Pyramidal Volume Research Articles

Real-time three-dimensional fetal echocardiography using matrix probe

To investigate the feasibility of using real-time three-dimensional echocardiography (3DE) to evaluate the fetal heart. Sixty fetuses were studied with gestational age between 22 and 34 weeks. The fetal heart was normal in 44 fetuses. In 16 fetuses, the fetal heart had morphologic abnormalities (hypoplastic left ventricle in 4, tetralogy of Fallot in 2, Ebstein anomaly in 2, rhabdomyomes in 2, hypoplastic right ventricle in 1) or myocardial dysfunction (in 5 fetuses). Real-time 3DE was performed with a cardiac matrix probe (2-4 MHz). Two modalities of 3D imaging were performed: Biplane and Live 3D imaging. Real-time 3DE was performed successfully in 93%. Biplane imaging allowed a multiplanar scanning of the fetal heart. Using rotation, lateral and vertical tilts, the normal cardiac structures were identified from a unique reference image plane: atria and ventricles, atrioventricular valves, aorta and pulmonary artery. Live 3D imaging allowed surface imaging of the fetal heart. 'En face' view of the foramen ovale from the right atrium was obtained, showing the shape of the orifice. By cropping the pyramidal imaging volume, ascending aorta, aortic arch and ductus arteriosus were depicted from a single dataset. In pathologic fetal hearts, 3DE was helpful for (1) localizing multiple cardiac tumors; (2) estimating size and function of the right and left ventricles; (3) evaluating mechanism of valvular regurgitation and pulmonary obstruction. Real-time 3DE is a feasible and non-time-consuming method, allowing a multiplanar scanning and new inside 3D views of the fetal heart.

A Chilling Project Integrating Mathematics, Science, and Technology

Principles and Standards for School Mathematics states that in the middle grades “measurement concepts and skills can be developed and used throughout the school year rather than treated exclusively as a separate unit of study” (NCTM 2000, p. 241). One part of my attempt to do that with my seventh-grade students involved a collaborative activity carried out with the school's technology education teacher, Todd Kelley. We decided to combine our classes for one period of the day for two weeks. We both taught seventh graders during that one period: my students were in an Advanced Math class; his students were in an elective Technology Design class. My students had just completed a unit on calculating surface areas and volumes; they were expected to be able to use formulas to find the surface area and volume of basic three-dimensional shapes, including prisms, cylinders, spheres, cones, and pyramids. The technology students had been working on the IDEATE design process, which gives six specific steps that students should follow in a design project: Identify and define the problem; Develop the design brief; Explore possible alternatives; Accumulate and assess the alternatives; Try out the best solution; and Evaluate the results (Todd 1996, p. 17). We wanted to give our students a chance to practice the skills learned from both classes by applying them to a realistic situation and in a setting that gave them maximum room for creativity, problem solving, and divergent thinking. With the help of our media specialist, Kris McGlaun, we were able to create a unit that accomplished these goals.

Pyramidal cell size reduction in schizophrenia: evidence for involvement of auditory feedforward circuits

BackgroundSubjects with schizophrenia have decreased gray matter volume of auditory cortex in structural imaging studies and exhibit deficits in auditory sensory processing that might reflect impairments of feedforward and/or feedback circuits within the auditory cortex. Recently, we reported that one component of these circuits, pyramidal cells in deep layer 3 of the auditory association cortex (area 42), has reduced mean somal volume in subjects with schizophrenia. To discriminate between involvement of feedforward and feedback circuit components, we examined pyramidal cell somal volume in layer 3 of primary auditory cortex (feedforward) and layer 5 of auditory association cortex (feedback). MethodsWe estimated somal volumes of pyramidal neurons in deep layer 3 of area 41 and layer 5 of area 42 in subjects with schizophrenia (area 41, n = 16; area 42, n = 18), each of whom was matched to one normal comparison subject for gender, age, and postmortem interval. ResultsIn deep layer 3 of area 41, mean pyramidal cell somal volume was significantly reduced, by 10.4%. No significant reduction was present in layer 5 of area 42. ConclusionsPyramidal cell somal volume is reduced in layer 3 of area 41 and area 42, but not in layer 5 of area 42, of subjects with schizophrenia. This pattern of abnormalities is consistent with impairments of auditory feedforward projection neurons.

