An algorithm for volume estimation based on polyhedral approximation

3D surface reconstruction of the femur and tibia from parallel 2D contours

Background

Segmented structures, such as bones, are typically stored as 2D contours contained on evenly spaced images (slices). Contour interpolation algorithms to turn 2D contours into a 3D surface may differ in their results, causing discrepancies in analysis. This study aimed to create an accurate and consistent algorithm for the interpolation of femur and tibial contours that can be used in computer-assisted surgical navigation systems.

Methods

The implemented algorithm performs contour interpolation in a step-by-step manner, determining an optimal surface between each pair of consecutive contours. Determining such a surface is reduced to the problem of finding certain minimum-cost cycles in a directed toroidal graph. The algorithm assumes that the contours are ordered. The first step in the algorithm is the determination of branching patterns, followed by the removal of keyholes from contours, optimization of a target function based on the surface area, and mesh triangulation based on the optimization results and mesh seal.

Results

The algorithm was tested on contours segmented on computed tomography images from femoral and tibial specimens; it was able to generate qualitatively good 3D meshes from the set of 2D contours for all the tested examples.

Conclusion

The contour interpolation algorithm proved to be quite effective using optimization based on minimizing the area of the triangles that form the 3D surface. The algorithm can be used for the 3D reconstruction of other types of 2D cuts, but special attention must be paid with the branches, since the proposed algorithm is not designed for complex branching structures.

Accurate estimation of the myocardium global function from reduced magnetic resonance image acquisitions

Evaluating the heart global function from magnetic resonance images is based on estimating a number of functional parameters such as the left ventricular (LV) volume, LV mass, ejection fraction, and stroke volume. Estimating these parameters requires accurate calculation of the volumes enclosed by the inner and outer surfaces of the LV chamber at the max contraction and relaxation states of the heart. Currently, this is achieved through acquisition and segmentation of a large number of short-axis (SAX) views of the LV, which is time-consuming and expensive. Reducing the number of acquisitions results in undersampling the LV surfaces and hence increases the calculation errors. In this work, we describe and evaluate a method for estimating the cardiac parameters from a small number of image acquisitions that includes one long-axis (LAX) view of the LV. In this method, the LAX contour is used to swipe the SAX contours to fill in the missed LV surface between the SAX slices. Results on 25 patients and CT phantoms shows that, given the same number of slices, the proposed method is superior to other methods.

Semi-automated method for estimating lesion volumes

Accurately measuring the volume of tissue damage in experimental lesion models is crucial to adequately control for the extent and location of the lesion, variables that can dramatically bias the outcome of preclinical studies. Many of the current commonly used techniques for this assessment, such as measuring the lesion volume with primitive software macros and plotting the lesion location manually using atlases, are time-consuming and offer limited precision. Here we present an easy to use semi-automated computational method for determining lesion volume and location, designed to increase precision and reduce the manual labor required. We compared this novel method to currently used methods and demonstrate that this tool is comparable or superior to current techniques in terms of precision and has distinct advantages with respect to user interface, labor intensiveness and quality of data presentation.

Efficient computation of enclosed volume and surface area from the same triangulated surface representation

We demonstrate that the volume enclosed by triangulated surfaces can be computed efficiently in the same elegant way the volume enclosed by digital surfaces can be computed by digital surface integration. Although digital surfaces are effective and efficient for visualization and volume measurement, their drawback is that surface area measurements derived from them are inaccurate. On the other hand, triangulated surfaces give more accurate surface area measurements, but volume measurements and visualization are less efficient. Our data structure (called t-shell) for representing triangulated digital surfaces retains advantages and overcomes difficulties of both the digital and the triangulated surfaces. We create a lookup table with area and volume contributions for each of the 256 Marching Cubes configurations. When scanning the shell (e.g., while creating it), the surface area and volume are incrementally computed by using the lookup table and the current x co-ordinate, where the sign of the x component of the triangle normal indicates the sign of the volume contribution. We have computed surface area and volume for digitized mathematical phantoms, physical phantoms, and real objects. The experiments show that triangulated surface area is more accurate, triangulated volume follows digital volume closely, and that the values get closer to the true value with decreasing voxel size.

Computer-assisted venous thrombosis volume quantification

Venous thrombosis (VT) volume assessment, by verifying its risk of progression when anticoagulant or thrombolytic therapies are prescribed, is often necessary to screen life-threatening complications. Commonly, VT volume estimation is done by manual delineation of few contours in the ultrasound (US) image sequence, assuming that the VT has a regular shape and constant radius, thus producing significant errors. This paper presents and evaluates a comprehensive functional approach based on the combination of robust anisotropic diffusion and deformable contours to calculate VT volume in a more accurate manner when applied to freehand 2-D US image sequences. Robust anisotropic filtering reduces image speckle noise without generating incoherent edge discontinuities. Prior knowledge of the VT shape allows initializing the deformable contour, which is then guided by the noise-filtering outcome. Segmented contours are subsequently used to calculate VT volume. The proposed approach is integrated into a system prototype compatible with existing clinical US machines that additionally tracks the acquired images 3-D position and provides a dense Delaunay triangulation required for volume calculation. A predefined robust anisotropic diffusion and deformable contour parameter set enhances the system usability. Experimental results pertinence is assessed by comparison with manual and tetrahedron-based volume computations, using images acquired by two medical experts of eight plastic phantoms and eight in vitro VTs, whose independently measured volume is the reference ground truth. Results show a mean difference between 16 and 35 mm(3) for volumes that vary from 655 to 2826 mm(3). Two in vivo VT volumes are also calculated to illustrate how this approach could be applied in clinical conditions when the real value is unknown. Comparative results for the two experts differ from 1.2% to 10.08% of the smallest estimated value when the image acquisition cadences are similar.

Three-dimensional echocardiography: research toy or clinical tool?

