Statistical analysis of signals from an intracavitary probe in a diseased heart.

A model study introduces the use of statistical signal processing to analyse the signals from an intracavitary probe. A complete derivation is given for the detection of one type of arrhythmogenic substrate, myocardial infarctions (MIs). Both the use of statistical signal processing and the detection of VT substrates, as opposed to activation maps, are unique. A quasi-stationary electromagnetic model with simplified geometry is presented. The model is used to simulate ventricular pacing in the presence of MI. The likelihood ratio is used for detection. A tabulation of the results from this model shows that an intracavitary probe can be used to detect MIs as small as 400 mm2 in 1 mV of noise with a detectability index of 0.495, where 0.5 indicates perfect detection. Sensitivity to noise can be reduced by analysing multiple heart beats. The results are only slightly affected by changing the probe from a cage frame design, which mechanically supports the electrodes on thin spokes, to a balloon design, which supports the electrodes on the surface of an insulating balloon.

Estimating defibrillation efficacy using combined upper limit of vulnerability and defibrillation testing.

It is frequently necessary, both clinically and in the laboratory, to estimate how strong a stimulus is required to defibrillate. Current techniques for forming such estimates require the repeated induction of ventricular fibrillation (VF) and subsequent attempts at defibrillation (DF testing). DF testing can be time consuming and in the operating room may increase the patient risks. A novel scheme is presented which combines DF testing with upper limit of vulnerability (ULV) testing. ULV testing is a relatively safe procedure which yields data well correlated with defibrillation efficacy. A Bayesian statistical model of combined ULV/DF testing is presented which is both powerful and concise. The model is used in two examples to design minimum rms error protocols and estimators for the DF95 (the stimulus strength which defibrillates 95% of the time). A simulation for humans of one example solution shows that a single VF episode of combined ULV/DF testing (rms error = 23% of the mean DF95) is better than two VF episodes with DF testing alone (25%). The simulation results for a second example are directly compared with laboratory results from six pigs, showing a less than 1.0% average difference between the simulated and measured rms errors.

Estimation of tissue resistivities from multiple-electrode impedance measurements.

In order to measure in vivo resistivity of tissues in the thorax, the possibility of combining anatomical data extracted from high-resolution images with multiple-electrode impedance measurements, a priori knowledge of the range of tissue resistivities, and a priori data on the instrumentation noise is assessed in this study. A statistically constrained minimum-mean-square error estimator (MIMSEE) that minimizes the effects of linearization errors and instrumentation noise is developed and compared to the conventional least-squares error estimator (LSEE). The MIMSEE requires a priori signal and noise information. The statistical constraint signal information was obtained from a priori knowledge of the physiologically allowed range of regional resistivities. The noise constraint information was obtained from a priori knowledge of the linearization error and the instrumentation noise. The torso potentials were simulated by employing a three-dimensional canine torso model. The model consists of four different conductivity regions: heart, right lung, left lung, and body. It is demonstrated that the statistically constrained MIMSEE performs significantly better than the LSEE in determining resistivities. The results based on the torso model indicate that regional resistivities can be estimated to within 40% accuracy of their true values by utilizing a statistically constrained MIMSEE, even if the instrumentation noise is comparable to the measured torso potentials. The errors obtained using the LSEE with the same linearized transfer function and level of instrumentation noise were about five times larger than those obtained using the MIMSEE. For larger measurement errors the MIMSEE performs even better when compared to the LSEE.

Comments on distinguishability in electrical impedance imaging.

In Electrical Impedance Imaging (EII), the spatial distribution of electrical resistivity of a volume conductor is reconstructed from measurements of potential which result from an externally applied electric field. The ability of such a system to distinguish a target inhomogeneity and the discussion of several measures of distinguishability has been a subject of a recent study. In this communication a few comments are added to those of. The medical device safety regulations limit the maximum total input current which can be applied to the human thorax. Based on the currently existing safety regulations, if the input current to the thorax is limited and constant, patterns applied between opposite electrodes result in higher distinguishability of a centered target than the cosine current patterns as suggested by.

