Inverse Electrocardiographic Source Localization of Ischemia: An Optimization Framework and Finite Element Solution

With the goal of non-invasively localizing cardiac ischemic disease using body-surface potential recordings, we attempted to reconstruct the transmembrane potential (TMP) throughout the myocardium with the bidomain heart model. The task is an inverse source problem governed by partial differential equations (PDE). Our main contribution is solving the inverse problem within a PDE-constrained optimization framework that enables various physically-based constraints in both equality and inequality forms. We formulated the optimality conditions rigorously in the continuum before deriving finite element discretization, thereby making the optimization independent of discretization choice. Such a formulation was derived for the L₂-norm Tikhonov regularization and the total variation minimization. The subsequent numerical optimization was fulfilled by a primal-dual interior-point method tailored to our problem's specific structure. Our simulations used realistic, fiber-included heart models consisting of up to 18,000 nodes, much finer than any inverse models previously reported. With synthetic ischemia data we localized ischemic regions with roughly a 10% false-negative rate or a 20% false-positive rate under conditions up to 5% input noise. With ischemia data measured from animal experiments, we reconstructed TMPs with roughly 0.9 correlation with the ground truth. While precisely estimating the TMP in general cases remains an open problem, our study shows the feasibility of reconstructing TMP during the ST interval as a means of ischemia localization.

Uncertainty Visualization in Forward and Inverse Cardiac Models

Quantification and visualization of uncertainty in cardiac forward and inverse problems with complex geometries is subject to various challenges. Specific to visualization is the observation that occlusion and clutter obscure important regions of interest, making visual assessment difficult. In order to overcome these limitations in uncertainty visualization, we have developed and implemented a collection of novel approaches. To highlight the utility of these techniques, we evaluated the uncertainty associated with two examples of modeling myocardial activity. In one case we studied cardiac potentials during the repolarization phase as a function of variability in tissue conductivities of the ischemic heart (forward case). In a second case, we evaluated uncertainty in reconstructed activation times on the epicardium resulting from variation in the control parameter of Tikhonov regularization (inverse case). To overcome difficulties associated with uncertainty visualization, we implemented linked-view windows and interactive animation to the two respective cases. Through dimensionality reduction and superimposed mean and standard deviation measures over time, we were able to display key features in large ensembles of data and highlight regions of interest where larger uncertainties exist.

Uncertainty Visualization in HARDI based on Ensembles of ODFs

In this paper, we propose a new and accurate technique for uncertainty analysis and uncertainty visualization based on fiber orientation distribution function (ODF) glyphs, associated with high angular resolution diffusion imaging (HARDI). Our visualization applies volume rendering techniques to an ensemble of 3D ODF glyphs, which we call SIP functions of diffusion shapes, to capture their variability due to underlying uncertainty. This rendering elucidates the complex heteroscedastic structural variation in these shapes. Furthermore, we quantify the extent of this variation by measuring the fraction of the volume of these shapes, which is consistent across all noise levels, the certain volume ratio. Our uncertainty analysis and visualization framework is then applied to synthetic data, as well as to HARDI human-brain data, to study the impact of various image acquisition parameters and background noise levels on the diffusion shapes.

The relation of mild traumatic brain injury to chronic lapses of attention

We assessed the extent to which failures in sustained attention were associated with chronic mild traumatic brain injury (mTBI) deficits in cognitive control among college-age young adults with and without a history of sport-related concussion. Participants completed the ImPACT computer-based assessment and a modified flanker task. Results indicated that a history of mTBI, relative to healthy controls, was associated with inferior overall flanker task performance with a greater number of omission errors and more frequent sequentially occurring omission errors. Accordingly, these findings suggest that failures in the ability to maintain attentional vigilance may, in part, underlie mTBI-related cognition deficits.