Conventional 2D echocardiography is an excellent qualitative imaging method, but its use for quantitation is limited by test-retest reproducibility of image planes. The increasing sophistication of medical treatments for left ventricular dysfunction, hypertension and valvular heart disease has created the need for accurate and reproducible measurements of chamber dimensions. Similarly, improvements in valve repair and catheter-based interventions for valve lesions and septal defects have created the need for better visualisation of cardiac structures. The use of 31) echocardiography may decrease variability both in the quality and interpretation of complex pathology among investigators. Three-dimensional echocardiography is achieved by using a 3D spatial registration device with a conventional 21) scanner, or by using a high-speed, phased-array real-time scanner. The latter are still developmental, so that the technique currently requires use of a 21) scanner, combined with a 31) spatial coordinate system, which may be external or internal to the scanning transducer. An external system permits data acquired from several cardiac windows to be integrated and reconstructed. Image reconstruction is performed using a wire-frame model or surface rendering. Wire-frame models are formed by manual or automatic connection of boundary data points; this approach uses fewer data points than rendering, can be rapidly processed and is sufficient for quantitative analysis. Surface-rendering uses lighting and shading applied to a wire-frame model to produce a realistic 31) display, which may be useful for surgical planning and increasing understanding of anatomic relations. Three-dimensional echocardiography yields more accurate measurements of ventricular volume and function, as well as new measurements such as infarct area. With increased reproducibility and reliability, 3D echocardiography may well prove to be the essential tool required for the serial follow up of left ventricular mass and volume.

Patient motion compensation during transthoracic 3-D echocardiography

Bulk patient motion during transthoracic 3-D echocardiography (3DE) produces image plane misregistration and errors in left ventricular (LV) volume and ejection fraction (EF). To correct for patient motion, we used a magnetic locating system to track both the ultrasound transducer and the chest wall of the patient, so images could be registered in a patient-centered coordinate system ("correction"). Fourteen subjects each underwent 3DE, with deliberate patient motion, to measure LV volume and EF. Results were compared to magnetic resonance imaging (MRI). Without correction, 3DE differed significantly from MRI (EF: r = 0.78, SEE = 5.8%). Application of correction increased 3DE accuracy, despite patient motion (EF: r = 0.91, SEE = 3.7%), to a level comparable to that of 3DE in the absence of motion (EF: r = 0.93, SEE = 3.5%). Patient motion during 3DE examination can be corrected using a magnetic spatial location system.

Positional localization: three-dimensional transthoracic echocardiographic techniques for the measurement of cardiac mass, volume, and function

An accurate and reproducible determination of cardiac volume and mass is important for the selection and timing of therapeutic interventions. Quantitative three-dimensional echocardiography has evolved to provide these measurements with the use of a noninvasive, readily available, and inexpensive technique. We introduce and review the principle of positional localization as well as the clinical application of this technique for the measurement of cardiac volume and mass.

Three-dimensional echocardiographic measurement of left ventricular mass: comparison with magnetic resonance imaging and two-dimensional echocardiographic determinations in man

This study was performed to compare a novel three-dimensional echocardiography (3DE) system to clinical two-dimensional echocardiography (2DE) and magnetic resonance imaging (MRI) for determination of left ventricular mass (LVM) in humans. LVM is an independent predictor of cardiac morbidity and mortality. Echocardiography is the most widely used clinical method for assessment of LVM, as it is non-invasive, portable and relatively inexpensive. However, when measuring LVM, 2DE is limited by assumptions about ventricular shape which do not affect 3D echo.

METHODS

A total of 25 unselected patients underwent 3DE, 2DE and MRI. Three-dimensional echo used a magnetic scanhead tracker allowing unrestricted selection and combination of images from multiple acoustic windows. Mass by quantitative 2DE was assessed using seven different geometric formulas.

RESULTS

LVM by MRI ranged from 91 to 316 g. There was excellent agreement between 3DE and MRI (r = 0.99, SEE = 6.9 g). Quantitative 2D methods correlated well with but underestimated MRI (r = 0.84-0.92) with SEEs over threefold greater (22.5-30.8 g). Interobserver variation was 7.6% for 3DE vs. 17.7% for 2DE.

CONCLUSIONS

LVM in humans can be measured accurately, relative to MRI, by transthoracic 3D echo using magnetic tracking. Compared to 2D echo, 3D echocardiography significantly improves accuracy and reproducibility.

Superiority of 3-dimensional versus 2-dimensional echocardiography for left ventricular volume assessment in small piglet hearts

To evaluate the accuracy of 3-dimensional (3D) echocardiography in the estimation of left ventricular (LV) volume in vivo, we studied 15 newborn piglets ranging in weight from 2.6 to 11.8 kg. Measurements of beating LV volumes by 3D echocardiograms were compared with measurements by conductance catheter and transthoracic 2-dimensional (2D) echocardiograms with the use of Simpson's rule. The results of both 3D and 2D echocardiograms correlated strongly with the actual volume (r = 0.98 and 0.95 for LV end-diastolic volume, and 0.998 and 0.95 for LV end-systolic volume, respectively). However, the standard error of estimate (SEE) for 2D echocardiography was larger than for 3D. The SEE values for LV end-diastolic volume for 2D and 3D echocardiograms were 2.30 mL and 1.85 mL, respectively, and 1.52 mL and 0.5 mL for LV end-systolic volume. We conclude that 3D echocardiography not only accurately measures LV volume and systolic function in a newborn heart, it is more precise than measurements from 2D echocardiography in the assessment of small beating hearts.