Sweet-Tooth Geometry

Surface area and volume of prisms, pyramids, and cylinders are challenging topics for middle school students. For the past five or six years, at the end of a unit covering these topics, I have reinforced this material by doing a project that involves the construction of a “creature” by each student. The creature had to be made out of a pyramid and a prism. Later, I added a cylinder as another choice to use in making the project. I provide the students with materials (see fig. 1), a scoring rubric, and class time to work on the project.

Real-time rectilinear volumetric imaging using a periodic array

Current real-time phased array volumetric scanners use a 2-D array to scan a pyramidal volume comprised of many sector scans stacked in the elevation direction. This scan format is primarily useful for cardiac imaging to avoid interference from the ribs. However, a real-time rectilinear volumetric scan with a wider field-of-view (FOV) close to the transducer could prove more useful for abdominal, breast or vascular imaging. In our previous work, a 94 × 94 Mills cross array operating at 5 MHz was fabricated, and the first real-time rectilinear volumetric images were made using a 2-D array and the Duke real-time 3-D scanner. The FOV for the Mills cross was 30 × 8 × 60 mm. Despite reasonable success with the Mills cross array, the array had limitations of poor off-axis sensitivity and a smaller FOV in one direction. To overcome these limitations, a new rectilinear array containing over 65,500 elements was developed with a periodic geometry to increase the FOV to 30 mm × 30 mm × 60 mm and improve the off-axis sensitivity. Images of tissue-mimicking phantoms and the carotid artery in vivo were obtained. In addition, spectral and color flow Doppler results from a pulsatile flow phantom were obtained. (E-mail: jesse.yen@duke.edu)

Impact of left ventricular outflow tract area on systolic outflow velocity in hypertrophic cardiomyopathy: A real-time three-dimensional echocardiographic study

ObjectivesThe aim of this study was to use real-time three-dimensional echocardiography (3DE) to investigate the quantitative relation between minimal left ventricular (LV) outflow tract area (ALVOT) and maximal LV outflow tract (LVOT) velocity in patients with hypertrophic obstructive cardiomyopathy (HCM). BackgroundIn patients with HCM, LVOT velocity should change inversely with minimal ALVOTunless LVOT obstruction reduces the pumping capacity of the ventricle. MethodsA total of 25 patients with HCM with systolic anterior motion (SAM) of the mitral valve leaflets underwent real-time 3DE. The smallest ALVOTduring systole was measured using anatomically oriented two-dimensional “C-planes” within the pyramidal 3DE volume. Maximal velocity across LVOT was evaluated by two-dimensional Doppler echocardiography (2DE). For comparison with 3DE ALVOT, the SAM-septal distance was determined by 2DE. ResultsReal-time 3DE provided unique information about the dynamic SAM-septal relation during systole, with ALVOTranging from 0.6 to 5.2 cm2(mean: 2.2 ± 1.4 cm2). Maximal velocity (v) correlated inversely with ALVOT(v = 496 ALVOT−0.80, r = −0.95, p < 0.001), but the exponent (−0.80) was significantly different from −1.0 (95% confidence interval: −0.67 to −0.92), indicating a significant impact of small ALVOTon the peak LVOT flow rate. By comparison, the best correlation between velocity and 2DE SAM-septal distance was significantly (p < 0.01) poorer at −0.83, indicating the superiority of 3DE for assessing ALVOT. ConclusionsThree-dimensional echocardiography-measured ALVOTprovides an assessment of HCM geometry that is superior to 2DE methods. These data indicate that the peak LVOT flow rate appears to be significantly decreased by reduced ALVOT. Real-time 3DE is a potentially valuable clinical tool for assessing patients with HCM.

Real-time rectilinear volumetric imaging.

