Biomedical subjects

C R Maurer

Publications and source records attributed to C R Maurer.

At least 19 recordsLinked to original sources

PubMed2000

Design and evaluation of a system for microscope-assisted guided interventions (MAGI).

The problem of providing surgical navigation using image overlays on the operative scene can be split into four main tasks--calibration of the optical system; registration of preoperative images to the patient; system and patient tracking, and display using a suitable visualization scheme. To achieve a convincing result in the magnified microscope view a very high alignment accuracy is required. We have simulated an entire image overlay system to establish the most significant sources of error and improved each of the stages involved. The microscope calibration process has been automated. We have introduced bone-implanted markers for registration and incorporated a locking acrylic dental stent (LADS) for patient tracking. The LADS can also provide a less-invasive registration device with mean target error of 0.7 mm in volunteer experiments. These improvements have significantly increased the alignment accuracy of our overlays. Phantom accuracy is 0.3-0.5 mm and clinical overlay errors were 0.5-1.0 mm on the bone fiducials and 0.5-4 mm on target structures. We have improved the graphical representation of the stereo overlays. The resulting system provides three-dimensional surgical navigation for microscope-assisted guided interventions (MAGI).

Computer Simulation↗

PubMed2000

Sources of error in comparing functional magnetic resonance imaging and invasive electrophysiological recordings.

OBJECT: Several authors have recently reported studies in which they aim to validate functional magnetic resonance (fMR) imaging against the accepted gold standard of invasive electrophysiological monitoring. The authors have conducted a similar study, and in this paper they identify and quantify two characteristics of these data that can make such a comparison problematic. METHODS: Eight patients in whom surgery for epilepsy was performed and five healthy volunteers underwent fMR imaging to localize the part of the sensorimotor cortex responsible for hand movement. In the patient group subdural electrode mats were subsequently implanted to identify eloquent regions of the brain and the epileptogenic zone. The fMR imaging data were processed to correct for motion during the study and then registered with a postimplantation computerized tomography (CT) scan on which the electrodes were visible. The motion during imaging in the two groups studied, and the deformation of the brain between the preoperative images and postoperative scans were measured. The patients who underwent epilepsy surgery moved significantly more during fMR imaging experiments than healthy volunteers performing the same motor task. This motion had a particularly increased out-of-plane component and was significantly more correlated with the stimulus than in the volunteers. This motion was especially increased when the patients were performing a task on the side affected by the lesion. The additional motion is hard to correct and substantially degrades the quality of the resulting fMR images, making it a much less reliable technique for use in these patients than in others. Also, the authors found that after electrode implantation, the brain surface can shift more than 10 mm relative to the skull compared with its preoperative location, substantially degrading the accuracy of the comparison of electrophysiological measurements made in the deformed brain and fMR studies obtained preoperatively. CONCLUSIONS: These two findings indicate that studies of this sort are currently of limited use for validating fMR imaging and should be interpreted with care. Additional image analysis research is necessary to solve the problems caused by patients' motion and brain deformation.

Cerebral Cortex↗

PubMed1999

Retrospective intermodality registration techniques for images of the head: surface-based versus volume-based.

The primary objective of this study is to perform a blinded evaluation of two groups of retrospective image registration techniques, using as a gold standard a prospective marker-based registration method, and to compare the performance of one group with the other. These techniques have already been evaluated individually [27]. In this paper, however, we find that by grouping the techniques as volume based or surface based, we can make some interesting conclusions which were not visible in the earlier study. In order to ensure blindness, all retrospective registrations were performed by participants who had no knowledge of the gold-standard results until after their results had been submitted. Image volumes of three modalities: X-ray computed tomography (CT), magnetic resonance (MR), and positron emission tomography (PET) were obtained from patients undergoing neurosurgery at Vanderbilt University Medical Center on whom bone-implanted fiducial markers were mounted. These volumes had all traces of the markers removed and were provided via the Internet to project collaborators outside Vanderbilt, who then performed retrospective registrations on the volumes, calculating transformations from CT to MR and/or from PET to MR. These investigators communicated their transformations, again via the Internet, to Vanderbilt, where the accuracy of each registration was evaluated. In this evaluation, the accuracy is measured at multiple volumes of interest (VOI's). Our results indicate that the volume-based techniques in this study tended to give substantially more accurate and reliable results than the surface-based ones for the CT-to-MR registration tasks, and slightly more accurate results for the PET-to-MR tasks. Analysis of these results revealed that the rotational component of error was more pronounced for the surface-based group. It was also apparent that all of the registration techniques we examined have the potential to produce satisfactory results much of the time, but that visual inspection is necessary to guard against large errors.