White matter structure assessment from reduced HARDI data using low-rank polynomial approximations

Assessing white matter fiber orientations directly from DWI measurements in single-shell HARDI has many advantages. One of these advantages is the ability to model multiple fibers using fewer parameters than are required to describe an ODF and, thus, reduce the number of DW samples needed for the reconstruction. However, fitting a model directly to the data using Gaussian mixture, for instance, is known as an initialization-dependent unstable process. This paper presents a novel direct fitting technique for single-shell HARDI that enjoys the advantages of direct fitting without sacrificing the accuracy and stability even when the number of gradient directions is relatively low. This technique is based on a spherical deconvolution technique and decomposition of a homogeneous polynomial into a sum of powers of linear forms, known as a symmetric tensor decomposition. The fiber-ODF (fODF), which is described by a homogeneous polynomial, is approximated here by a discrete sum of even-order linear-forms that are directly related to rank-1 tensors and represent single-fibers. This polynomial approximation is convolved to a single-fiber response function, and the result is optimized against the DWI measurements to assess the fiber orientations and the volume fractions directly. This formulation is accompanied by a robust iterative alternating numerical scheme which is based on the Levenberg-Marquardt technique. Using simulated data and in vivo, human brain data we show that the proposed algorithm is stable, accurate and can model complex fiber structures using only 12 gradient directions.

Short communication: characterization of early postpartum estrous behavior and ovulation in lactating dairy cows using radiotelemetry

The objective of this study was to describe early postpartum estrous behavior and ovulation in lactating dairy cows using radiotelemetry. Cows (n=50) were continuously monitored for behavioral estrus with a radiotelemetric system, HeatWatch II (CowChips LLC, Manalapan, NJ), from d 14 to approximately d 49 postpartum. Blood collection for analysis of progesterone and ovarian ultrasonography were performed once weekly starting on d 14. First ovulation was associated with behavioral estrus in 5 cows and occurred at 28.2±10.8 d (mean±SD; range 17 to 40 d). The average duration of estrus was 6.0±4.9 h (range 3 to 12.2 h), and the mean number of standing events was 18.4±8.9 (range 4 to 26). Based on progesterone concentrations of ≥1 ng/mL, estimated first postpartum ovulation occurred at 25.1±10.4 d (range 10 to 49 d) for 38 animals without evidence of behavioral estrus. The interval to estimated first ovulation without behavioral estrus was not different from the interval to first ovulation associated with behavioral estrus. Level of milk production and body condition score loss did not affect the interval to estimated first ovulation without estrus or first ovulation associated with estrus. Six animals did not show evidence of ovulation based on progesterone concentration, whereas 1 cow showed evidence of estrous behavior on the day before removal from the study. The majority of first postpartum ovulations (38/43; 88.4%) were not associated with behavioral estrus.

An optimization framework for inversely estimating myocardial transmembrane potentials and localizing ischemia

By combining a static bidomain heart model with a torso conduction model, we studied the inverse electrocardiographic problem of computing the transmembrane potentials (TMPs) throughout the myocardium from a body-surface potential map, and then used the recovered potentials to localize myocardial ischemia. Our main contribution is solving the inverse problem within a constrained optimization framework, which is a generalization of previous methods for calculating transmembrane potentials. The framework offers ample flexibility for users to apply various physiologically-based constraints, and is well supported by mature algorithms and solvers developed by the optimization community. By avoiding the traditional inverse ECG approach of building the lead-field matrix, the framework greatly reduces computation cost and, by setting the associated forward problem as a constraint, the framework enables one to flexibly set individualized resolutions for each physical variable, a desirable feature for balancing model accuracy, ill-conditioning and computation tractability. Although the task of computing myocardial TMPs at an arbitrary time instance remains an open problem, we showed that it is possible to obtain TMPs with moderate accuracy during the ST segment by assuming all cardiac cells are at the plateau phase. Moreover, the calculated TMPs yielded a good estimate of ischemic regions, which was of more clinical interest than the voltage values themselves. We conducted finite element simulations of a phantom experiment over a 2D torso model with synthetic ischemic data. Preliminary results indicated that our approach is feasible and suitably accurate for the common case of transmural myocardial ischemia.

