Born-Infeld Solitons and Existence & Non-uniqueness of Solutions to the Bj\"orling Problem

In this semi-expository article, we study Born-Infeld soliton surfaces as zero mean curvature surfaces and derive conformal parameters for them. Then we present two approaches to solve the Bj\"orling problem for such surfaces, one of them treating them as time-like minimal surfaces and the other one using the Barbashov-Chernikov representation. Finally, we show that the solution to the Bj\"orling problem may not be unique unlike minimal and maximal surfaces

Laboratory Development of a Self-Powered Fontan for Treatment of Congenital Heart Disease

Around 8% of all newborns with a Congenital Heart Defect (CHD) have only a single functioning ventricle. The Fontan operation has served as a palliation for this anomaly for decades, but the surgery entails multiple complications and survival rate is less than 50% by adulthood. A rapidly testable novel alternative is proposed by creating a bifurcating graft, or Injection Jet Shunt (IJS), used to “entrain” the pulmonary flow and thus provide assistance while reducing the caval pressure. A benchtop Mock Flow Loop (MFL) is configured to validate this hypothesis. The MFL is based on a Lumped-Parameter Model (LPM) of the Fontan circulation and is comprised of upper and lower systemic as well as left and right pulmonary compartments. Needle valves are used to accurately replicate vascular resistance (R) while compliance chambers are used to mimic vascular compliance values (C). The Fontan MFL is driven with cardiac pulsatility provided by a Harvard Apparatus medical pump. Patient-specific models of the centerpiece of the MFL along with the grafts (IJS) are produced via 3D printing. Baseline values are validated against patient-specific waveforms. Flow and pressure sensor data at specific points in the MFL are acquired via a National Instruments multichannel data acquisition board and processed using LabView. Several IJS nozzle diameters are tested to validate the hypothesis and optimize the improvement

In-Vitro and In-Silico Investigations of Alternative Surgical Techniques for Single Ventricular Disease

Single ventricle (SV) anomalies account for one-fourth of all cases of congenital Heart disease. The conventional second and third stage i.e. Comprehensive stage II and Fontan procedure of the existing three-staged surgical approach serving as a palliative treatment for this anomaly, entails multiple complications and achieves a survival rate of 50%. Hence, to reduce the morbidity and mortality rate associated with the second and third stages of the existing palliative procedure, the novel alternative techniques called “Hybrid Comprehensive Stage II” (HCSII), and a “Self-powered Fontan circulation” have been proposed. The goal of this research is to conduct in-vitro investigations to validate computational and clinical findings on these proposed novel surgical techniques. The research involves the development of a benchtop study of HCSII and self-powered Fontan circulation

Evaluation of haematological and behavioural changes in Channa punctatus (Bloch) on short-term exposure to a commercial-grade synthetic pyrethroid pesticide

This study aims to assess the acute toxicity of commercial-grade Cypermethrin (10% EC) and evaluate the hematological and behavioral alterations in a freshwater fish Channa punctatus upon short-term exposure to Cypermethrin. A four-day static acute toxicity test was performed to estimate the median lethal concentration (LC50) value of Cypermethrin. During the acute toxicity test, the behavior of the control and cypermethrin exposed fish was critically observed and recorded. After completing the acute toxicity test, the hematological effects of Cypermethrin in C. punctatus were evaluated using two sublethal dosages (0.08 mg/L and 0.12 mg/L). Results of the study revealed that this pesticide induced significant mortality in C. punctatus with a 96-h L50 value of 0.263 mg/L. Cypermethrin exposed fish showed hyperactivity, irritability, erratic swimming, frequent surface visit, etc. Exposure to sublethal concentrations of Cypermethrin for a short period resulted in a significant decline (P<0.05) in total erythrocytes count (TEC), packed cell volume (PCV), mean corpuscular volume (MCV), and hemoglobin (Hb) concentration as compared to control groups. In contrast, pesticide-exposed groups had a significant increase (P<0.05) in mean corpuscular hemoglobin concentration (MCHC) and total leucocyte count (TLC). It is apparent from the results of the study that this commercial formulation is toxic to the studied fish. This study also revealed hematological and behavioral alterations in C. Punctatus which could be used as biomarkers for incipient Cypermethrin intoxication