Algorithms↗

PubMed1999

A system for microscope-assisted guided interventions.

We present a system for surgical navigation using stereo overlays in the operating microscope aligned to the operative scene. This augmented reality system provides 3D information about nearby structures and offers a significant advancement over pointer-based guidance, which provides only the location of one point and requires the surgeon to look away from the operative scene. With a previous version of this system, we demonstrated feasibility, but it became clear that to achieve convincing guidance through the magnified microscope view, a very high alignment accuracy was required. We have made progress with several aspects of the system, including automated calibration, error simulation, bone-implanted fiducials and a dental attachment for tracking. We have performed experiments to establish the visual display parameters required to perceive overlaid structures beneath the operative surface. Easy perception of real and virtual structures with the correct transparency has been demonstrated in a laboratory and through the microscope. The result is a system with a predicted accuracy of 0.9 mm and phantom errors of 0.5 mm. In clinical practice errors are 0.5-1.5 mm, rising to 2-4 mm when brain deformation occurs.

Bone Cysts↗

PubMed1999

Stereo augmented reality in the surgical microscope.

We present an augmented reality system that allows surgeons to view features from preoperative radiological images accurately overlaid in stereo in the optical path of a surgical microscope. The purpose of the system is to show the surgeon structures beneath the viewed surface in the correct 3-D position. The technical challenges are registration, tracking, calibration and visualisation. For patient registration, or alignment to preoperative images, we use bone-implanted markers and a dental splint is used for patient tracking. Both microscope and patient are tracked by an optical localiser. Calibration uses an accurately manufactured object with high contrast circular markers which are identified automatically. All ten camera parameters are modelled as a bivariate polynomial function of zoom and focus. The overall system has a theoretical overlay accuracy of better than 1 mm. Implementations of the system have been tested on seven patients. Recent measurements in the operating room conformed to our accuracy predictions. For visualisation the system has been implemented on a graphics workstation to enable high frame rates with a variety of rendering schemes. Several issues of 3-D depth perception remain unsolved, but early results suggest that perception of structures in the correct 3-D position beneath the viewed surface is possible.

Depth Perception↗

PubMed1998

Measurement of intraoperative brain surface deformation under a craniotomy.

OBJECTIVE: Several causes of spatial inaccuracies in image-guided surgery have been carefully studied and documented for several systems. These include error in identifying the external features used for registration, geometrical distortion in the preoperative images, and error in tracking the surgical instruments. Another potentially important source of error is brain deformation between the time of imaging and the time of surgery or during surgery. In this study, we measured the deformation of the dura and brain surfaces between the time of imaging and the start of surgical resection for 21 patients. METHODS: All patients underwent intraoperative functional mapping, allowing us to measure brain surface motion at two times that were separated by nearly an hour after opening the dura but before performing resection. The positions of the dura and brain surfaces were recorded and transformed to the coordinate space of a preoperative magnetic resonance image, using the Acustar surgical navigation system (manufactured by Johnson & Johnson Professional, Inc., Randolph, MA) (the Acustar trademark and associated intellectual property rights are now owned by Picker International, Highland Heights, OH). This system performs image registration with bone-implanted markers and tracks a surgical probe by optical triangulation. RESULTS: The mean displacements of the dura and the first and second brain surfaces were 1.2, 4.4, and 5.6 mm, respectively, with corresponding mean volume reductions under the craniotomy of 6, 22, and 29 cc. The maximum displacement was greater than 10 mm in approximately one-third of the patients for the first brain surface measurement and one-half of the patients for the second. In all cases, the direction of brain shift corresponded to a "sinking" of the brain intraoperatively, compared with its preoperative position. Analysis of the measurement error revealed that its magnitude was approximately 1 to 2 mm. We observed two different patterns of the brain surface deformation field, depending on the inclination of the craniotomy with respect to gravity. Separate measurements of brain deformation within the closed cranium caused by changes in patient head orientation with respect to gravity suggested that less than 1 mm of the brain shift recorded intraoperatively could have resulted from the change in patient orientation between the time of imaging and the time of surgery. CONCLUSION: These results suggest that intraoperative brain deformation is an important source of error that needs to be considered when using surgical navigation systems.