A bidomain model with periodic intracellular junctions: a one-dimensional analysis.

The classical bidomain model of cardiac tissue views the intracellular and extracellular (interstitial) spaces as two coupled but separate continua. In the present study, the classical bidomain model has been extended by introducing a periodic conductivity in the intracellular space to represent the junctional discontinuity between abutting myocytes. In this model the junctional region of a myocyte is represented in a way that permits variation of junction size and conductivity profile. Employing spectral techniques, a new method was developed for solving the coupled differential equations governing the intracellular and extracellular potentials in a tissue preparation of finite dimensions. Different spectral representations are used for the aperiodic intra- and extracellular potentials (finite Fourier integral transform) and for the periodic intracellular conductivity (Fourier series). As a first application of the method, the response of a 50-cell, single interior fiber to a defibrillating current is examined under steady-state conditions. Transmembrane as well as intra- and extracellular potential distributions along the fiber were calculated.

Estimating the 95% effective defibrillation dose.

Minimum squared error (MinSE) testing protocols and a MinSE estimator are presented which accurately estimate the voltage that defibrillates 95% of the time (the ED95). The MinSE experimental procedures, presented in the form of lookup tables, detail the response to successful and unsuccessful trials. The lookup tables also show the ED95 estimates calculated from the observed results using the MinSE estimator. Two assumptions are required to develop the look-up tables: 1) the dose-response curve, chosen using a statistical analysis of a retrospective sample, and 2) the distribution of the ED95's in the population. The MinSE estimator and experimental procedure are examined in a prospective study of five dogs (19-25 kg, heart weights 139.3-236.9 gm) using nonthoracotomy implantable defibrillator electrodes and a biphasic defibrillation waveform (3.5 ms first phase, 2.0 ms second phase). Employing an ED95 population distribution assumption applicable to most implantable defibrillator electrodes and waveforms, e.g., the ED95 is between 0.0 and 800.0 V, the measured rms error was 15% of the mean measured ED95 for the MinSE, four test shock, ED95 estimates. If the protocols are designed with an ED95 population distribution assumption for animals of the same species and size, and defibrillation is constrained to one electrode configuration and waveform, the estimates improve by 3.8%. Using techniques from the Bayesian statistics literature, the MinSE approach can be extended to a variety of defibrillation parameter estimation problems.

Optical measurements of transmembrane potential changes during electric field stimulation of ventricular cells.

We evaluated transmembrane potential changes at the ends of isolated rabbit ventricular myocytes during defibrillation-strength shocks given in the cellular refractory period. The myocytes were stimulated (S1 pulse) to produce an action potential. Then a constant-field shock (S2 pulse) with an electric field of 20 or 40 V/cm was given at an S1-S2 interval of 50 msec. The cells were stained with potentiometric dye (di-4-ANEPPS), and the cell end facing the S2 anode or cathode was illuminated with a laser while the fluorescence was recorded. During S2, the cell end facing the S2 cathode became more positive intracellularly, whereas the cell end facing the S2 anode became more negative intracellularly. The S2-induced transmembrane potential change at the cell end (delta Vm) was determined relative to the amplitude of the S1-induced action potential (APA) in each recording (i.e., delta Vm/APA). In Tyrode's solution containing 4.5 mM potassium, delta Vm/APA for 40-V/cm S2 was 1.36 +/- 0.34 at the cell end facing the S2 cathode and -1.65 +/- 0.61 at the cell end facing the S2 anode (n = 9). For the 20-V/cm S2, delta Vm/APA was 0.61 +/- 0.33 at the cell end facing the S2 cathode and -0.71 +/- 0.33 at the cell end facing the S2 anode (n = 6). The delta Vm/APA was not significantly influenced by 20 mM diacetyl monoxime. These results indicate that large delta Vm values occurred at the ends of the cells during S2. The calculated values of delta Vm, assuming a nominal APA of 130 mV, were 177 and -214 mV for the 40-V/cm S2 and 79 and -93 mV for the 20-V/cm S2. The delta Vm was correlated with cell size (r > or = 0.95) and agreed with values predicted by the S2 electric field strength multiplied by half of the cell length to within 27%. When the potassium concentration was increased to 20 mM, delta Vm/APA for 40 V/cm S2 increased 85% and 67% at the cell ends facing the S2 cathode and anode, respectively (n = 9, p < 0.005 versus 4.5 mM potassium), consistent with reduced APA. Thus, with normal or elevated extracellular potassium, transmembrane potential changes at the ends of cells during defibrillation-type stimulation are large enough to produce activation or recovery of voltage-dependent ion channels and may produce the effects responsible for defibrillation.