Marine reserves reduce risk of climate-driven phase shift by reinstating size- and habitat-specific trophic interactions

Spatial closures in the marine environment are widely accepted as effective conservation and fisheries management tools. Given increasing human-derived stressors acting on marine ecosystems, the need for such effective action is urgently clear. Here we explore mechanisms underlying the utility of marine reserves to reinstate trophic dynamics and to increase resilience of kelp beds against climate-driven phase shift to sea urchin barrens on the rapidly warming Tasmanian east coast. Tethering and tagging experiments were used to examine size- and shelter-specific survival of the range-extending sea urchin Centrostephanus rodgersii (Diadematidae) translocated to reefs inside and outside no-take Tasmanian marine reserves. Results show that survival rates of C. rodgersii exposed on flat reef substratum by tethering were approximately seven times (small urchins 10.1 times; large urchins 6.1 times) lower on protected reef within marine reserve boundaries (high abundance of large predatory-capable lobsters) compared to fished reef (large predatory lobsters absent). When able to seek crevice shelter, tag-resighting models estimated that mortality rates of C. rodgersii were lower overall but remained 3.3 times (small urchins 2.1 times; large urchins 6.4 times) higher in the presence of large lobsters inside marine reserves, with higher survival of small urchins owing to greater access to crevices relative to large urchins. Indeed, shelter was 6.3 times and 3.1 times more important to survival of small and large urchins, respectively, on reserved relative to fished reef. Experimental results corroborate with surveys throughout the range extension region, showing greater occurrence of overgrazing on high-relief rocky habitats where shelter for C. rodgersii is readily available. This shows that ecosystem impacts mediated by range extension of such habitat-modifying organisms will be heterogeneous in space, and that marine systems with a more natural complement of large and thus functional predators, as achievable within no-take reserves, will minimize local risk of phase shifts by reinstating size and habitat-specific predator-prey dynamics eroded by fishing. Importantly, our findings also highlight the crucial need to account for the influence of size dynamics and habitat complexity on rates of key predator-prey interactions when managing expectations of ecosystem-level responses within marine reserve boundaries.

Biomedical Visual Computing: Case Studies and Challenges

Advances in computational geometric modeling, imaging, and simulation let researchers build and test models of increasing complexity, generating unprecedented amounts of data. As recent research in biomedical applications illustrates, visualization will be critical in making this vast amount of data usable; it's also fundamental to understanding models of complex phenomena.

INTERACTIVE VISUALIZATION OF PROBABILITY AND CUMULATIVE DENSITY FUNCTIONS

The probability density function (PDF), and its corresponding cumulative density function (CDF), provide direct statistical insight into the characterization of a random process or field. Typically displayed as a histogram, one can infer probabilities of the occurrence of particular events. When examining a field over some two-dimensional domain in which at each point a PDF of the function values is available, it is challenging to assess the global (stochastic) features present within the field. In this paper, we present a visualization system that allows the user to examine two-dimensional data sets in which PDF (or CDF) information is available at any position within the domain. The tool provides a contour display showing the normed difference between the PDFs and an ansatz PDF selected by the user and, furthermore, allows the user to interactively examine the PDF at any particular position. Canonical examples of the tool are provided to help guide the reader into the mapping of stochastic information to visual cues along with a description of the use of the tool for examining data generated from an uncertainty quantification exercise accomplished within the field of electrophysiology.

Minimum Information about a Cardiac Electrophysiology Experiment (MICEE): standardised reporting for model reproducibility, interoperability, and data sharing

Cardiac experimental electrophysiology is in need of a well-defined Minimum Information Standard for recording, annotating, and reporting experimental data. As a step towards establishing this, we present a draft standard, called Minimum Information about a Cardiac Electrophysiology Experiment (MICEE). The ultimate goal is to develop a useful tool for cardiac electrophysiologists which facilitates and improves dissemination of the minimum information necessary for reproduction of cardiac electrophysiology research, allowing for easier comparison and utilisation of findings by others. It is hoped that this will enhance the integration of individual results into experimental, computational, and conceptual models. In its present form, this draft is intended for assessment and development by the research community. We invite the reader to join this effort, and, if deemed productive, implement the Minimum Information about a Cardiac Electrophysiology Experiment standard in their own work.

