Mathematical Model of Ventilation Response to Inhaled Carbon Monoxide Raymond Yakura May 31, 2006 BIOEN 589 Stuhmiller & Stuhmiller, J Appl. Physiol. 98: (2005)

Uses of Model Fires generate noxious gases Fires generate noxious gases Results in increased carbon dioxide, increased carbon monoxide and reduced oxygenResults in increased carbon dioxide, increased carbon monoxide and reduced oxygen Dramatic effects on ventilation which vary with gas composition and exposure duration Dramatic effects on ventilation which vary with gas composition and exposure duration

Model Summary Dynamic Physiological Model Dynamic Physiological Model Authors used Matlab with Simulink Authors used Matlab with Simulink Incorporates models from many different sources into one integrated model Incorporates models from many different sources into one integrated model Sources include Duffin et al., Ursino et al., Hill et al., Gomez, Roughton and Darling, Doblar et al.Sources include Duffin et al., Ursino et al., Hill et al., Gomez, Roughton and Darling, Doblar et al.

Results from Publication With CO acute inhalation, hyperventilation first results and then a subsequent ventilation depression With CO acute inhalation, hyperventilation first results and then a subsequent ventilation depression Hyperventilation caused by hypoxia which activates the peripheral chemoreceptorsHyperventilation caused by hypoxia which activates the peripheral chemoreceptors Ventilation depression caused by generation of lactic acid in the brain and decreased brain activityVentilation depression caused by generation of lactic acid in the brain and decreased brain activity

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

Model Subsets Metabolism Metabolism Oxygen metabolism, oxygen transfer to the brain, lactic acid generation, anaerobic limitOxygen metabolism, oxygen transfer to the brain, lactic acid generation, anaerobic limit Cardiac Output Cardiac Output Blood flow to the brain increases during hypoxiaBlood flow to the brain increases during hypoxia Circulatory System Circulatory System Mass balance equations for O 2, CO 2 and COMass balance equations for O 2, CO 2 and CO Blood Chemistry Blood Chemistry Hemoglobin saturation, O 2 /CO partition, acid-base balance, CO 2 dissociationHemoglobin saturation, O 2 /CO partition, acid-base balance, CO 2 dissociation Ventilation Ventilation Chemoreceptor responseChemoreceptor response Brain activity responseBrain activity response Combined ventilatory responseCombined ventilatory response Respiration System Respiration System Total ventilation and effects of dead space and humidificationTotal ventilation and effects of dead space and humidification

Model Schematic

JSIM model JSim used for this project JSim used for this project Event driven to input O 2, CO 2 and CO Event driven to input O 2, CO 2 and CO Introduced memory into system to detect Lactate changes analogous to a D-Flip Flop in digital circuit design Introduced memory into system to detect Lactate changes analogous to a D-Flip Flop in digital circuit design

JSIM Model Results - Ventilation With increase in CO & CO 2, and decrease of O 2, ventilation initially increased and then decreased With increase in CO & CO 2, and decrease of O 2, ventilation initially increased and then decreased

JSIM results – Lactate Generation Lactate generation in the brain due to increased anaerobic respiration due to hypoxia Lactate generation in the brain due to increased anaerobic respiration due to hypoxia

JSIM results: Brain activity Brain activity decreased due to lower pressure in the brain capillaries Brain activity decreased due to lower pressure in the brain capillaries

JSIM results: Tidal volume and Breathing Frequency Tidal volume increased due to CO 2 increase Tidal volume increased due to CO 2 increase Combined f (breathing frequency) started to initially increase due to chemoreceptors activation, but decreased later on due to lower brain activity Combined f (breathing frequency) started to initially increase due to chemoreceptors activation, but decreased later on due to lower brain activity

JSIM results: CO 2 components CO 2 components CO 2 components HCO3 - is majority of the CO 2HCO3 - is majority of the CO 2 Carbamino and CO 2 in plasma is in small amounts of CO 2Carbamino and CO 2 in plasma is in small amounts of CO 2

Model Limitations Article Article Errors and notational changes in the articleErrors and notational changes in the article Model Schematic and equations do not indicate a feedback loop, although the graphs implicitly indicate a feedback loopModel Schematic and equations do not indicate a feedback loop, although the graphs implicitly indicate a feedback loop Model in JSIM Model 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 equations and initiation values resulting in increasing the error tolerance that decreases accuracy.Convergence issues due to the number of equations and initiation values resulting in increasing the error tolerance that decreases accuracy.