Current real-time volumetric scanners use a 2-D array to scan a pyramidal volume consisting of many sector scans stacked in the elevation direction. This scan format is primarily useful for cardiac imaging to avoid interference from the ribs. However, a real-time rectilinear volumetric scan with a wider field of view close to the transducer could prove more useful for abdominal, breast, or vascular imaging. In previous work, computer simulations of very sparse array transducer designs in a rectilinear volumetric scanner demonstrated that a Mills cross array showed the best overall performance given current system constraints. Consequently, a 94 x 94 Mills cross array including 372 active channels operating at 5 MHz has been developed on a flexible circuit interconnect. In addition, the beam former delay software and scan converter display software of the Duke volumetric scanner were modified to achieve real-time rectilinear volumetric scanning consisting of a 30-mm x 8-mm x 60-mm scan at a rate of 47 volumes/s. Real-time rectilinear volumetric images were obtained of tissue-mimicking phantoms, showing a spatial resolution of 1 to 2 mm. Images of carotid arteries in normal subjects demonstrated tissue penetration to 6 cm.

Activities for Students: The Volume of a Pyramid: Low-Tech and High-Tech Approaches

This lesson came about spontaneously during a geometry unit on volume. I had used the lesson shown here in activity sheet 1, in which students use cubic blocks to rediscover the formulas for volumes of right prisms, that is, V = Bh and V = lwh. This lesson was a simple review for my tenth-grade class, and they completed it easily before the end of the period. With the wooden cubes still on their desks, most of them used the remaining time to build towers and other objects. I noticed that many students piled the cubes into bumpy pyramidal shapes. Because the next day's lesson involved studying the volume of pyramids, I wondered whether these bumpy shapes could be useful for discovering the volume of a real pyramid with smooth sides. Students could compare the volumes of these “pyramids of cubes” with the volumes of corresponding right prisms and perhaps discover the ratio 1/3 to obtain the formula for the volume of a pyramid, V = (1/3)Bh. As it turns out, the ratio of 1/3 does not become evident right away. To my students' delight, we found that using a spreadsheet is an excellent way to investigate this problem. My geometry classes had not used spreadsheets before, and the students enjoyed the experience of using the efficiency of technology to compare hundreds— and even thousands—of shapes with ease.

Real-time three-dimensional echocardiography: an overview.

Conventional echocardiography and its representation of the heart in a two-dimensional format only provide partial information about cardiac function. Real-time three-dimensional echocardiography is a recently developed technique based on the design of an ultrasound transducer with a matrix array that instantaneously acquires the image contained in a pyramidal volume. The simultaneous display of multiple tomographic images allows the anatomically correct examination of any structure contained within the volumetric image. Software and technologies based on high performance computers designed for graphic handling of three-dimensional images permit the rapid mapping of the volumetric image and provide possibilities beyond those of the echograph. Using this methodology, it is possible to simultaneously visualize multiple superimposed planes in an interactive manner. Real-time three-dimensional echocardiography also allows a quantitative assessment of cardiac volumes, ventricular mass, and myocardium with contraction and/or perfusion abnormalities. This technique thus expands the abilities of non-invasive cardiology and may open new doors for the evaluation of cardiac disease.

F79Real‐time three‐dimensional fetal echocardiography

BackgroundFetal echocardiography employs high resolution two‐dimensional ultrasound (2DE) to detect structural heart disease. Three‐dimensional echocardiography (3DE) using reconstruction of a series of 2D images of the fetal heart has been hampered by technical problems. Real‐time 3DE (rt3DE) acquires volume data sets rather than 2D images.MethodThe rt3DE system (Volumetrics, Durham) uses a 2.5‐MHz matrix phased‐array transducer scanning a pyramidal volume. A multipanel screen displays cross‐sectional images of the same volume in real‐time: two perpendicular 2D images that can be freely oriented throughout 3‐D space plus up to three calculated sections not obtainable by 2DE.Resultsrt3DE could visualize the fetal heart satisfactorily. Due to real‐time volumetric scanning gating with the fetal cardiac cycle was not necessary. The image quality with regard to resolution was inferior to current high end 2D machines, but is bound to improve with technology. Volumes can also include color Doppler, but at the cost of low frame rates.ConclusionWith advancing technology volume rather than 2D data acquisition may emerge as a standard in fetal echocardiography. While examining one or two technically and physically optimized 2D views, the entire pyramidal volume surrounding these planes is acquired in real time. The dissociation of rapid data acquisition from its interpretation may be advantageous, enabling ‘virtual scanning’ for different aspects even without the patient present.

