Numerical Analysis of the Immersed Boundary Method for Cell-Based Simulation

Mathematical modelling provides a useful framework within which to investigate the organization of biological tissues. With advances in experimental biology leading to increasingly detailed descriptions of cellular behavior, models that consider cells as individual objects are becoming a common tool to study how processes at the single-cell level affect collective dynamics and determine tissue size, shape, and function. However, there often remains no comprehensive account of these models, their method of solution, computational implementation, or analysis of parameter scaling, hindering our ability to utilize and accurately compare different models. Here we present an efficient, open-source implementation of the immersed boundary (IB) method, tailored to simulate the dynamics of cell populations. This approach considers the dynamics of elastic membranes, representing cell boundaries, immersed in a viscous Newtonian fluid. The IB method enables complex and emergent cell shape dynamics, spatially heterogeneous cell properties, and precise control of growth mechanisms. We solve the model numerically using an established algorithm, based on the fast Fourier transform, providing full details of all technical aspects of our implementation. The implementation is undertaken within Chaste, an open-source C++ library that allows one to easily change constitutive assumptions. Our implementation scales linearly with time step, and subquadratically with mesh spacing and immersed boundary node spacing. We identify the relationship between the immersed boundary node spacing and fluid mesh spacing required to ensure fluid volume conservation within immersed boundaries, and the scaling of cell membrane stiffness and cell-cell interaction strength required when refining the immersed boundary discretization. Finally, we present a simulation study of a growing epithelial tissue to demonstrate the applicability of our implementation to relevant biological questions, highlighting several features of the IB method that make it well suited to address certain questions in epithelial morphogenesis

Sedation for fibre optic bronchoscopy

AbstractMost current sedative regimens for fibre optic bronchoscopy use an opioid, a benzodiazepine or a combination of both. This study compares midazolam (M) (a benzodiazepine), alfentanil (A) (an opioid) and a combination of both drugs (M + A).One hundred and three patients were randomized in double-blind manner into groups M(35), A(33) and M + A(35). The number of coughs, number of additional aliquots of lignocaine and duration of the procedures were recorded along with oxygen desaturation. The patient's level of discomfort was assessed by patient and bronchoscopist and expressed as a visual analogue score.There were significantly fewer coughs per minute in Group A compared with Group M (P=0·0053), and significantly less lignocaine was required in Group A (P=0·005) and in Groups M + A (P<0·002) compared with Group M. There was no significant difference in the assessment of discomfort between the groups. There was a trend for Group M + A to desaturate more than the other two with a significant difference between desaturation in Group M + A and Group A (P=0·033).Alfentanil is a more effective anti-tussive agent than midazolam for outpatient fibre optic bronchoscopy. The combination of alfentanil and midazolam does not provide any better anti-tussive effect and may have the risk of a greater degree of desaturation secondary to increased sedation

Delivery actuator for a transcervical sterilization device

The use of delivery systems in the human body for positioning and deploying implants, such as closure devices, dilation balloons, stents, coils and sterilization devices, are gaining more importance to preclude surgical incisions and general anesthesia. The majorities of the non-surgical medical devices are delivered in a low profile into human body form and subsequently require specialized operations for their deployment and release. An analogous procedure for permanent female sterilization is the transcervical approach that does not require either general anesthesia or surgical incision and uses a normal body passage. The objective of this paper is to detail the design, development and verification of an ergonomic actuator for a medical application. In particular, this actuator is designed for the deployment and release of an implant to achieve instant permanent female sterilization via the transcervical approach. This implant is deployed under hysteroscopic visualization and requires a sequence of rotary and linear operations for its deployment and release. More specifically, this manually operated actuator is a hand held device designed to transmit the required forces in a particular sequence to effect both implant deployment and release at a target location. In order to design the actuator and to investigate its mechanical behavior, a three-dimensional (3D) Computer Aided Design (CAD) model was developed and Finite Element Method (FEM) was used for simulations and optimization. Actuator validation was performed following a number of successful bench-top in-air deployments and in-vitro deployments in animal tissue and explanted human uteri. During these deployments it was observed that the actuator applied the required forces to the implant resulting in successful deployment. Initial results suggest that this actuator can be used single handedly during the deployment phase. The ongoing enhancement of this actuator is moving towards “first-in- man” clinical trials

Universal Field-Induced Charge-Density-Wave Phase Diagram: Theory versus Experiment

We suggest a theory of the Field-Induced Charge-Density-Wave (FICDW) phases, generated by high magnetic fields in quasi-low-dimensional conductors. We demonstrate that, in layered quasi-one-dimensional conductors, the corresponding critical magnetic fields ratios are universal and do not depend on any fitting parameter. In particular, we find that $H_1/H_0 = 0.73, \ H_2/H_0 = 0.59, H_3/H_0 = 0.49, H_4/H_0 = 0.42$, where$H_n$is a critical field of a phase transition between the FICDW phases with numbers$n$and$n+1$. The suggested theory is in very good qualitative and quantitative agreements with the existing experimental data in$\alpha$-(ET)$_2$KHg(SCN)$_4$ material.Comment: 9 pages, 2 figure

