Anthony J. Kearsley

Mathematical optimization of procedures for cryoprotectant equilibration using a toxicity cost function.

Cryopreservation nearly universally depends on the equilibration of cells and tissues with high concentrations of permeating chemicals known as cryoprotective agents, or CPAs. Despite their protective properties, CPAs can cause damage as a result of osmotically-driven cell volume changes, as well as chemical toxicity. In this study, we have used previously published data to determine a toxicity cost function, a quantity that represents the cumulative damage caused by toxicity. We then used this cost function to define and numerically solve the optimal control problem for CPA equilibration, using human oocytes as representative cell type with high clinical relevance. The resulting toxicity-optimal procedures are predicted to yield significantly less toxicity than conventional stepwise procedures. In particular, our results show that toxicity is minimized during CPA addition by inducing the cell to swell to its maximum tolerable volume and then loading it with CPA while in the swollen state. This counterintuitive result is considerably different from the conventional stepwise strategy, which involves exposure to successively higher CPA concentrations in order to avoid excessive shrinkage. The procedures identified in the present study have the potential to significantly reduce damage due to toxicity and warrant further investigation.

Primary phase field of the Pb-doped 2223 high-{Tc} superconductor in the (Bi,Pb)-Sr-Ca-Cu-O system

Both liquidus and subsolidus phase equilibrium data are of central importance for applications of high temperature superconductors in the (Bi, Pb)-Sr-Ca-Cu-O system, including material synthesis, melt processing and single crystal growth. The subsolidus equilibria of the 110 K high-Tc Pb-doped 2223 ([Bi, Pb], Sr, Ca, Cu) phase and the location of the primary phase field (crystallization field) have been determined in this study. For the quantitative determination of liquidus data, a wicking technique was developed to capture the melt for quantitative microchemical analysis. A total of 29 five-phase volumes that include the 2223 phase as a component was obtained. The initial melt compositions of these volumes range from a mole fraction of 7.3 % to 28.0 % for Bi, 11.3 % to 27.8 % for Sr, 1.2 % to 19.4 % for Pb, 9.8 % to 30.8 % for Ca, and 17.1 % to 47.0 % for Cu. Based on these data, the crystallization field for the 2223 phase was constructed using the convex hull technique. A section of this “volume” was obtained by holding two components of the composition at the median value, allowing projection on the other three axes to show the extent of the field.

Global and Local Optimization Algorithms for Optimal Signal Set Design

The problem of choosing an optimal signal set for non-Gaussian detection was reduced to a smooth inequality constrained mini-max nonlinear programming problem by Gockenbach and Kearsley. Here we consider the application of several optimization algorithms, both global and local, to this problem. The most promising results are obtained when special-purpose sequential quadratic programming (SQP) algorithms are embedded into stochastic global algorithms.

A numerical method for mass spectral data analysis

The new generation of mass spectrometers produces an astonishing amount of high-quality data in a brief period of time, leading to inevitable data analysis bottlenecks. Automated data analysis algorithms are required for rapid and repeatable processing of mass spectra containing hundreds of peaks, the part of the spectra containing information. New data processing algorithms must work with minimal user input, both to save operator time and to eliminate inevitable operator bias. Toward this end an accurate mathematical algorithm is presented that automatically locates and calculates the area beneath peaks. The promising numerical performance of this algorithm applied to raw data is presented.

Projections Onto Order Simplexes and Isotonic Regression

Isotonic regression is the problem of fitting data to order constraints. This problem can be solved numerically in an efficient way by successive projections onto order simplex constraints. An algorithm for solving the isotonic regression using successive projections onto order simplex constraints was originally suggested and analyzed by Grotzinger and Witzgall. This algorithm has been employed repeatedly in a wide variety of applications. In this paper we briefly discuss the isotonic regression problem and its solution by the Grotzinger-Witzgall method. We demonstrate that this algorithm can be appropriately modified to run on a parallel computer with substantial speed-up. Finally we illustrate how it can be used to pre-process mass spectral data for automatic high throughput analysis.