Initial clinical experience of real-time three-dimensional echocardiography in patients with ischemic and idiopathic dilated cardiomyopathy

The geometry of the left ventricle in patients with cardiomyopathy is often sub-optimal for 2-dimensional ultrasound when assessing left ventricular (LV) function and localized abnormalities such as a ventricular aneurysm. The aim of this study was to report the initial experience of real-time 3-D echocardiography for evaluating patients with cardiomyopathy. A total of 34 patients were evaluated with the real-time 3D method in the operating room (n = 15) and in the echocardiographic laboratory (n = 19). Thirteen of 28 patients with cardiomyopathy and 6 other subjects with normal LV function were evaluated by both real-time 3-D echocardiography and magnetic resonance imaging (MRI) for obtaining LV volumes and ejection fractions for comparison. There were close relations and agreements for LV volumes (r = 0.98, p <0.0001, mean difference = −15 ± 81 ml) and ejection fractions (r = 0.97, p <0.0001, mean difference = 0.001 ± 0.04) between the real-time 3D method and MRI when 3 cardiomyopathy cases with marked LV dilatation (LV end-diastolic volume >450 ml by MRI) were excluded. In these 3 patients, 3D echocardiography significantly underestimated the LV volumes due to difficulties with imaging the entire LV in a 60° × 60° pyramidal volume. The new real-time 3D echocardiography is feasible in patients with cardiomyopathy and may provide a faster and lower cost alternative to MRI for evaluating cardiac function in patients.

Feasibility of Real-Time 3-Dimensional Treadmill Stress Echocardiography

Rapid acquisition of echocardiographic images is critical for the predictive accuracy of stress echocardiography. Real-time 3-dimensional echocardiography (RT3D) allows review of several standard 2-dimensional images from a single volumetric data set. To assess the feasibility of RT3D for treadmill stress echocardiography, we performed treadmill stress RT3D on 20 volunteers (10 men and 10 women; mean age 32 ± 6 years) with a device that uses a matrix phased-array transducer in a 60-degree pyramidal volume. Images are displayed as 2 steerable, intersecting B-scan sectors with adjustable C-scan planes parallel to the transducer face. At pre-exercise and immediate postexercise assessment, the volumetric data were obtained from apical and parasternal windows, respectively. Left ventricular segments were divided into 16 standard segments according to criteria defined by the American Society of Echocardiography. The use of both volume sets resulted in visualization of 98% of the segments at peak exercise. Even with only an apical volume set, 89% of the segments were adequately visualized. Image optimization and acquisition time at peak exercise was 35 ± 18 seconds from the apical window and 50 ± 28 seconds from the parasternal window. This preliminary study indicates that RT3D treadmill stress echocardiography is feasible and may be an important application of this new 3-dimensional device. (J Am Soc Echocardiogr 1999;12:285-9.)

Real-time, three-dimensional echocardiography: Feasibility of dynamic right ventricular volume measurement with saline contrast

Background The asymmetry and complex shape of the right ventricle have made it difficult to determine right ventricular (RV) volume with 2-dimensional echocardiography. Three-dimensional cardiac imaging improves visualization of cardiac anatomy but is also complex and time consuming. A newly developed volumetric scanning system holds promise of obviating past limitations. Methods Real-time, transthoracic 3-dimensional echocardiographic images of the right ventricle were obtained with a high-speed volumetric ultrasound system that uses a 16:1 parallel processing schema from a 2.5 MHz matrix phased-array scanner to interrogate an entire pyramidal volume in real time. The instrumentation was used to measure RV volume in 8 excised canine hearts; dynamic real-time 3-dimensional images were also obtained from 14 normal subjects. Results Three-dimensional images were obtained in vitro and in vivo during intravenous hand-agitated saline injection to determine RV volumes. The RV volumes by real-time 3-dimensional echocardiography are well correlated with those of drained in vitro (y = 1.26x - 9.92, r = 0.97, P < .0001, standard error of the estimate = 3.26 mL). For human subjects, the end-diastolic and end-systolic RV volumes were calculated by tracing serial cross-sectional, inclined C scans; functional data were validated by comparing the scans with conventional 2-dimensional echocardiographic indexes of left ventricular stroke volume. Conclusions These data indicate that RV volume measurements of excised heart by real-time 3-dimensional echocardiography are accurate and that beat-to-beat RV quantitative measurement applying this imaging method is possible. The new application of real-time 3-dimensional echocardiography presents the opportunity to develop new descriptors of cardiac performance. (Am Heart J 1999;137:958-67.)

