David N. Mashburn

CellFIT: A Cellular Force-Inference Toolkit Using Curvilinear Cell Boundaries

Mechanical forces play a key role in a wide range of biological processes, from embryogenesis to cancer metastasis, and there is considerable interest in the intuitive question, “Can cellular forces be inferred from cell shapes?” Although several groups have posited affirmative answers to this stimulating question, nagging issues remained regarding equation structure, solution uniqueness and noise sensitivity. Here we show that the mechanical and mathematical factors behind these issues can be resolved by using curved cell edges rather than straight ones. We present a new package of force-inference equations and assessment tools and denote this new package CellFIT, the Cellular Force Inference Toolkit. In this approach, cells in an image are segmented and equilibrium equations are constructed for each triple junction based solely on edge tensions and the limiting angles at which edges approach each junction. The resulting system of tension equations is generally overdetermined. As a result, solutions can be obtained even when a modest number of edges need to be removed from the analysis due to short length, poor definition, image clarity or other factors. Solving these equations yields a set of relative edge tensions whose scaling must be determined from data external to the image. In cases where intracellular pressures are also of interest, Laplace equations are constructed to relate the edge tensions, curvatures and cellular pressure differences. That system is also generally overdetermined and its solution yields a set of pressures whose offset requires reference to the surrounding medium, an open wound, or information external to the image. We show that condition numbers, residual analyses and standard errors can provide confidence information about the inferred forces and pressures. Application of CellFIT to several live and fixed biological tissues reveals considerable force variability within a cell population, significant differences between populations and elevated tensions along heterotypic boundaries.

Enabling user-guided segmentation and tracking of surface-labeled cells in time-lapse image sets of living tissues.

To study the process of morphogenesis, one often needs to collect and segment time‐lapse images of living tissues to accurately track changing cellular morphology. This task typically involves segmenting and tracking tens to hundreds of individual cells over hundreds of image frames, a scale that would certainly benefit from automated routines; however, any automated routine would need to reliably handle a large number of sporadic, and yet typical problems (e.g., illumination inconsistency, photobleaching, rapid cell motions, and drift of focus or of cells moving through the imaging plane). Here, we present a segmentation and cell tracking approach based on the premise that users know their data best–interpreting and using image features that are not accounted for in any a priori algorithm design. We have developed a program, SeedWater Segmenter, that combines a parameter‐less and fast automated watershed algorithm with a suite of manual intervention tools that enables users with little to no specialized knowledge of image processing to efficiently segment images with near‐perfect accuracy based on simple user interactions.

Apical oscillations in amnioserosa cells: basolateral coupling and mechanical autonomy.

Holographic laser microsurgery is used to isolate single amnioserosa cells in vivo during early dorsal closure. During this stage of Drosophila embryogenesis, amnioserosa cells undergo oscillations in apical surface area. The postisolation behavior of individual cells depends on their preisolation phase in these contraction/expansion cycles: cells that were contracting tend to collapse quickly after isolation; cells that were expanding do not immediately collapse, but instead pause or even continue to expand for ∼40 s. In either case, the postisolation apical collapse can be prevented by prior anesthetization of the embryos with CO2. These results suggest that although the amnioserosa is under tension, its cells are subjected to only small elastic strains. Furthermore, their postisolation apical collapse is not a passive elastic relaxation, and both the contraction and expansion phases of their oscillations are driven by intracellular forces. All of the above require significant changes to existing computational models.

Polarity reversal lowers activation time during diastolic field stimulation of the rabbit ventricles: insights into mechanisms

To fully characterize the mechanisms of defibrillation, it is necessary to understand the response, within the three-dimensional (3D) volume of the ventricles, to shocks given in diastole. Studies that have examined diastolic responses conducted measurements on the epicardium or on a transmural surface of the left ventricular (LV) wall only. The goal of this study was to use optical imaging experiments and 3D bidomain simulations, including a model of optical mapping, to ascertain the shock-induced virtual electrode and activation patterns throughout the rabbit ventricles following diastolic shocks. We tested the hypothesis that the locations of shock-induced regions of hyperpolarization govern the different diastolic activation patterns for shocks of reversed polarity. In model and experiment, uniform-field monophasic shocks of reversed polarities (cathode over the right ventricle is RV-, reverse polarity is LV-) were applied to the ventricles in diastole. Experiments and simulations revealed that RV- shocks resulted in longer activation times compared with LV- shocks of the same strength. 3D simulations demonstrated that RV- shocks induced a greater volume of hyperpolarization at shock end compared with LV- shocks; most of these hyperpolarized regions were located in the LV. The results of this study indicate that ventricular geometry plays an important role in both the location and size of the shock-induced virtual anodes that determine activation delay during the shock and subsequently affect shock-induced propagation. If regions of hyperpolarization that develop during the shock are sufficiently large, activation delay may persist until shock end.

