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Long before it was technically possible to create computational validation methods, experimentalists developed physical and later animal models that provided insight into inverse problems and the entire field of electrocardiography. With the advent of modern data acquisition systems and computer storage and signal processing, these experimental approaches have become more detailed, more elaborate, and more similar to human-based validation. In this section, we provide an overview of the development of experimental models from the middle part of this century up to the present day and illustrate the strengths and weaknesses of this approach.
Experimental validation studies can involve animal preparations, completely synthetic physical materials, or even a combination of the two in order to simulate the ideal conditions of cardiac sources inside a human thorax. Given the technical challenges of measuring source parameters and geometry from animal models, it is no surprise that most of the earliest forms of validation in electrocardiographic inverse problems used synthetic electrical sources embedded in conducting media as a way to obtain controlled physical models of the heart and torso. Early implementations of these models used a current bipole to simulate the source because it is a direct equivalent of the single heart dipole vector that still serves as the basis of much of clinical electrocardiography. Later experimental validation models have made increasing use of biological tissues, either an intact animal with implanted instrumentation, or an isolated animal heart placed in a synthetic volume conductor that simulates a human thorax.
One of the earliest and certainly most thorough evaluations of a physical model based on a single bipolar source in a realistically shaped three-dimensional torso model was that of Burger and Van Milaan.[49,50] The physical model of the torso was an electrolytic tank made out of a michaplast shell molded on a statue of a supine human. The tank split horizontally to provide access to the interior, which was filled with copper sulfate and equipped with copper foil electrodes fixed to the inner surface (see Figure 1). Their heart source model was a set of copper disks oriented along one of the body axes and adjustable from outside the tank by means of a rod. The first model used only the electrolyte as the homogeneous volume conductor[49] but subsequent versions incorporated inhomogeneous regions constructed from cork and sand bags for spine and lungs, respectively.[50]
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The form of the inverse solution that Burger and van Milaan validated--derived, in fact--from their physical model differed from the more general formulations described elsewhere in this volume. They sought to describe the potentials measured from the limb leads on the body surface as the scalar product of the heart vector and a vector of weights (the ``lead vector''), an early description of what later became known as ``lead theory'' (see e.g., Horacek[51] for a recent review). By fitting their measurements of limb lead potentials for known heart vector positions to a simple linear equation, they were able to derive both algebraic and geometric forms of this relationship for each of the standard limb leads. Validation also included repeating the derivation after including various inhomogeneities in the tank and observing the effect on weighting coefficients.
A pair of later studies of electrocardiographic lead fields using more simplified physical models was from Grayzel and Lizzi, who used conductive paper (Teledeltos) to create two-dimensional inhomogeneous models of the human thorax to which they attached current source/sink pairs (bipoles) to represent the heart.[52,53] The advantage of this approach was the ability to control the extent and value of inhomogeneities by means of perforations or silver spots applied to the conductive paper. Their results indicated that the relationship between source location and body surface, as expressed by the lead field, was more variable and complex in the inhomogeneous than the homogeneous torso. More importantly, these investigators showed a sharp deterioration in performance of several standard lead systems after adding inhomogeneities to their torso model.
Nagata later described several further refinements of artificial source/medium models and subsequently introduced the use of biological sources.[54,55] In a preliminary study, Nagata placed a bipolar source in 27 different locations and measured the torso tank surface potentials at electrode sites equivalent to eight different lead systems in common usage at that time.[54] Like Burger and van Milaan, Nagata used a torso geometry based on a three-dimensional human thorax (see Figure 2) and made measurements both in the homogeneously conducting tank as well as (in a subsequent study) with inflated dog lungs and agar gel models of human lungs inserted into the tank.[55] In this later study, Nagata made a significant step in validation studies by replacing the synthetic source with a perfused dog heart, thus achieving a much higher degree of realism than available with simple current bipoles. The goal of his work using the bipole source was to derive the lead vector--expressed here as the ``impedance transform vector''--from measurements over a wide variety of bipole source locations and lead systems. A second goal was to evaluate the effects of torso boundaries and inhomogeneities on the shape of the lead vector field (for the bipole) and on the torso tank potentials (for the isolated heart). The limitations of this study lay in the lead field approach, which represents the heart as a single dipole, rather than a distributed source of bioelectric current. Nagata therefore had no means of describing the real heart quantitatively and did not measure cardiac potentials directly. Instead, his study focused on the relationship between ECG signal parameters such as R-wave amplitude and signal morphology and the presence or absence of torso inhomogeneities.
