Mathematical Model of Mathematical Model of Ventilation Response to Ventilation Response to

Inhaled Carbon MonoxideInhaled Carbon Monoxide

Raymond YakuraRaymond YakuraMay 31, 2006May 31, 2006

BIOEN 589BIOEN 589

Stuhmiller & Stuhmiller, Stuhmiller & Stuhmiller, J Appl. Physiol.J Appl. Physiol. 9898: : 2033-44 (2005)2033-44 (2005)

Uses of ModelUses of Model

Fires generate noxious gasesFires generate noxious gases• Results in increased carbon dioxide, Results in increased carbon dioxide,

increased carbon monoxide and reduced increased carbon monoxide and reduced oxygenoxygen

Dramatic effects on ventilation which Dramatic effects on ventilation which vary with gas composition and vary with gas composition and exposure durationexposure duration

Model SummaryModel Summary

Dynamic Physiological ModelDynamic Physiological Model Authors used Matlab with SimulinkAuthors used Matlab with Simulink Incorporates models from many Incorporates models from many

different sources into one integrated different sources into one integrated modelmodel• Sources include Duffin et al., Ursino et Sources include Duffin et al., Ursino et

al., Hill et al., Gomez, Roughton and al., Hill et al., Gomez, Roughton and Darling, Doblar et al. Darling, Doblar et al.

Results from PublicationResults from Publication With CO acute With CO acute

inhalation, inhalation, hyperventilation first hyperventilation first results and then a results and then a subsequent ventilation subsequent ventilation depressiondepression• Hyperventilation caused Hyperventilation caused

by hypoxia which by hypoxia which activates the peripheral activates the peripheral chemoreceptors chemoreceptors

• Ventilation depression Ventilation depression caused by generation of caused by generation of lactic acid in the brain lactic acid in the brain and decreased brain and decreased brain activityactivity

Publication ResultsPublication Results

Buildup of carboxyhemoglobin with Buildup of carboxyhemoglobin with reduction in oxygen delivery to the reduction in oxygen delivery to the brain leads to anaerobic glycolysis brain leads to anaerobic glycolysis and buildup of lactateand buildup of lactate

Model SubsetsModel Subsets MetabolismMetabolism

• Oxygen metabolism, oxygen transfer to the brain, lactic acid Oxygen metabolism, oxygen transfer to the brain, lactic acid generation, anaerobic limitgeneration, anaerobic limit

Cardiac OutputCardiac Output• Blood flow to the brain increases during hypoxiaBlood flow to the brain increases during hypoxia

Circulatory SystemCirculatory System• Mass balance equations for OMass balance equations for O22, CO, CO22 and CO and CO

Blood ChemistryBlood Chemistry• Hemoglobin saturation, OHemoglobin saturation, O22 /CO partition, acid-base balance, /CO partition, acid-base balance,

COCO22 dissociation dissociation VentilationVentilation

• Chemoreceptor responseChemoreceptor response• Brain activity responseBrain activity response• Combined ventilatory responseCombined ventilatory response

Respiration SystemRespiration System• Total ventilation and effects of dead space and humidificationTotal ventilation and effects of dead space and humidification

Model SchematicModel Schematic

JSIM modelJSIM model

JSim 1.6.62 used for this projectJSim 1.6.62 used for this project Event driven to input OEvent driven to input O22, CO, CO22 and CO and CO Introduced memory into system to Introduced memory into system to

detect Lactate changes analogous to detect Lactate changes analogous to a D-Flip Flop in digital circuit designa D-Flip Flop in digital circuit design

JSIM Model Results - VentilationJSIM Model Results - Ventilation

With increase in With increase in CO & COCO & CO22, and , and decrease of Odecrease of O22, , ventilation ventilation initially increased initially increased and then and then decreaseddecreased

JSIM results – Lactate GenerationJSIM results – Lactate Generation

Lactate Lactate generation in generation in the brain due to the brain due to increased increased anaerobic anaerobic respiration due respiration due to hypoxiato hypoxia

JSIM results: Brain activityJSIM results: Brain activity

Brain activity Brain activity decreased decreased due to lower due to lower pressure in pressure in the brain the brain capillariescapillaries

JSIM results: Tidal volume and JSIM results: Tidal volume and Breathing FrequencyBreathing Frequency

Tidal volume Tidal volume increased due to increased due to COCO22 increase increase

Combined f Combined f (breathing (breathing frequency) started frequency) started to initially increase to initially increase due to due to chemoreceptors chemoreceptors activation, but activation, but decreased later on decreased later on due to lower brain due to lower brain activityactivity

JSIM results: COJSIM results: CO22 components components

COCO22 componentscomponents• HCO3HCO3-- is is

majority of the majority of the COCO22

• Carbamino Carbamino and COand CO22 in in plasma is in plasma is in small amounts small amounts of COof CO22

Model LimitationsModel Limitations

ArticleArticle• Errors and notational changes in the articleErrors and notational changes in the article• Model Schematic and equations do not indicate Model Schematic and equations do not indicate

a feedback loop, although the graphs implicitly a feedback loop, although the graphs implicitly indicate a feedback loopindicate a feedback loop

Model in JSIMModel in JSIM• Not a feedback loopNot a feedback loop• P_O2_Brain and O2art are separate eventsP_O2_Brain and O2art are separate events• Convergence issues due to the number of Convergence issues due to the number of

equations and initiation values resulting in equations and initiation values resulting in increasing the error tolerance that decreases increasing the error tolerance that decreases accuracy.accuracy.