Accuracy of three-dimensional echocardiography with unrestricted selection of imaging planes for measurement of left ventricular volumes and ejection fraction

BACKGROUND

Accurate, reproducible, noninvasive determination of left ventricular (LV) volumes and ejection fraction (EF) is important for clinical assessment, risk stratification, selection of therapy, and serial monitoring of patients with cardiovascular disease. Three-dimensional echocardiography (3DE) approaches have demonstrated significantly greater accuracy than current clinical 2DE, but the clinical utility of 3DE has been limited because of the need for substantial modifications to scanning technique (eg, all image acquisition from a single acoustic window) or cumbersome additional hardware. We describe a novel 3DE system without these limitations and its application to patients.

METHODS AND RESULTS

Twenty-five patients were examined by 3DE, 2DE, and magnetic resonance imaging (MRI). The 3DE system used a magnetic scanhead tracking device, and volumes were computed with a novel deformable shell model. End-diastolic volumes and EF by MRI ranged from 96 to 375 mL and 18% to 73%, respectively. There was excellent correlation, without statistically significant differences, between MRI and 3DE for end-systolic volume (ESV) (r(2) = 0.99) and end-diastolic volume (EDV) (r(2) = 0.98), ventricular stroke volume (SV) (r(2) = 0.93), and EF (r(2) = 0.97), with standard error estimates less than 10 mL for volumes and 3% for EF. Conventional 2DE consistently underestimated volumes (EDV, P <.01; ESV, P <.01; SV, P <.05); correlations with MRI were r(2) = 0.91 for ESV, r(2) = 0.88 for EDV, r(2) = 0.62 for SV, and r(2) = 0.72 for EF. Standard error estimates ranged from 16 to 20 mL for ventricular volumes and 9% for EF. Interobserver variability was reduced 3-fold with use of 3DE.

CONCLUSIONS

The novel 3DE system allows unrestricted selection and combination of acoustic windows in a single examination, improves accuracy of estimates of LV volumes and EF 3-fold compared with 2DE, and is practical for routine clinical assessment of LV size and function in patients with a wide range of cardiac pathology.

Target volume definition in conformal radiotherapy for prostate cancer: quality assurance in the MRC RT-01 trial

BACKGROUND AND PURPOSE

Prior to randomization of patients into the UK Medical Research Council multicentre randomized trial (RT-01) of conformal radiotherapy (CFRT) in prostate cancer, clinicians at participating centres were required to complete a quality assurance (QA) clinical planning exercise to enable an investigation of inter-observer variability in gross target volume (GTV) and normal structure outlining.

MATERIALS AND METHODS

Thirteen participating centres and two investigators completed the clinical planning exercise of three practice planning cases. Clinicians were asked to draw outlines of the GTV, rectum and bladder on hard-copy computerized tomography (CT) films of the pelvis, which were transferred onto the Cadplan computer planning system by a single investigator. Centre, inferior and superior CT levels of GTV, rectum and bladder were noted, and volume calculations performed. Planning target volumes (PTV) were generated using automatic volume expansion of GTVs by a 1 cm margin. Anterior, right and left lateral beam eye views (BEV) of the PTVs were generated. Using a common central point, the BEV PTVs were superimposed for each beam direction of each case. Radial PTV variation was investigated by measurement of a novel parameter, termed the radial line measurement variation (RLMV).

RESULTS

GTV central slice and length were defined with reasonable consistency. The RLMV analysis showed that the main part of the prostate gland, bladder and inferior rectum were outlined with good consistency among clinicians. However, the outlining of the prostatic apex, superior aspect of the prostate projecting into the bladder, seminal vesicles, the base of seminal vesicles and superior rectum were more variable.

CONCLUSION

This exercise has demonstrated adequate consistency of GTV definition. The RLMV method of analysis indicates particular regions of clinician uncertainty. Appropriate feedback has been given to all participating clinicians, and the final RT-01 trial protocol has been modified to accommodate these findings.

Importance of imaging method over imaging modality in noninvasive determination of left ventricular volumes and ejection fraction: assessment by two- and three-dimensional echocardiography and magnetic resonance imaging

OBJECTIVES

This study sought to determine the concordance between biplane and volumetric echocardiography and magnetic resonance imaging (MRI) strategies and their impact on the classification of patients according to left ventricular (LV) ejection fraction (EF) (LVEF).

BACKGROUND

Transthoracic echocardiography and MRI are noninvasive imaging modalities well suited for serial evaluation of LV volume and LVEF. Despite the accuracy and reproducibility of volumetric methods, quantitative biplane methods are commonly used, as they minimize both scanning and analysis times.

METHODS

Thirty-five adult subjects, including 25 patients with dilated cardiomyopathies, were evaluated by biplane and volumetric (cardiac short-axis stack) cine MRI and by biplane and volumetric (three-dimensional) transthoracic echocardiography. Left ventricular volume, LVEF and LV function categories (LVEF > or =55%, >35% to <55% and < or =35%) were then determined.

RESULTS

Biplane echocardiography underestimated LV volume with respect to the other three strategies (p < 0.01). There were no significant differences (p > 0.05) between any of the strategies for quantitative LVEF. Volumetric MRI and volumetric echocardiography differed by a single functional category for 2 patients (8%). Six to 11 patients (24% to 44%) differed when comparing biplane and volumetric methods. Ten patients (40%) changed their functional status when biplane MRI and biplane echocardiography were compared; this comparison also revealed the greatest mean absolute difference in estimates of EF for those subjects whose EF functional category had changed.

CONCLUSIONS

Volumetric MRI and volumetric echocardiographic measures of LV volume and LVEF agree well and give similar results when used to stratify patients with dilated cardiomyopathy according to systolic function. Agreement is poor between biplane and volumetric methods and worse between biplane methods, which assigned 40% of patients to different categories according to LVEF. The choice of imaging method (volumetric or biplane) has a greater impact on the results than does the choice of imaging modality (echocardiography or MRI) when measuring LV volume and systolic function.