Adult↗

PubMed1998

Visual assessment of the accuracy of retrospective registration of MR and CT images of the brain.

In a previous study we demonstrated that automatic retrospective registration algorithms can frequently register magnetic resonance (MR) and computed tomography (CT) images of the brain with an accuracy of better than 2 mm, but in that same study we found that such algorithms sometimes fail, leading to errors of 6 mm or more. Before these algorithms can be used routinely in the clinic, methods must be provided for distinguishing between registration solutions that are clinically satisfactory and those that are not. One approach is to rely on a human observer to inspect the registration results and reject images that have been registered with insufficient accuracy. In this paper, we present a methodology for evaluating the efficacy of the visual assessment of registration accuracy. Since the clinical requirements for level of registration accuracy are likely to be application dependent, we have evaluated the accuracy of the observer's estimate relative to six thresholds: 1-6 mm. The performance of the observers was evaluated relative to the registration solution obtained using external fiducial markers that are screwed into the patient's skull and that are visible in both MR and CT images. This fiducial marker system provides the gold standard for our study. Its accuracy is shown to be approximately 0.5 mm. Two experienced, blinded observers viewed five pairs of clinical MR and CT brain images, each of which had each been misregistered with respect to the gold standard solution. Fourteen misregistrations were assessed for each image pair with misregistration errors distributed between 0 and 10 mm with approximate uniformity. For each misregistered image pair each observer estimated the registration error (in millimeters) at each of five locations distributed around the head using each of three assessment methods. These estimated errors were compared with the errors as measured by the gold standard to determine agreement relative to each of the six thresholds, where agreement means that the two errors lie on the same side of the threshold. The effect of error in the gold standard itself is taken into account in the analysis of the assessment methods. The results were analyzed by means of the Kappa statistic, the agreement rate, and the area of receiver-operating-characteristic (ROC) curves. No assessment performed well at 1 mm, but all methods performed well at 2 mm and higher. For these five thresholds, two methods agreed with the standard at least 80% of the time and exhibited mean ROC areas greater than 0.84. One of these same methods exhibited Kappa statistics that indicated good agreement relative to chance (Kappa > 0.6) between the pooled observers and the standard for these same five thresholds. Further analysis demonstrates that the results depend strongly on the choice of the distribution of misregistration errors presented to the observers.

Algorithms↗

PubMed1998

Predicting error in rigid-body point-based registration.

Guidance systems designed for neurosurgery, hip surgery, and spine surgery, and for approaches to other anatomy that is relatively rigid can use rigid-body transformations to accomplish image registration. These systems often rely on point-based registration to determine the transformation, and many such systems use attached fiducial markers to establish accurate fiducial points for the registration, the points being established by some fiducial localization process. Accuracy is important to these systems, as is knowledge of the level of that accuracy. An advantage of marker-based systems, particularly those in which the markers are bone-implanted, is that registration error depends only on the fiducial localization error (FLE) and is thus to a large extent independent of the particular object being registered. Thus, it should be possible to predict the clinical accuracy of marker-based systems on the basis of experimental measurements made with phantoms or previous patients. This paper presents two new expressions for estimating registration accuracy of such systems and points out a danger in using a traditional measure of registration accuracy. The new expressions represent fundamental theoretical results with regard to the relationship between localization error and registration error in rigid-body, point-based registration. Rigid-body, point-based registration is achieved by finding the rigid transformation that minimizes "fiducial registration error" (FRE), which is the root mean square distance between homologous fiducials after registration. Closed form solutions have been known since 1966. The expected value (FRE2) depends on the number N of fiducials and expected squared value of FLE, (FLE-2, but in 1979 it was shown that (FRE2) is approximately independent of the fiducial configuration C. The importance of this surprising result seems not yet to have been appreciated by the registration community: Poor registrations caused by poor fiducial configurations may appear to be good due to a small FRE value. A more critical and direct measure of registration error is the "target registration error" (TRE), which is the distance between homologous points other than the centroids of fiducials. Efforts to characterize its behavior have been made since 1989. Published numerical simulations have shown that (TRE2) is roughly proportional to (FLE2)/N and, unlike (FRE2), does depend in some way on C. Thus, FRE, which is often used as feedback to the surgeon using a point-based guidance system, is in fact an unreliable indicator of registration-accuracy. In this work we derive approximate expressions for (TRE2), and for the expected squared alignment error of an individual fiducial. We validate both approximations through numerical simulations. The former expression can be used to provide reliable feedback to the surgeon during surgery and to guide the placement of markers before surgery, or at least to warn the surgeon of potentially dangerous fiducial placements; the latter expression leads to a surprising conclusion: Expected registration accuracy (TRE) is worst near the fiducials that are most closely aligned! This revelation should be of particular concern to surgeons who may at present be relying on fiducial alignment as an indicator of the accuracy of their point-based guidance systems.