Real-time, 3-Dimensional Echocardiography Acquires All Standard 2-Dimensional Images from 2 Volume Sets: A Clinical Demonstration in 45 Patients

To test the hypothesis that real-time, 3-dimensional (3-D) echocardiography can obtain all standard 2-dimensional (2-D) views from acquisition of 2 volume sets, we scanned 45 patients (24 men, 21 women; mean age 49 ± 17 years). This real-time 3-D device (VOLUMETRICS Medical Imaging, Durham, NC) uses a matrix phased array transducer in a 60 degree pyramidal volume. Images are displayed as 2 steerable, intersecting, conventional 2-D image sectors that can be oriented throughout 3-D space. By using this equipment, we were able to obtain 93.3% of standard views from a parasternal volume set and 85.2% of standard views from an apical volume set. The mean scanning time was 91 ± 19 seconds for the parasternal volume set and 86 ± 22 seconds for the apical volume set. We conclude that standard 2-D views can be obtained in the majority of patients by using this method. This equipment has the potential to substantially decrease the imaging time compared with the standard 2-D echocardiography. (J Am Soc Echocardiogr 1999;12:1-6.)

Prenatal Gonadal Steroids Affect Adult Spatial Behavior, CA1 and CA3 Pyramidal Cell Morphology in Rats

The present study assessed whether prenatal androgen and estrogen exposure affected adult spatial learning and hippocampal morphology. Water maze performance, the CA1 and CA3 pyramidal cell field, and the dentate gyrus-granule cell layer (DG-GCL) morphology were assessed at adulthood (70+ days of age) in males, females, androgen-treated (testosterone propionate, TP, or dihydrotestosterone propionate, DHTP) females (2–4 mg/day), estradiol benzoate (EB)-treated females (100 μg/day), and males treated with the antiandrogen flutamide (8 mg/day). Pregnant rats were injected daily (sc) between Embryonic Day 16 and birth; all pups were delivered by cesarean section. Flutamide-treated males were castrated upon delivery, and adult castrates were used to control for activational effects. Steroid-sensitive sex differences were observed in water maze performance in favor of males. Males had larger CA1 and CA3 pyramidal cell field volumes and soma sizes than females, which were feminized with flutamide treatment. TP and EB, but not DHTP, masculinized CA1 pyramidal cell field volume and neuronal soma size; CA3 was masculinized in both TP- and DHTP-treated females, while EB was ineffective. No effects were observed in cell density, number, or DG-GCL volume or due to adult hormone levels. Thus, prenatal androgens and estrogen influence sex differences in adult spatial navigation and exert differential effects on CA1 and CA3 pyramidal cell morphology. Hence, in addition to the previously reported postnatal component, there is also a prenatal component to the critical period in which gonadal steroids organize the neural mechanisms underlying sex differences in adult spatial ability.

