Long-distance liquid transport in plants

A brief review of the thermodynamic and fluid dynamic problems related to long-distance liquid flow and signalling in plants is presented. Geometrical parameters of the plant leaf venation are measured and the general relationships between the diameters and lengths of the veins, branching angles at the vein bifurcations, and the corresponding drainage areas are obtained. The same relationships had been obtained before for the bifurcations of the pathways in the arterial and bronchial systems of mammals and humans; tree trunks, branches and roots; and river basins. The identity of the principle of design of the transportation systems in the nature can be understood on the concept of optimal networks that provide liquid delivery at total minimal energy costs. The corresponding models of the optimal vessels and branching systems of vessels with impermeable and permeable walls are presented and discussed

Morphological and functional properties of the conducting human airways investigated by in vivo CT and in vitro MRI

The accurate representation of the human airway anatomy is crucial for understanding and modeling the structure-function relationship in both healthy and diseased lungs. The present knowledge in this area is based on morphometric studies of excised lung casts, partially complemented by in vivo studies in which computed tomography (CT) was used on a small number of subjects. In the present study, we analyze CT scans of a cohort of healthy subjects and obtain comprehensive morphometric information down to the seventh generation of bronchial branching, including airway diameter, length, branching angle, and rotation angle. While some of the geometrical parameters (such as the child-to-parent branch diameter ratio) are found to be in line with accepted values, for others (such as the branch length-to-diameter ratio) our findings challenge the common assumptions. We also evaluate several metrics of self-similarity, including the fractal dimension of the airway tree. Additionally, we use phase-contrast magnetic resonance imaging (MRI) to obtain the volumetric flow field in the 3D printed airway model of one of the subjects during steady inhalation. This is used to relate structural and functional parameters and, in particular, to close the power-law relationship between branch flow rate and diameter. The diameter exponent is found to be significantly lower than in the usually assumed Poiseuille regime, which we attribute to the strong secondary (i.e. transverse) velocity component. The strength of the secondary velocity with respect to the axial component exceeds the levels found in idealized airway models, and persists within the first seven generations.Funding for this work was provided by the National Science Foundation (CBET-1453538) and the National Institutes of Health (NHLBI-R21HL129906). COPDGene was supported by Award Number R01 HL089897 and Award Number R01 HL089856 from the National Heart, Lung, and Blood Institute and by the COPD Foundation through contributions made to an Industry Advisory Board comprised of AstraZeneca, Boehringer Ingelheim, GlaxoSmithKline, Novartis, Pfizer, Siemens and Sunovion

Fractional order models of the human respiratory system

The fractional calculus is a generalization of classical integer-order integration and derivation to fractional (non-integer) order operators. Fractional order (FO) models are those models which contain such fractional order operators. A common representation of these models is in frequency domain, due to its simplicity. The dynamical systems whose model can be approximated in a natural way using FO terms, exhibit specific features, such as viscoelasticity, diffusion and a fractal structure; hence the respiratory system is an ideal application for FO models. Although viscoelastic and diffusive properties were intensively investigated in the respiratory system, the fractal structure was ignored. Probably one of the reasons is that the respiratory system does not pose a perfect symmetry, hence failing to satisfy one of the conditions for being a typical fractal structure. In the 70s, the respiratory impedance determined by the ratio of air-pressure and air-flow, has been introduced in a model structure containing a FO term. It has also been shown that the fractional order models outperform integer-order models on input impedance measurements. However, there was a lack of underpinning theory to clarify the appearance of the fractional order in the FO model structure. The thesis describes a physiologically consistent approach to reach twofold objectives: 1. to provide a physiologically-based mathematical explanation for the necessity of fractional order models for the input impedance, and 2. to determine the capability of the best fractional order model to classify between healthy and pathological cases. Rather than dealing with a specific case study, the modelling approach presents a general method which can be used not only in the respiratory system application, but also in other similar systems (e.g. leaves, circulatory system, liver, intestines). Furthermore, we consider also the case when symmetry is not present (e.g. deformations in the thorax - kyphoscoliose) as well as various pathologies. We provide a proof-of-concept for the appearance of the FO model from the intrinsic structure of the respiratory tree. Several clinical studies are then conducted to validate the sensitivity and specificity of the FO model in healthy groups and in various pathological groups

La viscosité : un architecte pour le système respiratoire ?

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

Numerical Simulation of Particle Deposition in the Human Lungs

We model, simulate and calculate breathing and particle depositions in the human lungs. We review the theory and discretization of fluid mechanics, the anatomy, physiology and measuring methods of lungs. A new model is introduced and investigated with a sensitivity analysis using the singular value decomposition. Particle depositions are simulated in patient-specific and schematized human lungs and compared to the particle deposition in a multiplicative model of subsequent bifurcations

Global energy minimisation of arterial trees with application to embolic stroke

Computer generation of optimal arterial trees has previously been limited to the production of locally optimal configurations. The application of a global optimisation algorithm allows for the generation of vasculatures with consistent structure. Comparison of this structure to that of in-vivo vasculatures allows the determination of to what extent the vascular structure is the result of energy minimisation. In this thesis an algorithm capable of generation globally optimal vascular trees in geometries derived from medical imaging is developed. We begin by outlining a small set of constraints which capture physiological principles guiding the organisation of arterial trees. The constraints are then used to produce an algorithm capable of finding the minimal energy configuration of a given arterial tree. The algorithm is used to produce both coronary and cerebral vasculature, and the latter is generated in geometries segmented from MRI data of a human brain. The trees are compared both morphologically and structurally to those found in-vivo. The morphological comparisons for the coronary vasculature show excellent agreement with experiment. The positions of the larger coronary arteries in the generated trees agree extremely well with experiment, suggesting that structure of the coronary vasculature is the result of energy minimisation. The generated cerebral vasculature approximates the vascular territories of the major cerebral arteries, however the morphological comparisons show that the structure of the cerebral arteries is likely not the result of energy minimisation. The cerebral vasculatures is used to extend a statistical model of embolic stroke to include the effects of branching asymmetry, and an analytic approximation to the statistical model of embolic stroke is developed and validated. It is found that branching asymmetry produces an overall reduction in the level of blockage occuring during an embolic event