Humans↗

PubMed1998

Surface-based registration of CT images to physical space for image-guided surgery of the spine: a sensitivity study.

This paper presents a method designed to register preoperative computed tomography (CT) images to vertebral surface points acquired intraoperatively from ultrasound (US) images or via a tracked probe. It also presents a comparison of the registration accuracy achievable with surface points acquired from the entire posterior surface of the vertebra to the accuracy achievable with points acquired only from the spinous process and central laminar regions. Using a marker-based method as a reference, this work shows that submillimetric registration accuracy can be obtained even when a small portion of the posterior vertebral surface is used for registration. It also shows that when selected surface patches are used, CT slice thickness is not a critical parameter in the registration process. Furthermore, the paper includes qualitative results of registering vertebral surface points in US images to multiple CT slices. The method has been tested with US points and physical points on a plastic spine phantom and with simulated data on a patient CT scan.

Humans↗

PubMed1998

Registration of head CT images to physical space using a weighted combination of points and surfaces.

Most previously reported registration techniques that align three-dimensional image volumes by matching geometrical features such as points or surfaces use a single type of feature. We recently reported a hybrid registration technique that uses a weighted combination of multiple geometrical feature shapes. In this study we use the weighted geometrical feature (WGF) algorithm to register computed tomography (CT) images of the head to physical space using the skin surface only, the bone surface only, and various weighted combinations of these surfaces and one fiducial point (centroid of a bone-implanted marker). We use data acquired from 12 patients that underwent temporal lobe craniotomies for the resection of cerebral lesions. We evaluate and compare the accuracy of the registrations obtained using these various approaches by using as a reference gold standard the registration obtained using three bone-implanted markers. The results demonstrate that a combination of geometrical features can improve the accuracy of CT-to-physical space registration. Point-based registration requires a minimum of three noncolinear points. The position of a bone-implanted marker can be determined much more accurately than that of a skin-affixed marker or an anatomic landmark. A major disadvantage of using bone-implanted markers is that an invasive procedure is required to implant each marker. By combining surface information, the WGF algorithm allows registration to be performed using only one or two such markers. One important finding is that the use of a single very accurate point (a bone-implanted marker) allows very accurate surface-based registration to be achieved using very few surface points. Finally, the WGF algorithm, which not only allows the combination of multiple types of geometrical information but also handles point-based and surface-based registration as degenerate cases, could form the foundation of a "flexible" surgical navigation system that allows the surgeon to use what he considers the method most appropriate for an individual clinical situation.

Algorithms↗

PubMed1998

Investigation of intraoperative brain deformation using a 1.5-T interventional MR system: preliminary results.

All image-guided neurosurgical systems that we are aware of assume that the head and its contents behave as a rigid body. It is important to measure intraoperative brain deformation (brain shift) to provide some indication of the application accuracy of image-guided surgical systems, and also to provide data to develop and validate nonrigid registration algorithms to correct for such deformation. We are collecting data from patients undergoing neurosurgery in a high-field (1.5 T) interventional magnetic resonance (MR) scanner. High-contrast and high-resolution gradient-echo MR image volumes are collected immediately prior to surgery, during surgery, and at the end of surgery, with the patient intubated and lying on the operating table in the operative position. In this paper we report initial results from six patients: one freehand biopsy, one stereotactic functional procedure, and four resections. We investigate intraoperative brain deformation by examining threshold boundary overlays and difference images and by measuring ventricular volume. We also present preliminary results obtained using a nonrigid registration algorithm to quantify deformation. We found that some cases had much greater deformation than others, and also that, regardless of the procedure, there was very little deformation of the midline, the tentorium, the hemisphere contralateral to the procedure, and ipsilateral structures except those that are within 1 cm of the lesion or are gravitationally above the surgical site.