A comparison of measured and calculated intracavitary potentials for electrical stimuli in the exposed dog heart.

The objective of this paper is to test the feasibility of using a multielectrode, intracavitary probe to solve a forward problem in which measured intracavitary potentials are compared to those calculated from subendocardial potentials and left ventricular (LV) cavity geometry. Intracavitary potentials and subendocardial potentials are measured simultaneously during electrical pacing stimuli from the LV apex, LV anterior base, LV posterior base, and right ventricular (RV) outflow tract of three exposed dog hearts. The LV cavity geometry is measured from postmortem magnetic resonance microscopy images of fixed hearts. Boundary integrals are approximated using a boundary element method and solved for intracavitary potentials. Correlation coefficients for LV apical pacing episodes are 0.989 +/- 0.002 while those for nonapical pacing episodes are 0.873 +/- 0.092. These results indicate that for electrical pacing from the apex, intracavitary stimulus potentials can be calculated with a high degree of accuracy. For nonapical pacing locations, the accuracy decreases since the calculations are more sensitive to errors in measuring probe position and LV cavity geometry near the septum. These results show that accurate geometric measurements of the intracavitary probe position and subendocardial surface are the primary concerns in solving future forward and inverse problems using an intracavitary probe.

Calculating endocardial potentials from epicardial potentials measured during external stimulation.

This paper presents a boundary integral method for calculating the potential field generated by external stimulation at locations within the heart using realistic heart geometry and samples of the potential taken from the epicardial surface. This method assumes the heart is homogeneous and isotropic. To test the method we made epicardial and endocardial measurements in dogs during transthoracic pacing stimuli. From the epicardial potential measurements we predicted the endocardial potential values and compared them with the measured data. Despite the seemingly gross assumptions, the mean correlation coefficient between the measured and predicted potentials for three dogs and eleven stimulation electrode configurations was 0.985, and the mean rms error was 17%.

Assessing the effect of uncertainty in intracavitary electrode position on endocardial potential estimates.

The aim of this simulation study is to determine the effect of uncertainty in intracavitary probe electrode position on the accuracy of estimated endocardial potentials. Intracavitary probe position uncertainty is simulated by randomly moving an idealized probe surface about the center of an idealized left ventricular endocardial surface. These random deviations represent possible probe locations that are incorporated as correlated noise. An optimum inverse transfer coefficient matrix, relating intracavitary potentials to endocardial potentials, is computed and subsequently used to calculate the best linear estimate of the true endocardial potentials. For uncorrelated endocardial potentials and probe position uncertainty within 1.5 mm of the coordinates of the exact probe electrode locations, a root-mean-square (rms) error of 34.0% is obtained. Increasing probe position uncertainties to 3.0 and 6.0 mm results in rms errors of 60.8 and 88.3%, respectively. For endocardial potentials that are 90% dipolar, the rms errors for probe position uncertainties of 1.5, 3.0, and 6.0 mm are 11.3, 19.6, and 28.5%, respectively. These simulation results imply that position uncertainty of a multielectrode, intracavitary probe can be a major source of error in estimating endocardial potentials from intracavitary potentials.

Rigid and flexible thin-film multielectrode arrays for transmural cardiac recording.