Fast surface and volume estimation from non-parallel cross-sections, for freehand three-dimensional ultrasound

Volume measurements from ultrasound B-scans are useful in many clinical areas. It has been demonstrated previously that using three-dimensional (3-D) ultrasound can greatly increase the accuracy of these measurements. Freehand 3-D ultrasound allows freedom of movement in scanning, but the processing is complicated by having non-parallel scan planes. Two techniques are proposed for volume measurement from such data, which also improve surface and volume estimation from data acquired on parallel planes. Cubic planimetry is a more accurate extension of a volume measurement technique involving vector areas and centroids of cross-sections. Maximal-disc shape-based interpolation is an extension of shape-based interpolation which uses maximal disc representations to adjust the interpolation direction locally and hence improve the quality of the surface generated. Both methods are tested in simulation and in vivo. Volumes estimated using cubic planimetry are more accurate than step-section planimetry, and require fewer cross-sections, even for complex objects. Maximal-disc shape-based interpolation provides a reliable means of reconstructing surfaces from a handful of cross-sections, and can therefore be used to give confidence in the segmentation and hence also the cubic planimetry volume.

Three-dimensional echocardiography improves accuracy and compensates for sonographer inexperience in assessment of left ventricular ejection fraction

This study was performed to determine whether 3-dimensional echocardiography (3DE) with a magnetic tracking system for image plane localization, which unlike standard 2-dimensional echocardiography (2DE), does not require acquisition of specific image planes or "standard views" for quantitative measurement of left ventricular volume and ejection fraction (EF), could compensate for sonographer inexperience. Eight adults underwent magnetic resonance imaging (MRI) scanning; they also had 2DE and 3DE performed by 2 experienced and 3 novice sonographers. Data were analyzed by a single expert reader blinded to patient and sonographer identity. Linear regression of MRI EF (reference standard) against echocardiographic EF yielded the following results, where RD indicates the residual difference between measured MRI values and those predicted using echocardiographic results: expert 3DE: r = 0.97, RD = 2.4%, and r = 0.96, RD = 2.8%; novice 3DE: r = 0. 83, RD = 5.1%, to r = 0.95, RD = 4.8%; expert 2DE: r = 0.85, RD = 4. 8%, and r = 0.86, RD = 4.9%; and novice 2DE: r = 0.34, RD = 11.7%, to r = 0.69, RD = 6.6%. Comparison of error variances indicated that novices who used 3DE equaled the performance of experts who used 2DE, although experts were always more accurate than novices when both used the same echocardiographic method (3DE vs 3DE, 2DE vs 2DE). In a comparison of methods, 3DE was always superior to 2DE, regardless of sonographer experience. Three-dimensional echocardiography allows even novice sonographers to obtain diagnostic-quality data sets, which they were unable to accomplish with 2DE. These results suggest that scanning with 3DE, combined with remote expert interpretation, may be useful in providing echocardiographic services in regions where they are presently unavailable.

The accuracy of a new system for estimating organ volume using ultrasound

A new system is described for estimating volume from a series of multiplanar 2D ultrasound images. Ultrasound images are captured using a personal computer video digitizing card and an electromagnetic localization system is used to record the pose of the ultrasound images. The accuracy of the system was assessed by scanning four groups of ten cadaveric kidneys on four different ultrasound machines. Scan image planes were oriented either radially, in parallel or slanted at 30 degrees to the vertical. The cross-sectional images of the kidneys were traced using a mouse and the outline points transformed to 3D space using the Fastrak position and orientation data. Points on adjacent region of interest outlines were connected to form a triangle mesh and the volume of the kidneys estimated using the ellipsoid, planimetry, tetrahedral and ray tracing methods. There was little difference between the results for the different scan techniques or volume estimation alogorithms, although, perhaps as expected, the ellipsoid results were the least precise. For radial scanning and ray tracing, the mean and standard deviation of the percentage errors for the four different machines were as follows: Hitachi EUB-240, -3.0 +/- 2.7%; Tosbee RM3, -0.1 +/- 2.3%; Hitachi EUB-415, 0.2 +/- 2.3%; Acuson, 2.7 +/- 2.3%.

Application of a new discreet form of Gauss' theorem for measuring volume

Volume measurements are useful in many branches of science and medicine. They are usually accomplished by acquiring a sequence of cross sectional images through the object using an appropriate scanning modality, for example x-ray computed tomography (CT), magnetic resonance (MR) or ultrasound (US). In the cases of CT and MR, a dividing cubes algorithm can be used to describe the surface as a triangle mesh. However, such algorithms are not suitable for US data, especially when the image sequence is multiplanar (as it usually is). This problem may be overcome by manually tracing regions of interest (ROIs) on the registered multiplanar images and connecting the points into a triangular mesh. In this paper we describe and evaluate a new discreet form of Gauss' theorem which enables the calculation of the volume of any enclosed surface described by a triangular mesh. The volume is calculated by summing the vector product of the centroid, area and normal of each surface triangle. The algorithm was tested on computer-generated objects, US-scanned balloons, livers and kidneys and CT-scanned clay rocks. The results, expressed as the mean percentage difference +/- one standard deviation were 1.2 +/- 2.3, 5.5 +/- 4.7, 3.0 +/- 3.2 and -1.2 +/- 3.2% for balloons, livers, kidneys and rocks respectively. The results compare favourably with other volume estimation methods such as planimetry and tetrahedral decomposition.

Validation of three-dimensional echocardiography for quantifying the extent of dyssynergy in canine acute myocardial infarction: comparison with two-dimensional echocardiography

OBJECTIVES

This study was designed to compare the accuracy of three- and two-dimensional echocardiography for quantifying the extent of abnormal wall motion in experimental acute myocardial infarction, as correlated with the pathologic determination of infarct size.