Magnetic Hydro-Dynamic Propulsion of Blood

The problem with current Ventricular Assist Devices is that the pump design imposes unnatural behavior to the flow of the blood such as stagnation and impingement regions due to the many moving parts, thus promoting the formation of blood clots. To solve this problem, a magneto hydromagnetic drive or MHD can replace the pump in the flow loop. MHD takes advantage of Lorenz’s force, which states that if a magnetic field is perpendicular to an electric field, a particle in the conducting fluid will experience a force orthogonal to both the magnetic and electric field thus to propelling the blood. The result is a unrestricted flow propelled by a electromagnetic force. The first step is to design and build a simple, low cost, and effective electromagnetic flow sensor that is easy to operate and integrates well with a bench-top flow loop. This loop is made up of half inch vinyl tubing, a voltage pump, and a commercial electromagnetic flow sensor. The next step is to use the knowledge from the flow sensor to develop a magnetohydrodynamic drive. The flow sensor design and operation are based on the magnetic flow sensing principle which is built upon Faraday’s Law. This law states that the voltage induced across any conductor as it moves orthogonally through a magnetic field is proportional to the velocity of that conductor. When applying this to a flow sensor, the resulting principle means that any conducting fluid flowing through a magnetic field will induce a voltage which can be read by two electrodes placed orthogonal to the magnetic field. Essentially, the job of the flow sensor is to read these voltage changes that are proportional to and arise from the changes in flow speed. After some post processing of the voltage readings the flow rate can be determined. To reduce the error in the system, the polarity of the magnetic field is changed at a certain rate. This changing field will produce two outputs for the readings of the induced voltages which can be subtracted to cancel out any external readings. Those external readings when taken out of the system will result in a proper flow rate value. After completing the flow sensor, the MHD design will be finalized using a 3D model finite element analysis done in COMSOL Multiphysics

MOCK FLOW LOOP (MFL) FOR SELF-POWERED FONTAN CIRCULATION

The Fontan procedure is the current treatment for babies born with Hypoplastic Left Heart Syndrome (HLHS). The surgery entails multiple severe complications and a survival rate of less than 50% by adulthood. Modification to the Fontan surgery is proposed to lower mortality rate in patients. A bifurcating graft (IJS) has been designed and validated via computational fluid dynamics (CFD) to increase velocity and reduce pressure within the pulmonary arteries. A dynamically scaled mock flow loop (MFL) will be configured to validate the optimized IJS results obtained from the CFD design. The MFL will be based on a reduced Fontan lumped-parameter model (LPM) and will be comprised of RLC components of the systemic and the pulmonary circuit. These RLC values are obtained from clinical references to approximate normal human physiology specific to each vessel bed. The Harvard Medical pulsatile pump provides the targeted flow rate through the IJS. Flow and pressure sensor data at critical points in the MFL are acquired via National Instruments multichannel data acquisition board and processed using LabView. A patient-specific 3D model of the Fontan junction (test section) will be produced via 3D printing (inferior and superior vena cavae attached to left and right pulmonary arteries)

Development of an automated CAD model parameterization scheme for Fontan Circulation

Hypoplastic Left Heart Syndrome (HLHS) is a congenital heart disease (CHD) that leads to a single ventricle circulation (SV). A multitude of complications can occur with the existing three-stage palliative operation leading to 50% survival rates. The Fontan circulation is a fragile system in which imperfections at any one of multiple levels may compromise quality of life, produce secondary pathophysiology, and shorten life span. Increased inferior vena caval (IVC) pressure itself may play some role in “Fontan failure”. Developing an accurate 3D phantom of Fontan physiology for conducting in-vitro measurement is of paramount importance. In this study, we propose to develop an automated model parameterization technique which will be able to create an optimized synthetic 3D phantom for the in-vitro simulation. To this end, we have coupled various design of experiments methodologies (e.g. response surface design and Fractional factorial designs) with the CAD model of the 3D phantom. These design of experiment techniques generate the key input parameters for the development of the synthetic Fontan geometries. The 3D phantom developed using the automated parameterization scheme matches closely with the dimensions of the 3D phantom used for conducting the in-silico simulations

Non-thermal warm dark matter limits from small-scale structure

We present small-scale structure constraints on sterile dark matter produced from a heavy mediator particle, inspired by models of moduli decay. Dark matter particles produced through this mechanism can contribute to the entire dark matter energy density but the particles have a non-thermal phase-space distribution; however, we show that the resulting linear matter power spectra can be mapped to effective thermal-relic warm dark matter models. This production mechanism is therefore subject to warm dark matter constraints from small-scale structure as probed by ultra-faint dwarf galaxy abundances and strong gravitational lensing flux ratio statistics. We use the correspondence to thermal-relic models to derive a lower bound on the non-thermal particle mass of $107\ \mathrm{keV}$, at $95\%$ confidence. These are the first and most stringent constraints derived on sterile dark matter produced via the heavy mediator decay scenario we consider.Comment: Comments are most welcom