Microfluidic laminate-based phantom for diffusion tensor-magnetic resonance imaging (DT-MRI)

This paper reports fabrication of a magnetic resonance imaging (MRI) phantom created by stacking of multiple thin polydimethylsiloxane (PDMS) layers. PDMS is spin coated on SU-8 molds to obtain the desired layer thickness and imprints of the microchannel patterns that define the phantom geometry. This paper also identifies the unique challenges related to the fabrication and assembly of multiple thin layers and reports for the first time assembly of a large number of thin laminates of this nature. Use of photolithography techniques allows us to create a wide range of phantom geometries. The target dimensions of the phantoms reported here are (i) a stack of 30 thin PDMS layers of 10 µm thickness (ii) curved 5 µm × 5 µm microchannels with 8.7 µm spacing, and (iii) straight 5 µm × 5 µm microchannels with 3.6 µm spacing. SEM scans of the assembled phantoms show open microchannels and a monolithic cross-section with no visible interface between PDMS layers. Based on the results of diffusion tensor magnetic resonance imaging (DT-MRI) scan, the anisotropic diffusion of water molecules due to the physical restriction of the microchannels was detected, which means that the phantom can be used to calibrate and optimize MRI instrumentation.

Finite-element-based discretization and regularization strategies for 3-D inverse electrocardiography

We consider the inverse electrocardiographic problem of computing epicardial potentials from a body-surface potential map. We study how to improve numerical approximation of the inverse problem when the finite-element method is used. Being ill-posed, the inverse problem requires different discretization strategies from its corresponding forward problem. We propose refinement guidelines that specifically address the ill-posedness of the problem. The resulting guidelines necessitate the use of hybrid finite elements composed of tetrahedra and prism elements. Also, in order to maintain consistent numerical quality when the inverse problem is discretized into different scales, we propose a new family of regularizers using the variational principle underlying finite-element methods. These variational-formed regularizers serve as an alternative to the traditional Tikhonov regularizers, but preserves the L(2) norm and thereby achieves consistent regularization in multiscale simulations. The variational formulation also enables a simple construction of the discrete gradient operator over irregular meshes, which is difficult to define in traditional discretization schemes. We validated our hybrid element technique and the variational regularizers by simulations on a realistic 3-D torso/heart model with empirical heart data. Results show that discretization based on our proposed strategies mitigates the ill-conditioning and improves the inverse solution, and that the variational formulation may benefit a broader range of potential-based bioelectric problems.

Detection of crossing white matter fibers with high-order tensors and rank-k decompositions

Fundamental to high angular resolution diffusion imaging (HARDI), is the estimation of a positive-semidefinite orientation distribution function (ODF) and extracting the diffusion properties (e.g., fiber directions). In this work we show that these two goals can be achieved efficiently by using homogeneous polynomials to represent the ODF in the spherical deconvolution approach, as was proposed in the Cartesian Tensor-ODF (CT-ODF) formulation. Based on this formulation we first suggest an estimation method for positive-semidefinite ODF by solving a linear programming problem that does not require special parameterization of the ODF. We also propose a rank-k tensor decomposition, known as CP decomposition, to extract the fibers information from the estimated ODF. We show that this decomposition is superior to the fiber direction estimation via ODF maxima detection as it enables one to reach the full fiber separation resolution of the estimation technique. We assess the accuracy of this new framework by applying it to synthetic and experimentally obtained HARDI data.

Monitoring associations between clade-level variation, overall community structure and ecosystem function in enhanced biological phosphorus removal (EBPR) systems using terminal-restriction fragment length polymorphism (T-RFLP)

The role of Candidatus "Accumulibacter phosphatis" (Accumulibacter) in enhanced biological phosphorus removal (EBPR) is well established but the relevance of different Accumulibacter clades to the performance of EBPR systems is unknown. We developed a terminal-restriction fragment length polymorphism (T-RFLP) technique to monitor changes in the relative abundance of key members of the bacterial community, including Accumulibacter clades, in four replicate mini-sequencing batch reactors (mSBRs) operated for EBPR over a 35-day period. The ability of the T-RFLP technique to detect trends was confirmed using fluorescence in situ hybridisation (FISH). EBPR performance varied between reactors and over time; by day 35, performance was maintained in mSBR2 whilst it had deteriorated in mSBR1. However, reproducible trends in structure-function relationships were detected in the mSBRs. EBPR performance was strongly associated with the relative abundance of total Accumulibacter. A shift in the ratio of the dominant Accumulibacter clades was also detected, with Type IA associated with good EBPR performance and Type IIC associated with poor EBPR performance. Changes in ecosystem function of the mSBRs in the early stages of the experiment were more closely associated with changes in the abundance of (unknown) members of the flanking community than of either Accumulibacter or Candidatus "Competibacter phosphatis". This study therefore reveals a hitherto unrecorded and complex relationship between Accumulibacter clades, the flanking community and ecosystem function of laboratory-scale EBPR systems.