BACKGROUND

Two-dimensional echocardiographic estimations of the fraction of myocardium showing abnormal wall motion are often used as an index of infarct size even though they rely on image plane positioning and geometric assumptions that may not be valid. Three-dimensional echocardiographic reconstruction of the endocardial surface eliminates the need for these assumptions and may improve echocardiographic estimates of infarct size.

METHODS

Coronary ligation was performed in 14 open chest dogs, and echocardiographic imaging of the ventricle was performed 6 h later. Three-dimensional echocardiography used seven or eight spatially registered short-axis images to measure percent of endocardial surface and mass showing abnormal wall motion. Three two-dimensional echocardiographic methods using multiple, nonpatially registered images were evaluated. One method used seven or eight-axis slices and a summation of discs algorithm for computing surface area. The second method used the same images and a conical model for the left ventricle. The third used basal, middle and apical short-axis plus apical four- and two-chamber views comparing summed endocardial lengths showing abnormal wall motion with the total of the endocardial dimensions, expressed as percent. The percent of left ventricular mass and surface area infarcted was determined by staining with triphenyltetrazolium chloride.

RESULTS

Three-dimensional echocardiographic measurements of endocardial surface and correlated more closely with infarct mass (r = 0.94, SEE +/- 3.6%) than did the two-dimensional method using the summation of discs algorithm (r = 0.85, SEE +/- 6.6%), he summation of conical sections algorithm (r = 0.82, SEE +/- 5.4%) or the method using summed endocardial lengths (r = 0.79, SEE +/- 7.4%). Limits of agreement analysis comparing mass showing abnormal wall motion with anatomic infarct mass surface area showing abnormal wall motion with anatomic infarct surface area showed the smallest limits for three-dimensional echocardiography.

CONCLUSIONS

Three-dimensional echocardiography is a more accurate means of noninvasively estimating myocardial infarct size in this canine model than two-dimensional echocardiography.

Volume estimation from multiplanar 2D ultrasound images using a remote electromagnetic position and orientation sensor

A system is described for calculating volume from a sequence of multiplanar 2D ultrasound images. Ultrasound images are captured using a video digitising card (Hauppauge Win/TV card) installed in a personal computer, and regions of interest transformed into 3D space using position and orientation data obtained from an electromagnetic device (Polhemus, Fastrak). The accuracy of the system was assessed by scanning 10 water filled balloons (13-141 mL), 10 kidneys (147-200 mL) and 16 fetal livers (8-37 mL) in water using an Acuson 128XP/10 (5 MHz curvilinear probe). Volume was calculated using the ellipsoid, planimetry, tetrahedral and ray tracing methods and compared with the actual volume measured by weighing (balloons) and water displacement (kidneys and livers). The mean percentage error for the ray tracing method was 0.9 +/- 2.4%, 2.7 +/- 2.3%, 6.6 +/- 5.4% for balloons, kidneys and livers, respectively. So far the system has been used clinically to scan fetal livers and lungs, neonate brain ventricles and adult prostate glands.

Three-dimensional echocardiography: limitations of apical biplane imaging for measurement of left ventricular volume

A new three-dimensional echocardiographic system creates a "line of intersection" display to allow precise and known positioning of echocardiographic images. Our purpose was to determine whether use of the line-of-intersection display will improve positioning of the apical four-chamber and apical two-chamber views and thereby improve the agreement between estimates of left ventricular volume by apical biplane echocardiography and cineventriculography. Unguided and line of intersection-guided apical biplane views were obtained in 31 patients immediately before cardiac catheterization and single-plane cineventriculography. In 15 patients the line-of-intersection display was used to measure the position of the image plane in studies of unguided and guided methods. Linear regression and limits of agreement analysis were used to assess the agreement between cineventriculographic volumes and echocardiographic volumes determined from each set of images. The Wilcoxon test was used to compare guided and unguided image positioning. The line-of-intersection display improved four-chamber and two-chamber view positioning closer to the center of the ventricle and rotation closer to orthogonal positioning. Guided-image positioning was not able to correct displacement of the ultrasound beam anterior to the ventricular apex without deterioration of image quality in most patients. Despite improvements in image plane positioning, the agreement between echocardiographic and cineventriculographic volumes was unchanged. For end-diastole views, the unguided images had an r value = 0.84, standard error of the estimate of +/- 23.0 cc, and limits of agreement of +/- 62.4 cc. Corresponding values for the guided images at end diastole were r = 0.85, standard error of the estimate of +/- 22.9 cc, and limits of agreement of +/- 60.8 cc. At end systole the unguided results were r = 0.91, standard error of the estimate of 16.8 cc, and limits of agreement of +/- 52.2 cc. The line-of-intersection guiding of image plane positioning can improve apical image positioning but does not improve the agreement between apical biplane echocardiographic and cineventriculographic left ventricular volumes. The optimal apical imaging window is frequently occluded by the rib cage, resulting in a decrease in image quality. This reduction of image quality, combined with assumptions of left ventricular geometry, limit the accuracy of estimates of left ventricular volume from apical biplane echocardiography.

Ultrasonic three-dimensional reconstruction of the heart

The recent advances in ultrasound equipment, digital image acquisition, and display techniques made three-dimensional (3D) echocardiography a clinically feasible and exciting technique which allows objective analysis of structure and pathological conditions of complex geometry. In this report, different image acquisition techniques are described and compared. In our experience, with rotational scanning the acquisition of cross-sections for 3D reconstruction becomes an integral part of a routine diagnostic study, both with a multiplane transesophageal imaging transducer, and in precordial echocardiography. After digital reformatting and image processing, a volumetric data set is obtained, which allows the display of synthetic cross-sections in various orientations independent from the point of origin of the sector scan [anyplane two-dimensional (2D) imaging]. This also offers the possibility of volume quantification, without the assumption of theoretical geometrical model of the cavity. Finally, dynamic volume rendered display can be applied for the objective display of the anatomy and the complex relationship among the different structures.