An Infeasible Point Method for Minimizing the Lennard-JonesPotential

Minimizing the Lennard-Jones potential, the most-studied modelproblem for molecular conformation, is an unconstrained globaloptimization problem with a large number of local minima. In thispaper, the problem is reformulated as an equality constrainednonlinear programming problem with only linear constraints. Thisformulation allows the solution to approached through infeasibleconfigurations, increasing the basin of attraction of the globalsolution. In this way the likelihood of finding a global minimizeris increased. An algorithm for solving this nonlinear program isdiscussed, and results of numerical tests are presented.

Recovering Circles and Spheres from Point Data

Methods for fitting circles and spheres to point sets are discussed. LADAR (LAser Detection And Ranging) scanners are capable of generating ‘point clouds’ containing the (x, y, z) coordinates of up to several millions of points reflecting the laser signals. In particular, coordinates collected off objects such as spheres may then be used to model these objects by fitting procedures. Fitting amounts to minimizing what is called here a “gauge function,” which quantifies the quality of a particular fit. This work analyzes and experimentally examines the impact of the choice of three such gauge functions. One of the resulting methods, termed here as “algebraic” fitting, formulates the minimization problem as a regression. The second, referred to as “geometric” fitting, minimizes the sum of squares of the Euclidean distances of the data points from the tentative sphere. This method, based on orthogonal distance minimization, is most highly regarded and widely used. The third method represents a novel way of fitting. It is based on the directions in which the individual data points have been acquired.

Bayesian Tomography for Projections with an Arbitrary Transmission Function with an Application in Electron Microscopy.

The vast majority of the developments in tomography assume that the transmission of the probe through the sample follows Beer’s Law, i.e., the rule of exponential attenuation. However, for transmission electron microscopy of samples a few times their mean free path, Beer’s Law is no longer an accurate description of the transmission of the probe as a function of the sample thickness. Recent simulations [Z. H. Levine, Appl. Phys. Lett. 82, 3943 (2003)] have demonstrated accounting for the correct transmission function leads to superior tomographic reconstructions for a photonic band gap sample 8 µm square. Those recent simulations assumed that data was available at all angles, i.e., over 180°. Here, we consider a limited-angle case by generalizing the Bayesian formalism of Bouman and Sauer to allow an arbitrary transmission function. The new formalism is identical to that of Bouman and Sauer when the transmission function obeys Beer’s Law. The examples, based on 140° of data, suggest that using the physical transmission function is a requirement for performing limited angle reconstructions.

An Approach to Parallelizing Isotonic Regression

Isotonic regression is the problem of fitting data to order constraints. We demonstrate that the isotonic regression of a finite set of numbers Y can be obtained by decomposing Y into subsets, performing parallel isotonic regressions on each subset, then performing a trivial isotonic regression on the resulting combined set. Numerical experiments confirm the efficacy of this approach.

Foundations of modeling in cryobiology I: Concentration, Gibbs energy, and chemical potential relationships

Mathematical modeling plays an enormously important role in understanding the behavior of cells, tissues, and organs undergoing cryopreservation. Uses of these models range from explanation of phenomena, exploration of potential theories of damage or success, development of equipment, and refinement of optimal cryopreservation/cryoablation strategies. Over the last half century there has been a considerable amount of work in bio-heat and mass-transport, and these models and theories have been readily and repeatedly applied to cryobiology with much success. However, there are significant gaps between experimental and theoretical results that suggest missing links in models. One source for these potential gaps is that cryobiology is at the intersection of several very challenging aspects of transport theory: it couples multi-component, moving boundary, multiphase solutions that interact through a semipermeable elastic membrane with multicomponent solutions in a second time-varying domain, during a two-hundred Kelvin temperature change with multi-molar concentration gradients and multi-atmosphere pressure changes. In order to better identify potential sources of error, and to point to future directions in modeling and experimental research, we present a three part series to build from first principles a theory of coupled heat and mass transport in cryobiological systems accounting for all of these effects. The hope of this series is that by presenting and justifying all steps, conclusions may be made about the importance of key assumptions, perhaps pointing to areas of future research or model development, but importantly, lending weight to standard simplification arguments that are often made in heat and mass transport. In this first part, we review concentration variable relationships, their impact on choices for Gibbs energy models, and their impact on chemical potentials.