Seabed characterization: developing fit for purpose methodologies

We briefly describe three methods of seabed characterization which are ‘fit for purpose’, in that each approach is well suited to distinct objectives e.g. characterizing glacial geomorphology and shallow glacial geology vs. rapid prediction of seabed sediment distribution via geostatistics. The methods vary from manual ‘expert’ interpretation to increasingly automated and mathematically based models, each with their own attributes and limitations. We would note however that increasing automation and mathematical sophistication does not necessarily equate to improve map outputs, or reduce the time required to produce them. Judgements must be made to select methodologies which are most appropriate to the variables mapped, and according to the extent and presentation scale of final maps

Novel Phases in the Field Induced Spin Density Wave State in (TMTSF)_2PF_6

Magnetoresistance measurements on the quasi one-dimensional organic conductor (TMTSF)_2PF_6 performed in magnetic fields B up to 16T, temperatures T down to 0.12K and under pressures P up to 14kbar have revealed new phases on its P-B-T phase diagram. We found a new boundary which subdivides the field induced spin density wave (FISDW) phase diagram into two regions. We showed that a low-temperature region of the FISDW diagram is characterized by a hysteresis behavior typical for the first order transitions, as observed in a number of studies. In contrast to the common believe, in high temperature region of the FISDW phase diagram, the hysteresis and, hence, the first order transitions were found to disappear. Nevertheless, sharp changes in the resistivity slope are observed both in the low and high temperature domains indicating that the cascade of transitions between different subphases exists over all range of the FISDW state. We also found that the temperature dependence of the resistance (at a constant B) changes sign at about the same boundary. We compare these results with recent theoretical models.Comment: LaTex, 4 pages, 4 figure

Bound Chains of Tilted Dipoles in Layered Systems

Ultracold polar molecules in multilayered systems have been experimentally realized very recently. While experiments study these systems almost exclusively through their chemical reactivity, the outlook for creating and manipulating exotic few- and many-body physics in dipolar systems is fascinating. Here we concentrate on few-body states in a multilayered setup. We exploit the geometry of the interlayer potential to calculate the two- and three-body chains with one molecule in each layer. The focus is on dipoles that are aligned at some angle with respect to the layer planes by means of an external eletric field. The binding energy and the spatial structure of the bound states are studied in several different ways using analytical approaches. The results are compared to stochastic variational calculations and very good agreement is found. We conclude that approximations based on harmonic oscillator potentials are accurate even for tilted dipoles when the geometry of the potential landscape is taken into account.Comment: 10 pages, 6 figures. Submitted to Few-body Systems special issue on Critical Stability, revised versio

Coexistence or Separation of the Superconducting, Antiferromagnetic, and Paramagnetic Phases in Quasi One-Dimensional (TMTSF)2PF6 ?

We report on experimental studies of the character of phase transitions in the quasi-1D organic compound (TMTSF)2PF6 in the close vicinity of the borders between the paramagnetic metal PM, antiferromagnetic insulator AF, and superconducting SC states. In order to drive the system through the phase border P_0(T_0), the sample was maintained at fixed temperature T and pressure P, whereas the critical pressure P_0 was tuned by applying the magnetic field B. In this approach, the magnetic field was used (i) for tuning (P-P_0), and (ii) for identifying the phase composition (due to qualitatively different magnetoresistance behavior in different phases). Experimentally, we measured R(B) and its temperature dependence R(B,T) in the pressure range (0 - 1)GPa. Our studies focus on the features of the magnetoresistance at the phase transition between the PM and AF phases, in the close vicinity to the superconducting transition at T~1K. We found pronounced history effects arising when the AF/PM phase border is crossed by sweeping the magnetic field: the resistance depends on a trajectory which the system arrives at a given point of the P-B-T phase space. In the transition from the PM to AF phase, the features of the PM phase extends well into the AF phase. At the opposite transition from the AF to PM phase, the features of the AF phase are observed in the PM phase. These results evidence for a macroscopically inhomogeneous state, which contains macroscopic inclusions of the minority phase. When the system is driven away from the transition, the homogeneous state is restored; upon a return motion to the phase boundary, no signatures of the minority phase are observed up to the very phase boundary.Comment: 10 figures, 23 page

Gauge-invariant fluctuations of scalar branes

A generalization of the Bardeen formalism to the case of warped geometries is presented. The system determining the gauge-invariant fluctuations of the metric induced by the scalar fluctuations of the brane is reduced to a set of Schr\"odinger-like equations for the Bardeen potentials and for the canonical normal modes of the scalar-tensor action. Scalar, vector and tensor modes of the geometry are classified according to four-dimensional Lorentz transformations. While the tensor modes of the geometry live on the brane determining the corrections to Newton law, the scalar and and vector fluctuations exhibit non normalizable zero modes and are, consequently, not localized on the brane. The spectrum of the massive modes of the fluctuations is analyzed using supersymmetric quantum mechanics.Comment: 29 pages in Latex styl