HAL Id: hal-03188987 https://hal.archives-ouvertes.fr/hal-03188987 Submitted on 2 Apr 2021 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Ventilatory oscillations at exercise in hypoxia: a mathematical model Eric Hermand, François Lhuissier, Nicolas Voituron, Jean-Paul Richalet To cite this version: Eric Hermand, François Lhuissier, Nicolas Voituron, Jean-Paul Richalet. Ventilatory oscillations at exercise in hypoxia: a mathematical model. Journal of Theoretical Biology, Elsevier, 2016, 411, pp.92-101. 10.1016/j.jtbi.2016.10.002. hal-03188987
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HAL Id: hal-03188987https://hal.archives-ouvertes.fr/hal-03188987
Submitted on 2 Apr 2021
HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.
Ventilatory oscillations at exercise in hypoxia: amathematical model
Eric Hermand, François Lhuissier, Nicolas Voituron, Jean-Paul Richalet
To cite this version:Eric Hermand, François Lhuissier, Nicolas Voituron, Jean-Paul Richalet. Ventilatory oscillations atexercise in hypoxia: a mathematical model. Journal of Theoretical Biology, Elsevier, 2016, 411,pp.92-101. �10.1016/j.jtbi.2016.10.002�. �hal-03188987�
QR and ventilatory equivalent for oxygen EVO2 are set at known physiological values for rest/exercise 364
and normoxia/hypoxia, as indicated in table 1. 365
The basal value of E for all phases is calculated as follows: 366
367
The arterial O2 pressure PaO2 and arterial O2 saturation follow the equation: 368
where P50 is the arterial O2 partial pressure at SaO2 = 50%, and NH is the Hill constant. 369
370
The alveolar-arterial difference in O2 (DAaO2) is determined as: 371
where DAaO20 is the alveolar-arterial difference in O2 at rest, DlimO2 a known coefficient of 372
diffusion, and crep the cardiac output at rest. 373
374
Peripheral chemoreceptors 375
This linear expression involves the peripheral gain to O2 (GO2) and to CO2 (GCO2P) and a pure delay 376
DeltaTp from lung to peripheral chemoreceptors (blood convection). 377
The peripheral gain to CO2, above a peripheral threshold PaCO2Pth is defined as: 378
if PaCO2(t)> PaCO2Pth, then the peripheral contribution from a CO2 stimulus is the linear term 379
with PaCO2C as a PaCO2 set point, 380
else it is null. 381
In the additive and central interactive models, the peripheral contribution is: 382
383
with SaCO2C as a SaCO2 set point. 384
In the interactive model, the peripheral contribution is: 385
386
387
22
Central chemoreceptors 388
The central component of ventilation, resulting from a variation of arterial CO2 content, includes a 389
static central gain to CO2 (GCO2C) and a delay DeltaTc (see section 2.1.4), above a central threshold 390
(PaCO2Cth): 391
if PaCO2(t)> PaCO2Cth, then 392
else . 393
In the central interactive model, the central gain to CO2 (GCO2C) depends on peripheral gains to O2 394
and CO2 (GO2 and GCO2P, respectively), modulated by a constant interac: 395
and 396
397
Equations of alveolar and arterial gas pressures: steady state and first order 398
At equilibrium, the alveolar partial pressures in O2 and CO2 as a function of time are defined as: 399
400
401
where PB and PH20 are atmospheric and water vapor pressures, respectively, FIO2 is the inhaled fraction 402
of O2. PB, PH20, FIO2, QR, O2 and rVAVE are predetermined as shown in table 1. 403
PACO2 is then described through a first-order relation: 404
where apCO2 and bpCO2 are defined as follows:
,
and 405
, is the variable determined by initial conditions of O2(t) and 406
E(t). 407
408
409
410
23
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