Thin-film transmural cardiac multielectric arrays were fabricated using integrated-circuit processing techniques. Several substantial improvements were achieved over conventional handmade arrays such as a smaller cross-sectional area, a larger number of recording sites per needle, more accurately controlled size and spacing of the recording sites, smaller bipolar spacings, and higher throughout yield. These advantages allow for a higher density of closely spaced bipolar electrodes capable of monitoring complex voltage and gradient fields present during ventricular fibrillation and defibrillation. Both rigid and flexible arrays were fabricated and used in the acquisition of transmural electrical signals. The rigid multielectrode arrays were made of gold electrodes on a molybdenum substate, and the flexible arrays of silver and gold electrodes on a polyimide substrate. In vitro and in vivo testing of the thin-film transmural cardiac multielectrode arrays indicates that there are no adhesion or delamination problems observed during acute studies, no implantation difficulties, and that unipolar and bipolar recordings during normal sinus rhythm and injury potentials in unipolar recordings are similar to those obtained using the handmade electrodes.

An assessment of variable thickness and fiber orientation of the skeletal muscle layer on electrocardiographic calculations.

This paper assesses the effectiveness of including variable thickness and fiber orientation characteristics of the skeletal muscle layer in calculations relating epicardial and torso potentials. A realistic model of a canine torso which includes extensive detail about skeletal muscle layer thickness and fiber orientation is compared with two other uniformly anisotropic models: one of constant thickness and the other of variable thickness. First, transfer coefficients are calculated from the model data. Then torso potentials for each model are calculated from the transfer coefficients and measured epicardial potentials. The comparison of calculated and observed torso potentials indicates that a simple model consisting of a uniformly anisotropic skeletal muscle layer of 1.0-1.5 cm constant thickness significantly improves the model. However, if photographic slices of the canine torso are used to introduce more detailed data about the variation in skeletal muscle thickness and fiber orientation into the model, the agreement and between calculated and measured torso potentials decreased, although a finite element mesh of over 5000 nodes was used to describe the skeletal muscle in the more detailed model. One source of error increase was considered to be due to numerical discretization and could be reduced with a much finer mesh or by utilizing higher order polynomials to represent the potential distribution within each finite element. However, the results presented in this paper show that high precision computation (64-bit word length) on the mainframe IBM 3081 with an attached FPS-164 gives a slow rate of improvement with reduced discretization intervals and that utilizing higher order polynomials within each finite element gives an even slower rate of improvement.(ABSTRACT TRUNCATED AT 250 WORDS)

The volume conductor effects of anisotropic muscle on body surface potentials using an eccentric spheres model.

The purpose of this paper is to determine the volume conductor effects of muscle anisotropy on body surface potentials using an eccentric spheres model with a uniform double layer source configuration. Previous eccentric spheres work assumed that cardiac muscle anisotropy was small and that skeletal muscle effects could be accounted for by boundary extension, i.e., by scaling the conductivities and dimensions. However, in this paper, anisotropy for both the myocardium and the skeletal muscle is explicitly incorporated into the eccentric spheres volume conductor model. The anisotropy is treated as having uniform orthogonal components in the radial and tangential directions for both the skeletal muscle and myocardium. The solution for Laplace's equation is written in a series expansion of appropriate basis functions for each region. In the isotropic regions spherical harmonics with integer radial dependence and Legendre polynomial azimuthal dependence are utilized. For the anisotropic regions, Legendre polynomials are still appropriate for the azimuthal dependence, but noninteger powers of radial dependence are required. The approximate representation for anisotropy, i.e., the boundary extension method for the skeletal muscle and a scaled homogeneous conductivity without boundary extension for the myocardium are compared with explicit representations for the two regions. Two basic conclusions are drawn from the results. First, the treatment of skeletal muscle anisotropy by the boundary extension method is a valid and useful simplification which yields errors of 2% for the peak body surface potential. The second conclusion drawn from this study is that myocardial anisotropy has a significant effect on the magnitude of body surface potentials.(ABSTRACT TRUNCATED AT 250 WORDS)

Potential distribution in three-dimensional periodic myocardium--Part I: Solution with two-scale asymptotic analysis.