Fluid Flow Simulation and Optimisation with Lattice Boltzmann Methods on High Performance Computers - Application to the Human Respiratory System

An overall strategy for numerical simulations of the full human respiratory system is introduced. The integrative approach takes advantage of numerical simulation, high performance computing and newly developed mathematical optimisation techniques, all based on a mesoscopic model description and on lattice Boltzmann methods as discretisation strategies. Validated numerical results are presented for the simulation of respirations in a real human lung and nose geometry captured by CT

Comparison of the real and idealised human airways model

Cílem této práce je vyhledat hlavní parametry idealizovaných geometrických modelů plicních trubic – Weibelova a Horsfieldova a zjistit délky a průměry jednotlivých větví do 4. generace větvení. Na 3D modelu, vzniklém naskenováním odlitku skutečných plic člověka odměřit odpovídající průměry a délky trubic a tyto následně porovnat s hodnotami obou modelů. Pro skutečné plíce určit úhly větvení v jednotlivých generacích a též celkovou geometrii. Pomocí známých hodnot rychlosti proudění vzduchu ve vybraných trubicích spočítat Reynoldsovo číslo pro skutečné plíce a pro oba modely a porovnat je.The purpose of this thesis is to find basic parametres of idealized geometrical lung models – Weibel’s and Horsfield’s and to measure length and diameters of each pipe from trachea to 4th generation of bifurcation. Using 3D model (scanned casting of bronchial tree of man) measure matching diameters and lengths of airways and compare them with lengths and diameters of both models. Define bifurcation angles and total geometry of real lungs. Calculate Reynolds number knowing velocity in some of the airways for real lungs and both models and compare them.

Efficient Motion and Inspection Planning for Medical Robots with Theoretical Guarantees

Medical robots enable faster and safer patient care. Continuum medical robots (e.g., steerable needles) have great potential to accomplish procedures with less damage to patients compared to conventional instruments (e.g., reducing puncturing and cutting of tissues). Due to their complexity and degrees of freedom, such robots are often harder and less intuitive for physicians to operate directly. Automating robot-assisted medical procedures can enable physicians and patients to harness the full potential of medical robots in terms of safety, efficiency, accuracy, and precision.Motion planning methods compute motions for a robot that satisfy various constraints and accomplish a specific task, e.g., plan motions for a mobile robot to move to a target spot while avoiding obstacles. Inspection planning is the task of planning motions for a robot to inspect a set of points of interest, and it has applications in domains such as industrial, field, and medical robotics. With motion and inspection planning, medical robots would be able to automatically accomplish tasks like biopsy and endoscopy while minimizing safety risks and damage to the patient. Computing a motion or inspection plan can be computationally hard since we have to consider application-specific constraints, which come from the robotic system due to the mechanical properties of the robot or come from the environment, such as the requirement to avoid critical anatomical structures during the procedure.I develop motion and inspection planning algorithms that focus on efficiency and effectiveness. Given the same computing power, higher efficiency would shorten the procedure time, thus reducing costs and improving patient outcomes. Additionally, for the automation of medical procedures to be clinically accepted, it is critical from a patient care, safety, and regulatory perspective to certify the correctness and effectiveness of the algorithms involved in procedure automation. Therefore, I focus on providing theoretical guarantees to certify the performance of planners. More specifically, it is important to certify if a planner is able to find a plan if one exists (i.e., completeness) and if a planner is able to find a globally optimal plan according to a given metric (i.e., optimality).Doctor of Philosoph

Design and simulation of nanofluidic branching betworks

Branching networks play a major role in a variety of physiological and engineering structures over a range of physical scales. However, increasingly, artificial systems are being tailored towards the nanoscale to reduce costs and improve performance and process control. In this thesis, analytical and numerical models are developed to enable the efficient design and accurate simulation of nanofluidic branching networks, where non-continuum/non-equilibrium effects prohibit the use of common solutions. A hybrid molecular-continuum method is presented for the design and simulation of general high-aspect-ratio nanofl uidic networks. This increases the scope of hybrid techniques in two main ways: 1) the method is generalised to accurately model any nanofluidic network of connected channels, regardless of its size or complexity; 2) by generalising the application of constraints, the geometry or governing pressures can be the output of the method, enabling the design of networks without the need for a costly trial-and-error process. For a variety of constraint combinations, it is shown that the hybrid method converges quickly to the solution of a full molecular dynamics simulation, with relative errors of < 4% for all variables across all cases. Network design is further advanced by the development of a generalised optimisation principle that finds the daughter-parent area ratio maximising flow conductance per unit volume in all branches. Through numerically verified analytical models, it is demonstrated that the common branching principle `Murray's law' is sub-optimal for asymmetric branching (where the local optimisation of each individual channel does not correspond to the global optimum for the network as a whole), while the generalised law presented in this thesis is valid for 1) symmetric and asymmetric branching, 2) slip and plug fl flows, which occur at very small scales, and 3) any cross-sectional shape; making it a powerful tool for nanofluidic biomimetic modelling