Two-dimensional scatter integration method for brachytherapy dose calculations in 3D geometry

In brachytherapy clinical practice, applicator shielding and tissue heterogeneities are usually not explicitly taken into account. None of the existing dose computational methods are able to reconcile accurate dose calculation in complex three-dimensional (3D) geometries with high efficiency and simplicity. We propose a new model that performs two-dimensional integration of the scattered dose component. The model calculates the effective primary dose at the point of interest and estimates the scatter dose as a superposition of the scatter contributions from pyramid-shaped minibeams. The approach generalizes a previous scatter subtraction model designed to calculate the dose for axial points in simple cylindrically symmetric geometry by dividing the scattering volume into spatial regions coaxial with the source-to-measurement point direction. To allow for azimuthal variation of the primary dose, these minibeams were divided into equally spaced azimuthally distributed pyramidal volumes. The model uses precalculated scatter-to-primary ratios (SPRs) for collimated isotropic sources. Effective primary dose, which includes the radiation scattered in the source capsule, is used to achieve independence from the source structure. For realistic models of the HDR and PDR sources, the algorithm agrees with Monte Carlo within 2.5% and for the type 6702 seed within 6%. The 2D scatter integration (2DSI) model has the potential to estimate the dose behind high-density heterogeneities both accurately and efficiently. The algorithm is much faster than Monte Carlo methods and predicts the dose around sources with different -ray energies and differently shaped capsules with high accuracy.

Spatial distribution of stacking faults and microtwins in isolated crystals and textured diamond films

A relationship between the planar defect distribution observed by TEM and the surface topography observed by SEM is verified for both near 〈100〉 and near 〈111〉 textured diamond films. This relationship leads to precise the description of the microstructure by use of pyramidal crystalline volumes which are defined by the homothetical growth of the principal facets constituting the film surface during the synthesis. Depending on the facet type, {111} or {100}, these volumes are respectively filled or free of planar defects. The observations made on textured films also allowed estimation of the crystalline quality of isolated crystals according to their morphology.

In situ approach to realization of three-dimensionally confined structures via substrate encoded size reducing epitaxy on nonplanar patterned substrates

We report the first realization of three-dimensionally confined semiconductor heterostructures via a one-step growth on nonplanar patterned substrate. Truncated pyramidal shaped mesas on GaAs (111)B patterned substrates are employed and a substrate encoded size reducing epitaxical growth process exploited to realize GaAs pinched-off pyramidal volumes of base ∼50 nm and height 13 nm.

A Newly Designed Minigraft to Achieve Angularity and Projection of the Nasal Tip: The Asymmetrical Bipyramidal Graft

A new systematization for onlay tip grafting is described, using a minigraft constructed from either irradiated, glutaraldehyde-processed bovine cartilage or soft-grade silicone blocks. The graft design consists of two pyramidal volumes amputated in the apex and carved with mild concave surfaces. The lateral profile of the graft is asymmetrical with an acute inclination in the front and a slight inclination in the back. The graft height ranges from 1.5 to 3.8 mm. With this type of implant, high tip projection with a natural appearance can be achieved easily. Since 1986, we have performed 39 tip implants (12 cartilage grafts and 27 silicone grafts). Silicone graft fate has been excellent with no complications, whereas cartilage grafts underwent a 25% resorption rate. Thus, the current technique is now solely undertaken with silicone minigrafts. Main indications are primary tip plasty in normal-size noses with poor tip projection, and secondary noses. This technique is not recommended for simultaneous use with primary rhinoplasty. For more than 4 years, this technique has provided consistent results, being highly effective in achieving the objective of increasing tip projection.

Methodology for three-dimensional reconstruction of the left ventricle from transesophageal echocardiograms

A technique is presented for three-dimensional (3-D) reconstruction of the left-ventricular endocardial surface from multiplanar transesophageal echocardiograms, using both commercial software and investigator written Fortran programs for Intel 80286 and 80386 microcomputers. The approach provides quantitative global and regional cardiac performance measures and allows viewing the endocardial surface, at end-diastole and end-systole, from chosen perspectives. Anatomical landmarks are incorporated to aid in orientation. For regional calculation, the surface is divided into equal angular elements with each conceptually connected to the left-ventricular end-diastole centroid, forming a pyramidal volume element. This angular division automatically normalizes for heart size. The fractional change of these elements over the cardiac cycle provides a regional ejection fraction measure which is color-coded on the reconstructed endocardial surface. Composite perspective views, regional ejection fraction histograms and calculations of global end-diastolic, end-systolic, and stroke volumes, are all performed by the method.