POCS-enhanced correction of motion artifacts in parallel MRI

A new method for correction of MRI motion artifacts induced by corrupted k-space data, acquired by multiple receiver coils such as phased arrays, is presented. In our approach, a projections onto convex sets (POCS)-based method for reconstruction of sensitivity encoded MRI data (POCSENSE) is employed to identify corrupted k-space samples. After the erroneous data are discarded from the dataset, the artifact-free images are restored from the remaining data using coil sensitivity profiles. The error detection and data restoration are based on informational redundancy of phased-array data and may be applied to full and reduced datasets. An important advantage of the new POCS-based method is that, in addition to multicoil data redundancy, it can use a priori known properties about the imaged object for improved MR image artifact correction. The use of such information was shown to improve significantly k-space error detection and image artifact correction. The method was validated on data corrupted by simulated and real motion such as head motion and pulsatile flow.

Overfishing reduces resilience of kelp beds to climate-driven catastrophic phase shift

A key consideration in assessing impacts of climate change is the possibility of synergistic effects with other human-induced stressors. In the ocean realm, climate change and overfishing pose two of the greatest challenges to the structure and functioning of marine ecosystems. In eastern Tasmania, temperate coastal waters are warming at approximately four times the global ocean warming average, representing the fastest rate of warming in the Southern Hemisphere. This has driven range extension of the ecologically important long-spined sea urchin (Centrostephanus rodgersii), which has now commenced catastrophic overgrazing of productive Tasmanian kelp beds leading to loss of biodiversity and important rocky reef ecosystem services. Coincident with the overgrazing is heavy fishing of reef-based predators including the spiny lobster Jasus edwardsii. By conducting experiments inside and outside Marine Protected Areas we show that fishing, by removing large predatory lobsters, has reduced the resilience of kelp beds against the climate-driven threat of the sea urchin and thus increased risk of catastrophic shift to widespread sea urchin barrens. This shows that interactions between multiple human-induced stressors can exacerbate nonlinear responses of ecosystems to climate change and limit the adaptive capacity of these systems. Management actions focused on reducing the risk of catastrophic phase shift in ecosystems are particularly urgent in the face of ongoing warming and unprecedented levels of predator removal from the world's oceans.

Resolution strategies for the finite-element-based solution of the ECG inverse problem

Successful employment of numerical techniques for the solution of forward and inverse ECG problems requires the ability to both quantify and minimize approximation errors introduced as part of the discretization process. Our objective is to develop discretization and refinement strategies involving hybrid-shaped finite elements so as to minimize approximation errors for the ECG inverse problem. We examine both the ill-posedness of the mathematical inverse problem and the ill-conditioning of the discretized system in order to propose strategies specifically designed for the ECG inverse problem. We demonstrate that previous discretization and approximation strategies may worsen the properties of the inverse problem approximation. We then demonstrate the efficacy of our strategies on both a simplified and a realistic 2-D torso model.

Subject-specific, multiscale simulation of electrophysiology: a software pipeline for image-based models and application examples

Many simulation studies in biomedicine are based on a similar sequence of processing steps, starting from images and running through geometric model generation, assignment of tissue properties, numerical simulation and visualization of the results--a process known as image-based geometric modelling and simulation. We present an overview of software systems for implementing such a sequence both within highly integrated problem-solving environments and in the form of loosely integrated pipelines. Loose integration in this case indicates that individual programs function largely independently but communicate through files of a common format and support simple scripting, so as to automate multiple executions wherever possible. We then describe three specific applications of such pipelines to translational biomedical research in electrophysiology.

