literature, primarily following Gallo et al. and The model code and all model parameters are available from the corresponding author on reasonable request. Mohammadyari et al. who did a comprehensive review of this literature for long- and short-duration space flight respectively. The rational for the long-duration setting can be found in the Received: 17 January 2022; Accepted: 15 July 2022; supplementary information of Gallo et al.’s work . 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A., van Meurs, W. L., Sá Couto, C. D., Beneken, J. E. W. & Graves, S. A. A L.M.vL. and E.T. build the model and designed the experiments. L.M.vL., E.T., and A.S. model for educational simulation of infant cardiovascular physiology. Anesth. analyzed the data. All authors validated the results. L.M.vL. wrote the paper. All Analg. 99, 1655–1664, table of contents (2004). authors reviewed and approved the final version of the manuscript. Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 34 L.M. van Loon et al. 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