The use of two-scale asymptotic analysis allows development of a model of the steady-state potential distribution in three-dimensional cardiac muscle preserving the underlying cellular network. The myocardium is modeled as a periodic structure consisting of cylindrical cells embedded in extracellular fluid and connected by longitudinal and side junctions. The method is applicable to cardiac muscle of arbitrary extent since the periodicity of the tissue is dealt with analytically, and thus numerical computations require no more resources than a continuous volume conductor problem. The asymptotic analysis approach reveals that the potential in a periodic myocardium consists of two components. The large-scale component provides the baseline for the total solution and can be determined from the anisotropic monodomain model associated with the original periodic problem. The method provides the formula for calculating the conductivity of the equivalent monodomain model on the basis of cell geometry and conductivity distribution in the cardiac tissue. The small-scale component reflects the periodicity of the underlying structure and oscillates with periods determined by the dimensions of cardiac cells. The magnitude of these oscillations depends upon the gradient of the large-scale component. During stimulation with extracellular electrodes, the small-scale component determines both the shape and the magnitude of the transmembrane potential, while the influence of the large-scale component is negligible. Hence, the small-scale component merits closer attention in pacing and defibrillation studies, especially since the model based on two-scale asymptotic analysis provides an effective means of its computation.

Potential distribution in three-dimensional periodic myocardium--Part II: Application to extracellular stimulation.

Modeling potential distribution in the myocardium treated as a periodic structure implies that activation from high-current stimulation with extracellular electrodes is caused by the spatially oscillating components of the transmembrane potential. This hypothesis is tested by comparing the results of the model with experimental data. The conductivity, fiber orientation, the extent of the region, the location of the pacing site, and the stimulus strength determined from experiments are components of the model used to predict the distributions of potential, potential gradient, and the transmembrane potential throughout the region. Next, assuming that a specific value of the transmembrane potential is necessary and sufficient to activate fully repolarized myocardium, the model provides an analytical relation between large-scale field parameters, such as gradient and current density, and small-scale parameters, such as transmembrane potential. This relation is used to express the stimulation threshold in terms of gradient or current density components and to explain its dependence upon fiber orientation. The concept of stimulation threshold is generalized to three dimensions, and an excitability surface is constructed, which for cardiac muscle is approximately conical in shape. The numerical values of transmembrane potential and stimulation thresholds calculated using asymptotic analysis are in agreement with the results of animal experiments, confirming the validity of this approach to study the electrophysiology of periodic cardiac muscle.

The combination method: a numerical technique for electrocardiographic calculations.

This paper presents a method for electrocardiographic and other bioelectric calculations combining the Green's function boundary integral technique with the finite element method. Both the boundary integral method and the finite element method have been used extensively in electrocardiography for calculating epicardial and torso potentials. The boundary integral method is well suited for finding potentials in regions of isotropic conductivity and is computationally efficient, requiring unknown potentials to be calculated on the bounding surfaces only. It also compares favorably in accuracy with the finite element method in those regions. The finite element method is used in solving for potentials in regions of anisotropic conductivity since no simplifying assumptions or transformations of anisotropic regions into isotropic regions before solution are required. Combining the two methods, using the boundary integral method in isotropic regions and the finite element method is anisotropic regions, allows the advantages of both methods to be exploited.

Modelling the periodicity of cardiac muscle.

The intractable problem of modelling cardiac muscle of arbitrary extent while preserving cellular structure has been solved using an analytical rather than numerical approach with a method called two-scale asymptotic analysis. In this method, the myocardium was modelled as a collection of bundles arranged periodically in space and connected by junctions, and the distribution of the steady-state potential and current density was determined. The potential both along and across fibers was found to contain a distinct periodic component that determines the transmembrane potential. The magnitude of the transmembrane potential depends on the gradient of applied potential, the dimensions of the bundles, and their internal conductivity. Current flows primarily in the extracellular space, and the extracellular pathway also determines the apparent conductivity of cardiac muscle.

Status and trends in biomedical engineering education.

An overview of graduate and undergraduate programs is given, including a brief history of each. With respect to undergraduate studies, the issues of accreditation, department status versus option programs, employment, registration, and medical and professional school opportunities are examined. Enrollment trends are examined. A survey of biomedical engineering textbooks and a bibliography containing 102 references are given in an appendix.