Comparison of two- and three-dimensional echocardiography with cineventriculography for measurement of left ventricular volume in patients

OBJECTIVES

We compared two- and three-dimensional echocardiography with cineventriculography for measurement of left ventricular volume in patients.

BACKGROUND

Three-dimensional echocardiography has been shown to be highly accurate and superior to two-dimensional echocardiography in measuring left ventricular volume in vitro. However, there has been little comparison of the two methods in patients.

METHODS

Two- and three-dimensional echocardiography were performed in 35 patients (mean age 48 years) 1 to 3 h before left ventricular cineventriculography. Three-dimensional echocardiography used an acoustic spatial locator to register image position. Volume was computed using a polyhedral surface reconstruction algorithm based on multiple nonparallel, unevenly spaced short-axis cross sections. Two-dimensional echocardiography used the apical biplane summation of disks method. Single-plane cineventriculographic volumes were calculated using the summation of disks algorithm. The methods were compared by linear regression and a limits of agreement analysis. For the latter, systematic error was assessed by the mean of the differences (cineventriculography minus echocardiography), and the limits of agreement were defined as +/- 2 SD from the mean difference.

RESULTS

Three-dimensional echocardiographic volumes demonstrated excellent correlation (end-diastole r = 0.97; end-systole r = 0.98) with cineventriculography. Standard errors of the estimate were approximately half of those of two-dimensional echocardiography (end-diastole +/- 11.0 ml vs. +/- 21.5 ml; end-systole +/- 10.2 ml vs. +/- 17.0 ml). By limits of agreement analysis the end-diastolic mean differences for two- and three-dimensional echocardiography were 21.1 and 12.9 ml, respectively. The limits of agreement (+/- 2 SD) were +/- 54.0 and +/- 24.8 ml, respectively. For end-systole, comparable improvement was obtained by three-dimensional echocardiography. Results for ejection fraction by the two methods were similar.

CONCLUSIONS

Three-dimensional echocardiography correlates highly with cineventriculography for estimation of ventricular volumes in patients and has approximately half the variability of two-dimensional echocardiography for these measurements. On the basis of this study, three-dimensional echocardiography is the preferred echocardiographic technique for measurement of ventricular volume. Three-dimensional echocardiography is equivalent to two-dimensional echocardiography for measuring ejection fraction.

Three-dimensional echocardiography: in vitro and in vivo validation of left ventricular mass and comparison with conventional echocardiographic methods

OBJECTIVES

This study aimed to validate a method for mass computation in vitro and in vivo and to compare it with conventional methods.

BACKGROUND

Conventional echocardiographic methods of determining left ventricular mass are limited by assumptions of ventricular geometry and image plane positioning. To improve accuracy, we developed a three-dimensional echocardiographic method that uses nonparallel, nonintersecting short-axis planes and a polyhedral surface reconstruction algorithm for mass computation.

METHODS

Eleven fixed hearts were imaged by three-dimensional echocardiography, and mass was determined in vitro by multiplying the myocardial volume by the density of each heart and comparing it with the true mass. Mass at diastole and systole by three-dimensional echocardiography and magnetic resonance imaging (MRI) was compared in vivo in 15 normal subjects. Ten subjects also underwent imaging by one- and two-dimensional echocardiography, and mass was determined by Penn convention, area-length and truncated ellipsoid algorithms.

RESULTS

In vitro results were r = 0.995, SEE 2.91 g, accuracy 3.47%. In vivo interobserver variability for systole and diastole was 16.7% to 27%, 14% to 18.1% and 6.3% to 12.8%, respectively, for one-, two- and three-dimensional echocardiography and was 7.5% for MRI at end-diastole. The latter two agreed closely with regard to diastolic mass (r = 0.895, SEE 11.1 g) and systolic mass (r = 0.926, SEE 9.2 g). These results were significantly better than correlations between MRI and the Penn convention (r = 0.725, SEE 25.6 g for diastole; r = 0.788, SEE 28.7 g for systole), area-length (r = 0.694, SEE 24.2 g for diastole; r = 0.717, SEE 28.2 g for systole) and truncated ellipsoid algorithms (r = 0.687, SEE 21.8 g for diastole; r = 0.710, SEE 24.5 g for systole).

CONCLUSIONS

Image plane positioning guidance and elimination of geometric assumptions by three-dimensional echocardiography achieve high accuracy for left ventricular mass determination in vitro. It is associated with higher correlations and lower standard errors than conventional methods in vivo.

Three-dimensional echocardiographic measurement of left ventricular volume in vitro: comparison with two-dimensional echocardiography and cineventriculography

OBJECTIVES

This study was designed to compare three-dimensional echocardiography, two-dimensional echocardiography and cineventriculography for the purpose of measuring left ventricular volume in vitro.

BACKGROUND

Three-dimensional echocardiographic systems have been shown to be highly accurate in measuring the volumes of balloon phantoms. However, three-dimensional techniques have not been compared with standard two-dimensional echocardiography in vitro or with cineventriculography, the clinical standard for left ventricular volume measurement.

METHODS

Excised porcine hearts were prepared with an internal latex sheath that could be filled and maintained with a known ("true") volume of liquid. Each heart was then imaged by cineventriculography, standard two-dimensional echocardiography and three-dimensional echocardiography. Left ventricular volumes were calculated from 15 hearts at 25 volumes ranging from 50 to 280 ml by the following methods: 1) biplane cineventriculography using the area-length method; 2) two-dimensional echocardiography by the apical biplane method using a summation of discs algorithm in 15 cases and the single-plane, four-chamber method using a summation of discs algorithm in 10 cases; and 3) three-dimensional echocardiography using a polyhedral surface reconstruction volume computation algorithm based on multiple nonparallel, nonevenly spaced short-axis cross sections.