Adult↗

PubMed1998

The EASI project--improving the effectiveness and quality of image-guided surgery.

In recent years, advances in computer technology and a significant increase in the accuracy of medical imaging have made it possible to develop systems that can assist the clinician in diagnosis, planning, and treatment. This paper deals with an area that is generally referred to as computer-assisted surgery, image-directed surgery, or image-guided surgery. We report the research, development, and clinical validation performed since January 1996 in the European Applications in Surgical Interventions (EASI) project, which is funded by the European Commission in their "4th Framework Telematics Applications for Health" program. The goal of this project is the improvement of the effectiveness and quality of image-guided neurosurgery of the brain and image-guided vascular surgery of abdominal aortic aneurysms, while at the same time reducing patient risks and overall cost. We have developed advanced prototype systems for preoperative surgical planning and intraoperative surgical navigation, and we have extensively clinically validated these systems. The prototype systems and the clinical validation results are described in this paper.

Quality of Health Care↗

PubMed1997

Registration of head volume images using implantable fiducial markers.

In this paper, we describe an extrinsic-point-based, interactive image-guided neurosurgical system designed at Vanderbilt University, Nashville, TN, as part of a collaborative effort among the Departments of Neurological Surgery, Computer Science, and Biomedical Engineering. Multimodal image-to-image (II) and image-to-physical (IP) registration is accomplished using implantable markers. Physical space tracking is accomplished with optical triangulation. We investigate the theoretical accuracy of point-based registration using numerical simulations, the experimental accuracy of our system using data obtained with a phantom, and the clinical accuracy of our system using data acquired in a prospective clinical trial by six neurosurgeons at four medical centers from 158 patients undergoing craniotomies to resect cerebral lesions. We can determine the position of our markers with an error of approximately 0.4 mm in X-ray computed tomography (CT) and magnetic resonance (MR) images and 0.3 mm in physical space. The theoretical registration error using four such markers distributed around the head in a configuration that is clinically practical is approximately 0.5-0.6 mm. The mean CT-physical registration error for the phantom experiments is 0.5 mm and for the clinical data obtained with rigid head fixation during scanning is 0.7 mm. The mean CT-MR registration error for the clinical data obtained without rigid head fixation during scanning is 1.4 mm, which is the highest mean error that we observed. These theoretical and experimental findings indicate that this system is an accurate navigational aid that can provide real-time feedback to the surgeon about anatomical structures encountered in the surgical field.

Brain Diseases↗

PubMed1996

An automatic technique for finding and localizing externally attached markers in CT and MR volume images of the head.

An image processing technique is presented for finding and localizing the centroids of cylindrical markers externally attached to the human head in computed tomography (CT) and magnetic resonance (MR) image volumes. The centroids can be used as control points for image registration. The technique, which is fast, automatic, and knowledge-based, has two major steps. First, it searches the entire image volume to find one voxel inside each marker-like object. We call this voxel a "candidate" voxel, and we call the object a candidate marker. Second, it classifies the voxels in a region surrounding the candidate voxel as marker or nonmarker voxels using knowledge-based rules and calculates an intensity-weighted centroid for each true marker. We call this final centroid the "fiducial" point of the marker. The technique was developed on 42 scans of six patients-one CT and six MR scans per patient. There are four markers attached to each patient for a total of 168 marker images. For the CT images the false marker rate was zero. For MR the false marker rate was 1.4% (Two out of 144 markers). To evaluate the accuracy of the fiducial points, CT-MR registration was performed after correcting the MR images for geometrical distortion. The fiducial registration accuracy averaged 0.4 mm and was better than 0.6 mm for each of the eighteen image pairs.

Algorithms↗

PubMed1996

A universal method for geometric correction of magnetic resonance images for stereotactic neurosurgery.

Accurate stereotactic navigation depends strongly upon the spatial fidelity of the image used for registration. Clinically significant levels of geometric distortion are present in standard MR images, limiting their utility. A technique for correction of all geometric distortions in spine echo MR images was assessed in a prospective clinical trial of 19 stereotactic craniotomies. The Euclidean error in target registration between CT and MR was significantly reduced, from 3.833 +/- 0.992 to 1.986 +/- 0.605 mm. The results of this clinical trial support the incorporation of this MR image rectification protocol into standard clinical practice.

Evaluation Studies as Topic↗

PubMed1987

Comparison of labeled propanediol and urea as markers of lung vascular injury.

