Role of Kidney Stones in Renal Pelvis Flow.

Ureteroscopy is a commonly performed medical procedure to treat stones in the kidney and ureter using a ureteroscope. Throughout the procedure, saline is irrigated through the scope to aid visibility and wash-out debris from stone fragmentation. The key challenge that this research addresses is to build a fundamental understanding of the interaction between the kidney stones/stone fragments and the flow dynamics in the renal pelvis flow. We examine the time-dependent flow dynamics inside an idealized renal pelvis in the context of a surgical procedure for kidney stone removal. Here, we examine the time-dependent evolution of these vortical flow structures in three dimensions, and incorporate the presence of rigid kidney stones. We perform direct numerical simulations, solving the transient Navier-Stokes equations in a spherical domain. Our numerical predictions for the flow dynamics in the absence of stones are validated with available experimental and numerical data, and the governing parameters and flow regimes are chosen carefully in order to satisfy several clinical constraints. The results shed light on the crucial role of flow circulation in the renal cavity and its effect on the trajectories of rigid stones. We demonstrate that stones can either be washed out of the cavity along with the fluid, or be trapped in the cavity via their interaction with vortical flow structures. Additionally, we study the effect of multiple stones in the flow field within the cavity in terms of the kinetic energy, entrapped fluid volume, and the clearance rate of a passive tracer modeled via an advection-diffusion equation. We demonstrate that the flow in the presence of stones features a higher vorticity production within the cavity compared with the stone-free cases.

A temperature model for laser lithotripsy.

OBJECTIVE: To derive and validate a mathematical model to predict laser-induced temperature changes in a kidney during kidney stone treatment. METHODS: A simplified mathematical model to predict temperature change in the kidney for any given renal volume, irrigation flow rate, irrigation fluid temperature, and laser power was derived. We validated our model with matched in vitro experiments. RESULTS: Excellent agreement between the mathematical model predictions and laboratory data was obtained. CONCLUSION: The model obviates the need for repeated experimental validation. The model predicts scenarios where risk of renal tissue damage is high. With real-time knowledge of flow rate, irrigating fluid temperature and laser usage, safety warning levels could be predicted. Meanwhile, clinicians should be aware of the potential risk from thermal injury and take measures to reduce the risk, such as using room temperature irrigation fluid and judicious laser use.

The role of mechanics in the growth and homeostasis of the intestinal crypt.

We present a mechanical model of tissue homeostasis that is specialised to the intestinal crypt. Growth and deformation of the crypt, idealised as a line of cells on a substrate, are modelled using morphoelastic rod theory. Alternating between Lagrangian and Eulerian mechanical descriptions enables us to precisely characterise the dynamic nature of tissue homeostasis, whereby the proliferative structure and morphology are static in the Eulerian frame, but there is active migration of Lagrangian material points out of the crypt. Assuming mechanochemical growth, we identify the necessary conditions for homeostasis, reducing the full, time-dependent system to a static boundary value problem characterising a spatially heterogeneous "treadmilling" state. We extract essential features of crypt homeostasis, such as the morphology, the proliferative structure, the migration velocity, and the sloughing rate. We also derive closed-form solutions for growth and sloughing dynamics in homeostasis, and show that mechanochemical growth is sufficient to generate the observed proliferative structure of the crypt. Key to this is the concept of threshold-dependent mechanical feedback, that regulates an established Wnt signal for biochemical growth. Numerical solutions demonstrate the importance of crypt morphology on homeostatic growth, migration, and sloughing, and highlight the value of this framework as a foundation for studying the role of mechanics in homeostasis.

Mathematical modelling of stretch-induced membrane traffic in bladder umbrella cells.

The bladder is a complex organ that is highly adaptive to its mechanical environment. The umbrella cells in the bladder uroepithelium are of particular interest: these cells actively change their surface area through exo- and endocytosis of cytoplasmic vesicles, and likely form a critical component in the mechanosensing process that communicates the sense of 'fullness' to the nervous system. In this paper we develop a first mechanical model for vesicle trafficking in umbrella cells in response to membrane tension during bladder filling. Recent experiments conducted on a disc of uroepithelial tissue motivate our model development. These experiments subject bladder tissue to fixed pressure differences and exhibit counterintuitive area changes. Through analysis of the mathematical model and comparison with experimental data in this setup, we gain an intuitive understanding of the biophysical processes involved and calibrate the vesicle trafficking rate parameters in our model. We then adapt the model to simulate in vivo bladder filling and investigate the potential effect of abnormalities in the vesicle trafficking machinery on bladder pathologies.

A morphoelastic model for dermal wound closure.