RESULTS

Results were compared with true volume, and a nonparametric analysis of variance was performed. Both measurement bias (systematic error) and imprecision (random error) were assessed. All methods tended to underestimate the true volume (two-dimensional echocardiography -6.1 +/- 17.6%, three-dimensional echocardiography -4.7 +/- 5.0% and biplane cineventriculography -3.9 +/- 8.2%), although differences were not significant. Although there was a significant correlation between the magnitude of measurement bias and the size of the volume being measured for two-dimensional echocardiography and cineventriculography, the bias of three-dimensional echocardiography was fairly constant over the range of volumes. When bias was accounted for, two-dimensional echocardiography was significantly less precise than cineventriculography and three-dimensional echocardiography in terms of percent error (15.3 +/- 11.9%, 5.6 +/- 5.7% and 3.9 +/- 3.4%, respectively).

CONCLUSIONS

Three-dimensional echocardiography using a polyhedral surface reconstruction algorithm for volume computation provides accuracy comparable to that of biplane cineventriculography in this in vitro model. Standard two-dimensional echocardiographic volume computation is significantly less accurate than the other two methods.

Three-dimensional echocardiographic volume computation: in vitro comparison to standard two-dimensional echocardiography

Two-dimensional (2D) echocardiographic methods for quantitative left ventricular volume computation have been shown to have a low predictive accuracy and reproducibility. To address the problem of geometric assumptions and image plane positioning errors inherent in 2D echocardiography, three-dimensional (3D) echocardiographic systems have been constructed that provide spatial registration and display of transducer-image position and orientation. Although 3D echocardiography has been shown to accurately measure volume in vitro and in vivo, only preliminary data exist demonstrating its superiority over standard 2D echocardiography. We calculated the volume of 30 water-filled latex balloon phantoms of varying size (40 to 200 ml) and shape using each method. Fifteen phantoms were nondistorted (ellipsoid or pear shaped); 15 were symmetrically distorted (dumbbell shaped). Although both 2D and 3D echocardiography showed an excellent correlation to the true volume (r = 0.97 and 0.99, respectively), the standard error of the estimate for 2D echocardiography was twofold larger than for 3D echocardiography (SEE = 6.7 ml and 3.52 ml, respectively). The true volume was slightly underestimated by 3D echocardiography (-2.83 ml), whereas 2D echocardiography overestimated a similar amount (+2.87 ml). The accuracy and variability for 2D echocardiography were significantly poorer (5.22% +/- 5.66% and 5.29% +/- 5.6%, p = 0.001 and 0.002, respectively) as compared with 3D echocardiography (3.7% +/- 2.65% and 2.65% +/- 1.9%, respectively). We conclude that 3D echocardiography with guided image plane positioning and a novel algorithm for volume computation (polyhedral surface reconstruction) achieves significantly more accurate and reproducible results than conventional 2D echocardiography with the modified Simpson's rule.(ABSTRACT TRUNCATED AT 250 WORDS)

Left ventricular volume and endocardial surface area by three-dimensional echocardiography: comparison with two-dimensional echocardiography and nuclear magnetic resonance imaging in normal subjects

OBJECTIVES

We evaluated a three-dimensional echocardiographic method for ventricular volume and surface area determination that uses polyhedral surface reconstruction. Six to eight nonparallel, unequally spaced, nonintersecting short-axis planes were positioned with a line of intersection display to overcome limitations associated with two-dimensional echocardiography.

BACKGROUND

Two-dimensional echocardiographic methods of ventricular volume and surface area determination are limited by assumptions about ventricular shape and image plane position.

METHODS

Left ventricular end-diastolic and end-systolic volumes and endocardial surface areas determined by three-dimensional echocardiography and nuclear magnetic resonance (NMR) imaging were compared in 15 normal subjects (7 men, 8 women, aged 23 to 41 years, body surface area 1.38 to 2.17 m2). Ten of these subjects also underwent two-dimensional echocardiography; and end-diastolic and end-systolic volumes were determined by the apical biplane summation of discs method and compared with results of NMR imaging.

RESULTS

Interobserver variability was 5% to 8% for three-dimensional echocardiography and 6% to 9% for NMR imaging. Both methods were in close agreement on end-diastolic volume (r = 0.92, SEE = 6.99 ml) and end-systolic volume (r = 0.81, SEE = 4.01 ml) and on end-diastolic surface area (r = 0.84, SEE = 8.25 cm2) and end-systolic surface area (r = 0.84, SEE = 4.89 cm2). Three-dimensional echocardiography and NMR imaging correlated significantly better for end-diastolic volume (r = 0.90, SEE = 7.0 ml) and end-systolic volume (r = 0.88, SEE = 3.1 ml) than did two-dimensional echocardiography and NMR imaging (r = 0.48, SEE = 20.5 ml for end-diastolic volume; r = 0.70, SEE = 5.6 ml for end-systolic volume).

CONCLUSIONS

Three-dimensional echocardiography is an in vivo method of measuring left ventricular end-diastolic and end-systolic volumes and endocardial surface area with results comparable to those of NMR imaging. Additionally, three-dimensional echocardiography is superior to the two-dimensional echocardiographic apical biplane summation method because the technique eliminates geometric assumptions and image plane positioning error.