The purpose of these studies was a comparison of [14C]urea (U) and 1,3-[14C]propanediol (Pr) as measures of lung vascular permeability-surface area (PS) under base-line conditions and after lung injury caused by alloxan infusion in isolated perfused dog lungs. Indicator mixtures of 125I-albumin, 51Cr-red blood cells, 3HOH, and U or Pr were injected under base-line conditions, after 1.2 g of alloxan, and after an additional 0.8 g of alloxan. Indicator-dilution curves were analyzed from sampled outflow blood to provide PS, the square root of effective extravascular diffusivity multiplied by exchange surface area (D1/2S), and extravascular lung water (EVLW) from the tracer mean transit times (VW). Results show that alloxan increases PS and D1/2S for U, D1/2S for Pr, and VW and EVLW by desiccation. All indicator-dilution parameters correlate significantly with alloxan dose. Interpretation of Pr transport suggests that materials with lipid and hydrophilic pathways might be used in conjunction with U to minimize the effects of surface area changes and increase the sensitivity of these tracers to permeability alteration. In addition Pr may be a useful alternative to U as a marker of vascular damage.

Alloxan↗

PubMed1986

Dependence of heart chamber dimensions and dynamics on chamber demands and myocardial properties.

A heart chamber undergoes eccentric hypertrophy in response to a chronic elevation of stroke-displacement demand, and it undergoes concentric hypertrophy in response to a chronic elevation of systolic-pressure demand. Both of these adaptations, which occur in various combinations, involve two myocardial plastic properties, "stretch normalization" and "stress normalization". We have developed a model which predicts dimensions and dynamics of the left ventricle as functions of myocardial properties and of the loads to which the chamber is adapted. The model involves: a stress-normalization rule which describes how myocardial volume depends on average systolic pressure, cavity volumes and the responsiveness of growth to stress; a stretch-normalization rule which describes how the cavity volume of standard stretch relates to average end-diastolic and end-systolic volumes; and a pressure-volume-curve equation giving isometric pressures as functions of cavity volume and myocardial volume relative to standard-stretch cavity volume, and elastic properties including contractility. The model shows how the relations among average dimensions, dynamics and loads depend on myocardial properties, particularly contractility and the growth response to stress. These properties are the main determinants of myocardial performance. In addition to the load adaptations mentioned above, the model predicts eccentric hypertrophy incident to reduced contractility, chronic dilation incident to reduced growth response to stress, myocardial stricture incident to excessive growth response to stress, and concentric hypertrophy (similar to high-pressure adaptation) incident to deposition of inert material. It allows some refinements in the evaluation of myocardial performance and in the evaluation of the abnormal properties responsible for abnormal performance.

Adaptation, Physiological↗

PubMed1986

Evaluation of myocardial properties from image/pressure data: chronic conditions.

Since the wall/cavity ratio of a heart chamber is not a biological constant, fractional cavity-surface motion is not a valid performance index and the stresses most commonly used in the myocardial-mechanics literature are not valid expressions of pulling action or contractility. We have developed a system for analyzing and expressing left-ventricular performance and abilities which avoids these problems. It allows one to estimate the following quantities from left-ventricular image data and arterial pressures: "Fractional midwall excursion", the fractional change in a weighted average of inner- and outer-surface dimensions, which is a valid but preload-dependent expression of performance regardless of wall/cavity ratio. "Fractional midwall excursion rate", fractional midwall excursion divided by EKG-normalized ejection time, which is a relatively preload-independent expression of performance regardless of wall/cavity ratio. "Pressure safety factor", systolic pressure-making ability relative to demanded systolic pressure. "Myocardial fiberstress", the intensity of circumferential pulling force in the wall (pulling force per unit cross-sectional area). "Myocardial growth ability", the anabolic responsiveness to habitual systolic fiberstresses, expressed as the reciprocal of long-term-average systolic fiberstresses. (6) "Contractility", the stress-developing ability of the myocardium, specifically the amplitude of the developed stress-stretch function at peak activation. On the average, these quantities are related as follows: Growth ability determines average systolic fiberstresses; contractility and growth ability (or systolic stress) largely determine safety factor; safety factor largely determines fractional midwall excursion and its rate. We have developed a microcomputer program which evaluates these quantities from image/pressure data and displays them digitally and graphically.

Adult↗