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De Ambroggi and Taccardi described a two-dimensional form of the physical model approach in which they examined in great detail the electric field of two bipolar sources in a shallow circular bath.[56] Their aim was to establish whether it was possible to characterize sources composed of two eccentrically placed bipoles based on potentials measured at sites distributed throughout the bath. Hence it was not a validation of a quantitative inverse solution but more a qualitative evaluation of the relationship between cardiac sources and body surface potentials. A three-dimensional animal source study with similar aims was subsequently performed by Mirvis with rabbit hearts placed inside spherical electrolytic tanks.[57]
Perhaps the first true validation of a computed inverse solution was by Ideker et al., who created small epicardial burns in isolated rabbit hearts and then suspended each heart in a transparent, spherical electrolytic tank.[58] The goal of their inverse solution was to determine the location of the burns and also of discrete epicardial pacing sites by assuming that each represented a dipolar source that could be localized with an equivalent source model. To validate the accuracy of their computed locations, the investigators used visual measurements to determine burn location relative to the electrodes embedded in the clear epoxy surface of the sphere. The accuracy achieved with this approach was in the range of 3-4 mm differences between predicted and measured locations.
Mirvis et al. carried out a sequence of studies using a variety of discrete sources to represent not only the location of injury, but of the entire cardiac cycle.[59,60] As the geometric model, they used a spherical electrolytic tank of 6.35 cm diameter with 32 embedded electrodes. The sources were isolated rabbit hearts suspended near the center of the sphere. They found that a single moving dipole was not an adequate representation of the heart's electrical activity but that any of three different higher order discrete sources they tested did virtually equally well at reproducing the potentials on the surface of the tank in which the hearts were suspended. The important result of this study was to demonstrate on an experimental model that the single heart dipole model of electrocardiography was incomplete. A new source description was necessary.
It was Barr et al. who provided the new source description when they proposed representing the heart in terms of the epicardial potential distribution.[61,62] This also led to a new series of validation studies based on this formulation, the first of which Barr et al. carried out, not using an electrolytic tank, but instead a complete instrumented animal model to validate their inverse solution.[63] This preparation included surgical implantation of 75 epicardial electrodes, re-closure of the chest wall in order to restore the integrity of the thoracic volume conductor, and after a two-week recovery period, measurement of both epicardial and 150 body-surface potentials with a 24-channel acquisition system. To record geometric information, the thorax of the animal was later sliced and photographed to create a model consisting of the electrode locations on the epicardial and torso surfaces. This landmark study provided data that have been used by several other investigators to validate their inverse solutions.[64,65] The major limitation of this validation model was that the spatial resolution of the geometric model was modest (the geometric model consisted of only the electrical measurement sites). Furthermore, because of the limited number of recording channels available (20), the potential measurements were performed in sequence and then time aligned, increasing the risk that changes occurring on a beat to beat basis or over the time of the measurements would be captured in only a subset of the recordings.
Only very recently has the complete, instrumented animal preparation been repeated in studies reported by Chengand et al., in which they recorded simultaneous epicardial and torso surface potentials from an acutely instrumented pig.[66] Rather than measuring the geometry from each one of their animals, they have fitted a set of Hermite polynomial finite elements to the tomographic scans of a single animal and developed a scheme with which to fit this model to all subsequent subjects. Complete results of these validation studies have not yet been published.
Most of the experimental model validation studies performed since those of Barr et al. have been of the hybrid type pioneered by Nagata using an isolated heart either with an electrolytic tank[3,21,23,24,25,67,68,69,70,71,72,73,74,75,76,77,78,79] or with endocardial and catheter measurements for the endocardial inverse solution.[80,81,82] The main advantages of this type of preparation over instrumented whole animal experiments are the relative ease of carrying out the experiments and the increased level of control they provide. The isolated heart is more directly accessible when suspended in an electrolytic tanks, which permits manipulations of its position, pacing site, coronary flow, temperature, etc., as well as the injection of drugs. The simplified geometry of the (usually homogeneous) tank also makes constructing customized geometric models simpler and faster than when a complete medical imaging scan is required for a whole animal.
The experimental validation study which has had the greatest impact to date used an isolated heart preparation suspended in a cylindrically shaped electrolytic tank, a preparation developed by Taccardi to validate inverse solutions generated by Colli Franzone et al..[67,68,69,70] The source potentials for this study were recorded from 122 electrodes mounted in a rigid cage in which the isolated heart was suspended, and the cage, in turn, placed inside the torso tank, which contained 156 electrodes. To provide some variety of sources, validation of the inverse solution was based on three different activation sequences (one atrial and two ventricular pacing sites). The data from this study have been used by other groups to validate their own inverse solutions.[12,21] One possible limitation of this study was the fact that potentials were measured up to several centimeters away from the heart surface, which resulted in smaller spatial gradients and thus an ``easier'' case against which to validate the inverse solution.
Soucy et al. conducted a similar study, but used an isolated dog heart from which they measured the potentials directly from the epicardial surface by means of a 128-electrode sock.[71] Another key element of their validation strategy, which we described in the previous section, is that they used the measured epicardial potentials to compute torso potentials with a forward solution and used these as the input signals for the inverse solution. This approach, with noise added to the resulting forward computed torso potentials before applying the inverse, has been used by many other investigators[12,23,24,25,75,76,77] Soucy et al. found that forward computed and measured tank potentials were fairly similar (correlation coefficients of 0.95 and relative errors of 29%), but that inverse solutions computed from the measured potentials were dramatically worse than those computed from the forward computed signals.