Three-dimensional echocardiographic volume computation by polyhedral surface reconstruction: in vitro validation and comparison to magnetic resonance imaging

Two-dimensional echocardiographic methods of left ventricular volume computation are limited by geometric assumptions and image plane positioning error in the nonvisualized dimension. We evaluated a three-dimensional (3D echocardiographic method that addresses these limitations. Our method uses a volume computation algorithm based on polyhedral surface reconstruction (PSR) and nonparallel, unequally spaced, nonintersecting short-axis planes. Seventeen balloon phantoms were subjected to volume computation by the 3D echocardiography-PSR method and by magnetic resonance imaging (MRI) and compared to true volumes determined by water displacement. The results for 3D echocardiography-PSR were: accuracy = 2.27%, interobserver variability = 4.33%, r = 0.999, SEE = 2.45 ml, and p less than 0.001. Results for MRI were 8.01%, 13.78%, r = 0.995, SEE = 7.01 ml, and p less than 0.001. There was no statistically significant difference between the methods. We conclude that precise image plane positioning and use of the 3D echocardiographic-PSR volume computation method achieves high accuracy and reproducibility in vitro. The excellent in vitro correlation between 3D echocardiography-PSR and MRI indicates that MRI may also serve as an in vivo standard of comparison.

Problems with ratio and proportion measures of imaged cerebral structures

Ratio measures, such as the ventricle-brain ratio (VBR) based on computed tomography or magnetic resonance imaging, are widely used in psychiatric research in studies of brain function and morphology. While imaging techniques have advanced considerably, the form of the index of a structure's size has remained the same--a proportion based on an estimate of the structure's size divided by a like estimate of the whole brain size. We demonstrate that ratio and similar indices can suffer greatly in reliability when compared with simple volume measures. This loss of reliability is related to the relation of a structure's size and whole brain size. We review various methods for measuring the size of structures and discuss their strengths and limitations in terms of reliability and validity. In many instances, other methods of "correcting" for brain size (e.g., regression or covariance) may yield measurements that are more appropriate than ratios.

Three-dimensional computerized reconstruction of histologic serial sections for orthopedic research

New programs in image processing and computer graphics can now render three-dimensional images from serial tissue slices. Although neuroanatomists have used these techniques most intensively, there are exciting applications of this methodology in orthopedic research and investigative embryology. Three-dimensional reconstructions of histologic sections from newborn clubfeet have been used to determine the rotational alignment of the hindfoot bones. Similar studies could be undertaken to improve understanding of the normal and pathologic perinatal development of the spine, hip, and hand.

A three-dimensional Fourier descriptor for human body representation/reconstruction from serial cross sections

This paper presents a three-dimensional Fourier descriptor (FD3) for shape representation/reconstruction. The FD3 is a double Fourier transform of serial cross-sectional contours of a shape in three dimensions (3D), which retains all shape information and gives a compact and invariant representation. The inverse Fourier transform of the FD3 reconstructs the original 3D shape; and it also estimates volume in the process. The upper bound of error introduced by the 3D reconstruction from the FD3 is derived in the sense of supremum norm. The FD3 method is compatible with medical imaging technologies such as computed tomography (CT) or magnetic resonance imaging (MRI). As an illustration of the FD3 methodology, a human head shape is reconstructed from its MR images.

Toward computerized morphometric facilities: a review of 58 software packages for computer-aided three-dimensional reconstruction, quantification, and picture generation from parallel serial sections

This review gives an inventory of 58 computer-aided three-dimensional reconstruction applications in the domain of biomedical research. It is devoted to the formulation of a set of recommendations thought to be necessary for improved performance of software packages in this field. These recommendations can be used to select packages and to guide future developments of existing reconstruction systems. The survey is restricted to three-dimensional reconstructions based upon a series of parallel sections of an object. Subjects treated are programming languages, resolution and sampling, input preparation, realignment, local deformation of slices, numerical quantifications, topological complexity, internal representation, display complexity (hidden surfaces, shading, smoothing), structure extraction, descriptive elements, database, data compression, time efficiency of systems and algorithms, hardware configuration, input devices, input media, interactive aids, display devices, and output devices. Information for this survey comes from articles that appeared between 1965 and 1985.

A method for volume estimation by two-dimensional echocardiography: examination with excised animal left ventricles

Applicability of a newly developed volume estimation method was examined with excised left ventricles of pigs and dogs. Serial oblique-sectional images of a left ventricle were recorded with a two-dimensional echocardiograph. The probe of the echocardiograph was fixed at one point and was tilted stepwise. Contours of the left ventricle in the images were traced to put into a computer and volume was calculated. Calculated volume of 19 left ventricles agreed well with true volume in wide range (r = 0.982 for left ventricular myocardium and r = 0.989 for left ventricular cavity).

Separation and spread of nuclear fragments ("nucleotesimals") in colonic neoplasms

After multiple fragmentation of neoplastic nuclei into "nucleotesimals," a recently discovered variety of amitosis, some fragments appear to be inflated to full nuclear size; other probably lyse, releasing nucleic acid, which may assist in the synthesis of new cytoplasm around newly formed nuclei. This observation may be useful in elucidating one mechanism of neoplastic growth.

The use of a computerized algorithm to determine single cardiac cell volumes

Single cardiac muscles cell volume data have been difficult to obtain, especially because the shape of a cell is quite complex. With the aid of a surface reconstruction method, a cell volume estimation algorithm has been developed that can be used on serial of cells. The cell surface is reconstructed by means of triangular tiles so that the cell is represented as a polyhedron. When this algorithm was tested on computer generated surfaces of a known volume, the difference was less than 1.6%. Serial sections of two phantoms of a known volume were also reconstructed and a comparison of the mathematically derived volumes and the computed volume estimations gave a per cent difference of between 2.8% and 4.1%. Finally cell volumes derived using conventional methods and volumes calculated using the algorithm were compared. The mean atrial muscle cell volume derived using conventional methods was 7752.7 +/- 644.7 micrometers3, while the mean computerized algorithm estimated atrial muscle cell volume was 7110.6 +/- 625.5 micrometers3. For AV bundle cells the mean cell volume obtained by conventional methods was 484.4 +/- 88.8 micrometers3 and the volume derived from the computer algorithm was 506.0 +/- 78.5 micrometers3. The differences between the volumes calculated using conventional methods and the algorithm were not significantly different.