We develop a model of wound healing in the framework of finite elasticity, focussing our attention on the processes of growth and contraction in the dermal layer of the skin. The dermal tissue is treated as a hyperelastic cylinder that surrounds the wound and is subject to symmetric deformations. By considering the initial recoil that is observed upon the application of a circular wound, we estimate the degree of residual tension in the skin and build an evolution law for mechanosensitive growth of the dermal tissue. Contraction of the wound is governed by a phenomenological law in which radial pressure is prescribed at the wound edge. The model reproduces three main phases of the healing process. Initially, the wound recoils due to residual stress in the surrounding tissue; the wound then heals as a result of contraction and growth; and finally, healing slows as contraction and growth decrease. Over a longer time period, the surrounding tissue remodels, returning to the residually stressed state. We identify the steady state growth profile associated with this remodelled state. The model is then used to predict the outcome of rewounding experiments designed to quantify the amount of stress in the tissue, and also to simulate the application of pressure treatments.

The morpho-mechanical basis of ammonite form.

Ammonites are a group of extinct cephalopods that garner tremendous interest over a range of scientific fields and have been a paradigm for biochronology, palaeobiology, and evolutionary theories. Their defining feature is the spiral geometry and ribbing pattern through which palaeontologists infer phylogenetic relationships and evolutionary trends. Here, we develop a morpho-mechanical model for ammonite morphogenesis. While a wealth of observations have been compiled on ammonite form, and several functional interpretations may be found, this study presents the first quantitative model to explain rib formation. Our approach, based on fundamental principles of growth and mechanics, gives a natural explanation for the morphogenesis and diversity of ribs, uncovers intrinsic laws linking ribbing and shell geometry, and provides new opportunities to interpret ammonites' and other mollusks' evolution.

An ordinary differential equation model for full thickness wounds and the effects of diabetes.

Wound healing is a complex process in which a sequence of interrelated phases contributes to a reduction in wound size. For diabetic patients, many of these processes are compromised, so that wound healing slows down. In this paper we present a simple ordinary differential equation model for wound healing in which attention focusses on the dominant processes that contribute to closure of a full thickness wound. Asymptotic analysis of the resulting model reveals that normal healing occurs in stages: the initial and rapid elastic recoil of the wound is followed by a longer proliferative phase during which growth in the dermis dominates healing. At longer times, fibroblasts exert contractile forces on the dermal tissue, the resulting tension stimulating further dermal tissue growth and enhancing wound closure. By fitting the model to experimental data we find that the major difference between normal and diabetic healing is a marked reduction in the rate of dermal tissue growth for diabetic patients. The model is used to estimate the breakdown of dermal healing into two processes: tissue growth and contraction, the proportions of which provide information about the quality of the healed wound. We show further that increasing dermal tissue growth in the diabetic wound produces closure times similar to those associated with normal healing and we discuss the clinical implications of this hypothesised treatment.

Mechanical growth and morphogenesis of seashells.

Seashells grow through the local deposition of mass along the aperture. Many mathematical descriptions of the shapes of shells have been provided over the years, and the basic logarithmic coiling seen in mollusks can be simulated with few parameters. However, the developmental mechanisms underlying shell coiling are largely not understood and the ubiquitous presence of ornamentation such as ribs, tubercles, or spines presents yet another level of difficulty. Here we develop a general model for shell growth based entirely on the local geometry and mechanics of the aperture and mantle. This local description enables us to efficiently describe both arbitrary growth velocities and the evolution of the shell aperture itself. We demonstrate how most shells can be simulated within this framework. We then turn to the mechanics underlying the shell morphogenesis, and develop models for the evolution of the aperture. We demonstrate that the elastic response of the mantle during shell deposition provides a natural mechanism for the formation of three-dimensional ornamentation in shells.

Possible role of differential growth in airway wall remodeling in asthma.

Airway remodeling in patients with chronic asthma is characterized by a thickening of the airway walls. It has been demonstrated in previous theoretical models that this change in thickness can have an important mechanical effect on the properties of the wall, in particular on the phenomenon of mucosal folding induced by smooth muscle contraction. In this paper, we present a model for mucosal folding of the airway in the context of growth. The airway is modeled as a bilayered cylindrical tube, with both geometric and material nonlinearities accounted for via the theory of finite elasticity. Growth is incorporated into the model through the theory of morphoelasticity. We explore a range of growth possibilities, allowing for anisotropic growth as well as different growth rates in each layer. Such nonuniform growth, referred to as differential growth, can change the properties of the material beyond geometrical changes through the generation of residual stresses. We demonstrate that differential growth can have a dramatic impact on mucosal folding, in particular on the critical pressure needed to induce folding, the buckling pattern, as well as airway narrowing. We conclude that growth may be an important component in airway remodeling.

Reverse draining of a magnetic soap film.

We investigate the draining of a vertical magnetic soap film in the presence of a strong, nonuniform magnetic field. A colloidal suspension of magnetic nanoparticles in a regular soap solution yields a magnetic soap solution, from which a soap film is formed across an isolated frame. Experiments demonstrate that with a strong magnet placed above the frame, the film may be made to flow upward against gravity. The amount of film draining upward is altered by varying the distance between the frame and magnet. A first mathematical model is developed for the evolution of the film. Simulations demonstrate qualitative agreement with the experiment.