Practical aspects of the cellular force inference toolkit (CellFIT)

If we are to fully understand the reasons that cells and tissues move and acquire their distinctive geometries during processes such as embryogenesis and wound healing, we will need detailed maps of the forces involved. One of the best current prospects for obtaining this information is noninvasive force-from-images techniques such as CellFIT, the Cellular Force Inference Toolkit, whose various steps are discussed here. Like other current quasistatic approaches, this one assumes that cell shapes are produced by interactions between interfacial tensions and intracellular pressures. CellFIT, however, allows cells to have curvilinear boundaries, which can significantly improve inference accuracy and reduce noise sensitivity. The quality of a CellFIT analysis depends on how accurately the junction angles and edge curvatures are measured, and a software tool we describe facilitates determination and evaluation of this information. Special attention is required when edges are crenulated or significantly different in shape from a circular arc. Because the tension and pressure equations are overdetermined, a select number of edges can be removed from the analysis, and these might include edges that are poorly defined in the source image, too short to provide accurate angles or curvatures, or noncircular. The approach works well for aggregates with as many as 1000 cells, and introduced errors have significant effects on only a few adjacent cells. An understanding of these considerations will help CellFIT users to get the most out of this promising new technique.

A high-voltage cardiac stimulator for field shocks of a whole heart in a bath

Defibrillators are a critical tool for treating heart disease; however, the mechanisms by which they halt fibrillation are still not fully understood and are the subject of ongoing research. Clinical defibrillators do not provide the precise control of shock timing, duration, and voltage or other features needed for detailed scientific inquiry, and there are few, if any, commercially available units designed for research applications. For this reason, we have developed a high-voltage, programmable, capacitive-discharge stimulator optimized to deliver defibrillation shocks with precise timing and voltage control to an isolated animal heart, either in air or in a bath. This stimulator is capable of delivering voltages of up to 500 V and energies of nearly 100 J with timing accuracy of a few microseconds and with rise and fall times of 5 micros or less and is controlled only by two external timing pulses and a control computer that sets the stimulation parameters via a LABVIEW interface. Most importantly, the stimulator has circuits to protect the high-voltage circuitry and the operator from programming and input-output errors. This device has been tested and used successfully in field shock experiments on rabbit hearts as well as other protocols requiring high voltage.

A Phased-Array Stimulator System for Studying Planar and Curved Cardiac Activation Wavefronts

Wavefront propagation in cardiac tissue is affected greatly by the geometry of the wavefront. We describe a computer-controlled stimulator system that creates reproducible wavefronts of a predetermined shape and orientation for the investigation of the effects of wavefront geometry. We conducted demonstration experiments on isolated perfused rabbit hearts, which were stained with the voltage-sensitive dye, di-4-ANEPPS. The wavefronts were imaged using a laser and a charge-coupled device (CCD) camera. The stimulator and imaging systems have been used to characterize the relationship between wavefront velocity and fiber orientation. This approach has potential applications in investigating curvature effects, testing numerical models of cardiac tissue, and creating complex wavefronts using one-, two-, or three-dimensional electrode arrays.

Transmembrane Current Imaging in the Heart during Pacing and Fibrillation

Recently, we described a method to quantify the time course of total transmembrane current (Im) and the relative role of its two components, a capacitive current (Ic) and a resistive current (Iion), corresponding to the cardiac action potential during stable propagation. That approach involved recording high-fidelity (200 kHz) transmembrane potential (Vm) signals with glass microelectrodes at one site using a spatiotemporal coordinate transformation via measured conduction velocity. Here we extend our method to compute these transmembrane currents during stable and unstable propagation from fluorescence signals of Vm at thousands of sites (3 kHz), thereby introducing transmembrane current imaging. In contrast to commonly used linear Laplacians of extracellular potential (Ve) to compute Im, we utilized nonlinear image processing to compute the required second spatial derivatives of Vm. We quantified the dynamic spatial patterns of current density of Im and Iion for both depolarization and repolarization during pacing (including nonplanar patterns) by calibrating data with the microelectrode signals. Compared to planar propagation, we found that the magnitude of Iion was significantly reduced at sites of wave collision during depolarization but not repolarization. Finally, we present uncalibrated dynamic patterns of Im during ventricular fibrillation and show that Im at singularity sites was monophasic and positive with a significant nonzero charge (Im integrated over 10 ms) in contrast with nonsingularity sites. Our approach should greatly enhance the understanding of the relative roles of functional (e.g., rate-dependent membrane dynamics and propagation patterns) and static spatial heterogeneities (e.g., spatial differences in tissue resistance) via recordings during normal and compromised propagation, including arrhythmias.