A Passive Model of the Heat, Oxygen and Carbon Dioxide Transport in the Human Body

The aim of this work is the development of a mathematical model which integrates a model of the human respiratory system and a model of the human thermal system. Both models were previously developed at the same laboratory, based on classical works. The human body was divided in 15 segments: head, neck, trunk, arms, forearms, hands, thighs, legs and feet. Those segments have the form of a cylinder (circular cross-section) or a parallelogram (hands and feet) with the following tissue layers: muscle, fat, skin, bone, brain, lung, heart and viscera. Two different geometries are used to model the transport of mass and heat in the tissues. For the mass transfer, those layers are considered as tissue compartments. For the heat transfer, the body geometry is taken into account. Each segment contains an arterial and a venous compartment, representing the large vessels. The blood in the small vessels are considered together with the tissues. The gases are transported by the blood dissolved and chemically reacted. Metabolism takes place in the tissues, where oxygen is consumed generating carbon dioxide and heat. In the lungs, mass transfer happens by diffusion between an alveolar compartment and several pulmonary capillaries compartments. The skin exchanges heat with the environment by convection, radiation and evaporation. The differential transport equations were obtained by heat and mass balances. The discretization heat equations were obtained applying the finite volume method. The regulation mechanisms were considered as model inputs. The results show three different environment situations. It was concluded that the gas transport is most influenced by the temperature effects on the blood dissociation curves and the metabolism rise in a cold environment by shivering.