A molecular approach to identify prey of the southern rock lobster

We demonstrate the use of molecular techniques to detect specific prey consumed by the southern rock lobster (Jasus edwardsii). A quick and non-lethal method was used to collect rock lobster faecal material and a molecular protocol was employed to isolate prey DNA from faecal samples. The isolated DNA was amplified using the polymerase chain reaction (PCR) with PCR primers designed to target specific prey items. Feeding experiments determined that DNA from black-lipped abalone (Haliotis rubra) and sea urchins (Centrostephanus rodgersii and Heliocidaris erythrogramma) can be detected in rock lobster faecal samples within seven hours and remains present for up to 60 h after ingestion.

A randomised controlled trial of the reciprocating syringe in arthrocentesis

OBJECTIVE

To evaluate the outcomes of arthrocentesis with the new highly controllable, one handed reciprocating procedure syringe compared with a conventional syringe.

METHODS

100 arthrocentesis procedures were randomised between the reciprocating syringe and the conventional syringe. Outcome measures included patient pain, procedure duration, operator satisfaction, synovial fluid volume, cell counts, and complications.

RESULTS

50 arthrocentesis procedures with the conventional syringe resulted in a mean (SD) procedure time of 3.39 (1.88) minutes, a mean VAPS (patient pain) score of 5.35 (3.15), and a mean VASS (operator satisfaction) score of 4.88 (1.92); 30 of the 50 subjects experienced moderate to severe pain (VAPS score 5 or greater) during arthrocentesis. In contrast, the reciprocating syringe resulted in a reduced procedure time of 1.94 (1.14) minutes (p<0.001), a reduced VAPS (patient pain) score of 2.54 (1.60) (p<0.001), and an increased VASS (operator satisfaction) score of 8.91 (0.79) (p<0.001). Only five of the 50 of subjects experienced moderate to severe pain with the reciprocating syringe. Synovial cell counts were similar between the two syringes (p>0.05), but there was a trend toward greater volume (greater synovial fluid yield) and fewer red blood cells with the reciprocating syringe.

CONCLUSIONS

Arthrocentesis with a conventional syringe results in moderate to severe pain in 60% of subjects. The reciprocating syringe prevents significant pain, reduces procedure time, and improves physician performance of arthrocentesis. The reciprocating syringe is superior to the conventional syringe in arthrocentesis.

Caspase-9 regulation: an update

The complex sequence of events leading to apoptotic cell death is governed by an elaborate regulatory scheme involving the actions of both initiator and executioner proteases. Among the most intensively studied of the initiator caspases is caspase-9, an essential throughput element in the so-called intrinsic or mitochondrially gated pathway of apoptosis. Previous reviews have described the proteolytic processing and activation of this protease in much detail; here we provide an update on caspase-9 regulation. A comprehensive description of the intra- and intermolecular events involved in modulating protein expression and activity are presented. Particular emphasis is placed on the role alternative splicing plays in the expression of functionally divergent protein isoforms, as well as, the participation of specific post-translational events in regulating caspase-9 activity. Such discrete modulation in reported activity characterizes, not only the pivotal role of this protease in the final commitment process itself, but also emphasizes the more general interplay that exists between mutually opposing cytotoxic and cytoprotective influences in maintaining cellular homeostasis.

Noise-adaptive nonlinear diffusion filtering of MR images with spatially varying noise levels

Anisotropic diffusion filtering is widely used for MR image enhancement. However, the anisotropic filter is nonoptimal for MR images with spatially varying noise levels, such as images reconstructed from sensitivity-encoded data and intensity inhomogeneity-corrected images. In this work, a new method for filtering MR images with spatially varying noise levels is presented. In the new method, a priori information regarding the image noise level spatial distribution is utilized for the local adjustment of the anisotropic diffusion filter. Our new method was validated and compared with the standard filter on simulated and real MRI data. The noise-adaptive method was demonstrated to outperform the standard anisotropic diffusion filter in both image error reduction and image signal-to-noise ratio (SNR) improvement. The method was also applied to inhomogeneity-corrected and sensitivity encoding (SENSE) images. The new filter was shown to improve segmentation of MR brain images with spatially varying noise levels.