Viscosity: an architect for the respiratory system?
La viscosité : un architecte pour le système respiratoire ?
Résumé
The mammals respiratory system characteristics have been selected because they bring benefits other characteristics do not. At first approximation, such benefices can be estimated through the minimization of energetic costs relatively to one or several of these characteristics. The cost is the consequence of a complex interaction between many phenomena, amongst which physiology, organ development, its inner physics and chemistry, and its surrounding environment. My work aims at building idealized cost functions which, I hypothesized, represent approximations of the real cost optimized by evolution. To build and study these cost functions, I use mathematical modeling processes often based on dedicated mathematical and numerical tools. The costs we propose try to retain only the core phenomena involved in the organ functioning. Then I compare the model predictions with physiology and discuss its validity. I applied this approach to different organs of the respiratory system where the role of viscous dissipation of fluids on the selection of their characteristics may have been the strongest.
The cost function we built for the tracheobronchial tree is based on the trade-off between lung’s hydrodynamic resistance and the size of the lung’s exchange surface. We showed that a tree structure associated to such a cost is stable for a dynamic process such as evolution only if the air flows in the bottom of the tree are regulated. We proposed an original and parsimonious model for tracheobronchial tree development based on a physical instability. The predictions of this model are in agreement with most of the experiments in the literature. We were able to relate the geometrical parameters of the adult lungs with parameters of our development model. We showed that biological noise during lung’s development may have influenced the selection of the geometry of the tracheobronchial tree by shifting its multi-scaled geometry to branches slightly wider than the theoretical optimal and by implying asymmetric branching. The role of biological noise on tracheobronchial tree selection is an archetypal example of a more general framework we developed about the role of biological noise on evolution. Cliff-edge theory states that biological noise can be viewed as an evolutionary mechanism. We proposed and validated a general population dynamics model that includes cliff-edge effects and explains its mechanisms.
Our models and results for the tracheobronchial tree were also used in the frame of two medical applications. The first, based on patients data, aimed at testing whether variations at patient level of the multi-scale geometry may be correlated with chronic obstructive pulmonary disease (COPD). The second medical application aimed at understanding the underlying biophysics involved in chest physiotherapy and at arising a scientific background to a discipline that is, as of today, mostly empirical.
Another important organ involved in the respiratory system that uses a fluid to transport oxygen is blood network, and more specifically arterial network, where most of the system pressure drop occurs. Arterial system couples a multi-scaled tree structure with a non-Newtonian rheofluidifying fluid (blood), submitted to phase separation effects in small vessels (F ̊ahræus effect). We proposed that both the multi- scale property of arterial network geometry and the red blood cells fraction in blood (hematocrit) may have been selected through a trade-off inspired from Murray’s original optimization principle. The cost we propose is based on fluid dissipation, metabolic energetic cost of blood and a given total oxygen flow in the tree. We showed that the dissipation is mostly driven by branches mean shear rates which checks a scaling law related to that of the tree. The multi-scaled geometry of arterial network and blood hematocrit are close to the minimal configuration for the cost we propose, thus indicating it may have played a role on the selection of blood arterial network properties.
In capillaries, the red blood cells fraction in blood is smaller than in the large circulation because of a phase separation effects on plasma and red blood cells. Thus, we modeled by numerical means the flow and deformation of a periodic train of red blood cells in a capillary using a dedicated numerical method - the camera method. Using the same cost function than for the arterial network, we predicted that the typical concentration of red blood cells in the capillaries also optimized the same cost in capillaries. With our numerical model, we also studied the oxygen transfer through the alveolo-capillary membrane and its capture by the red blood cells in the pulmonary capillaries.
My work brought out scenarios that explain how viscous dissipation of biological fluids may have played a role on the selection of some mammals respiratory system characteristics, and most particularly of its geometries. These scenarios are however based on simplification hypotheses which must be accounted for when confronted with the real objects. Nevertheless, the predictions made by the different models studied are consistent with physiology, which indicates that the models probably capture main behaviors. My research also highlights that the inherent fluctuations arising from organ’s development may affect the adult organ function and consequently the organ selection. Finally, some of the models and concepts developed in my work expanded into medical applications.
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