A contemporary example of the isolated dog heart and human shaped electrolytic tank preparation is shown in Figure 3. This preparation uses a second dog to provide circulatory support for the isolated heart, which achieves very stable physiologic conditions over many hours. With the isolated heart it is also possible to cannulate individual arteries and then regulate the coronary flow rate, blood temperature, and the infusion of cardioactive drugs in order to examine the effects of physiologic change on forward and inverse solutions.[74,78,83,84,85] Rudy and a number of collaborators have used data from this preparation to validate their inverse solutions for the specific cases of locating sites of early activation[3] and reconstructing the effects of myocardial infarction.[25] A group including MacLeod, Brooks, and Ahmad has examined the behavior of the inverse solution under a variety of conditions including different pacing protocols, physiologic interventions, torso inhomogeneities, and geometrical arrangements with ever finer spatial measurement resolution, as well as developed novel inverse solution methods.[23,74,78,85,86] Oostendorp et al. have used this preparation to validate an inverse solution based on epicardial and endocardial activation times.[87]
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We conclude this section with a brief summary of the strengths and limitations of physical and animal models for validation of electrocardiographic inverse problems. We concentrate on the most popular and perhaps successful of these approaches, using animal, primarily canine, hearts as sources inside electrolytic torso-shaped tanks. The most significant utility of this approach is the ability to include a high level of realism and yet maintain adequate control over the relevant parameters. The tank or phantom can take on virtually any reasonable shape using modern rigid materials and can be instrumented with an almost unlimited number of recording electrodes located both on the surface and within the volume of the tank. The isolated animal heart provides a very realistic and versatile bioelectric source, which can be instrumented extensively and manipulated to mimic many pathologies. The physical component of the model permits variation in parameters such as conductivity or geometry of the volume conductor, both of which can be altered quickly during the experiment. This isolated animal heart preparation does require consider experimental expertise and the multichannel acquisition systems represent a significant investment in electronic and computational resources, although the difficulty lies more in the lack of commercial systems than the overwhelming difficulties of the technology.
One specific technical challenge that can generate significant errors is the measurement of geometry. The coordinates of the electrolytic tank and the electrodes embedded in it are usually recorded carefully at the time of construction and are seldom altered. The heart, on the other hand, has a different shape, location, and electrode arrangement for each experiment, all of which must be measured in order to construct specific forward and inverse solutions. Acquisition of geometric information typically involves two components, the heart geometry and the location of the heart relative to the electrolytic tank. Only rarely do researchers have access to large scale tomographic imaging systems in the animal lab to acquire both components simultaneously so that, normally, they measure the heart location in the tank first, then remove the heart for detailed imaging or anatomical measurements. One way to establish heart location in the tank is to take multiple distance measurements from landmarks on the heart to known sites on the tank and triangulate the heart locations or to take direct measurements of heart and tank with mechanical digitizers. One source of error in these measurements arises because the electrolyte must usually be drained from the tank before performing the measurements so that the heart takes on a different position in the tank. For measuring the detail of the heart itself, mechanical digitizers as well as medical imaging devices are commonly available. A final step is to align the detailed heart measurements with the torso tank geometry based on landmark locations measured in both reference frames, a process known as ``registration.'' For this, there exist different linear and even non-linear algorithms, the best known of which is the Procrustes method.[88,89] In Procrustes fitting one computes a rigid transformation (optionally with scaling) that is optimal in a least squares sense. This approach provides several error metrics (mean, maximum, and variance of the distances between landmarks after fitting) that can be used to guide the interpretation of subsequent validation errors. A persistent limitation of any measurement of the heart is that depending on the technique used, the heart may not be perfused as it is measured and so undergoes changes in shape and size. A further source of error is the fact that the heart of course changes its shape quite dramatically during each contraction.
And as with all findings based on animal models, great care is required in extending any validation results from an animal model to the case of humans and clinical applications. The isolated heart contracts, but against no mechanical load. The mechanical behavior of the heart is further altered because it hangs freely in the electrolyte without pericardium or the constraining influences of other organs. There is also no autonomic nervous system present in the isolated heart so that many responses to external physiological influences may be either blunted or exacerbated, depending on the mechanisms involved. Likewise, the perfusion conditions of the heart are greatly altered because even when the isolated heart is not contracting fully (or at all), perfusion of the coronary arteries is maintained because it is driven by the support animal or external mechanical pumps. This external perfusion is especially relevant when one wishes to follow the response of the heart to acute myocardial ischemia, which in the intact animal will lead to a local reduction in contraction and a build up of metabolites and electrolytes.[90] This response will change in poorly defined ways under the conditions of the isolated, externally perfused heart. All these obstacles provide motivation for the human-based validation studies we discuss below. As with any experimental studies, because measurements are involved, there are also inevitable sources of error that cannot be completely controlled, a limitation not experienced in the computational validation approaches described in the previous section.