Pyramidal Volume Research Articles

Error analysis in solving prism and pyramid problems

This research is descriptive qualitative research. This study aims to analyze students’ mistake in solving problems of surface area and volume on the prism and pyramid then to expose the causal factors. The subject of this research was 29 students in 9th class of one junior high school in Bandung, that was chosen by purposive sampling technique. Data was collected from students through validated essay tests and interviews. The data was analyzed by descriptive method. The results show that some of students (1) did not understand the problems, (2) could not represent the prism and pyramid in other form, (3) did some error in using formula of surface area and volume of prism and pyramid, (4) did some error in calculations and (5) had misconceptions. The causal factors were students were not accustomed to identify and write what known and asked when solving a mathematical problem, difficulty in reading information, did not understand concept of the prism and pyramid, carelessness in calculation, haste in answering questions, and lack of effort.

A new learning trajectory on the pyramid volume for secondary school

This research aims to design Learning Trajectory (LT) for pyramid volume learning. This LT was designed based on curriculum review on the volume of pyramid in secondary schools and study of learning obstacles based on didactic, ontogenic, and epistemological aspects identified through diagnostic tests, interviews with mathematics teachers, and analysis of lesson plan used by the teacher in learning then analyzed using Didactical Design Research. This study involved 27 8th grade students and one mathematics teacher. The results showed that the concept of Pythagoras and volume of cube with learning media support played an important role in the learning trajectory of the pyramid volume.

Magic Numbers of the Great Pyramid: A Surprising Result

Recently attention has been drawn to the frequently observed fifth power of the golden mean in many disciplines of science and technology. Whereas in a forthcoming contribution the focus will be directed towards Fibonacci number-based helical structures of living as well as inorganic matter, in this short letter the geometry of the Great Pyramid of the ancient Egyptians was investigated once more. The surprising main result is that the ratio of the in-sphere volume of the pyramid and the pyramid volume itself is given by π⋅φ5, where φ = 0.618033987⋅⋅⋅ is nature’s most important number, the golden mean. In this way not only phase transitions from microscopic to cosmic scale are connected with φ5, also ingenious ancient builders have intuitively guessed its magic before.

Validity of maxillary sinus volumetric measurements using the 3D orthogonal cone beam computed tomography images versus direct skull volumetric measurements: An in vitro study

Introduction: the total volume of maxillary sinus is important for maxillofacial reconstruction, plastic surgeries and prosthetic rehabilitation. It is important to diagnose sinus hypoplasia secondary to craniofacial syndromes, sinus obliteration caused by infections or blood dyscrasis. Aim of the study: The aim of this study was to assess the accuracy of CBCT volumetric measurements of maxillary sinus using the geometric rule of pyramid volume based on CBCT linear measurements versus real skull measurements.Materials and methods: fourteen skulls were scanned using Planmeca Promax 3D MID and the maxillary sinus pyramid height, length and width were measured in cm. The volume of 24 sinuses were calculated from pyramid volume (cm3) = 1/3 Height × Length × Width. The CBCT volumes and the reference standard were analyzed for error assessment using Dahelberg error and Relative Dahelberg Error.Results: 4.3- 4.7% was the error obtained from CBCT volumetric measurements using the rule of pyramid volume. 0.9 correlation was detected between the CBCT volume and the reference standard, between the observers and within the same observer.Conclusion: the geometric rule of pyramid volume based on CBCT linear measurements can be used to assess maxillary sinus volume.

Assessing of student’s performance and their math test in Islamic school: a Rasch perspective

This research tries to assess the student’s ability on math. This research involved 159 students at Islamic Junior High School. We evaluated the student’s ability on math based on basic statistics and geometry. The materials created became 40 items mathematics final exam and has been implemented by students on May, 2018. The data were analysed using the Rasch Measurement Tool (RMT). The results indicated are capable of reaching the final exam (+1.30 logit). Further, determining the diagonal line from the side of a beam is the most blank question for students. Instead, determine the value of the equation to calculate the pyramid volume that is most easily achieved by the entire students. The difference to students in mathematics also appeared on our analysis. Another impressive phenomenon is the quality of the math test still needs to be reviewed. Furthermore, there are also students who are not optimally answering math tests. This suggests the instructor to establish the quality of learning on math in the classroom.

Stereological Assessments of Neuronal Pathology in Auditory Cortex in Schizophrenia.

It has long been known that auditory processing is disrupted in schizophrenia. More recently, postmortem studies have provided direct evidence that morphological alterations to neurons in auditory cortex are implicated in the pathophysiology of this illness, confirming previous predictions. Potential neural substrates for auditory impairment and gray matter loss in auditory cortex in schizophrenia have been identified, described, and are the focus of this review article. Pyramidal cell somal volume is reduced in auditory cortex, as are dendritic spine density and number in schizophrenia. Pyramidal cells are not lost in this region in schizophrenia, indicating that dendritic spine reductions reflect fewer spines per pyramidal cell, consistent with the reduced neuropil hypothesis of schizophrenia. Stereological methods have aided in the proper collection, reporting and interpretation of this data. Mechanistic studies exploring relationships between genetic risk for schizophrenia and altered dendrite morphology represent an important avenue for future research in order to further elucidate cellular pathology in auditory cortex in schizophrenia.

Modular Classification of Endoscopic Endonasal Transsphenoidal Approaches to Sellar Region: Anatomic Quantitative Study

Endoscopic visualization does not necessarily correspond to an adequate working space. The need for balancing invasiveness and adequacy of sellar tumor exposure has recently led to the description of multiple endoscopic endonasal transsphenoidal approaches. Comparative anatomic data on these variants are lacking. We sought to quantitatively compare endoscopic endonasal transsphenoidal approaches to the sella and parasellar region, using the concept of "surgical pyramid." Four endoscopic transsphenoidal approaches were performed in 10 injected specimens: 1) hemisphenoidotomy; 2) transrostral; 3) extended transrostral (with superior turbinectomy); and 4) extended transrostral with posterior ethmoidectomy. ApproachViewer software (part of GTx-Eyes II, University Health Network, Toronto, Canada) with a dedicated navigation system was used to quantify the surgical pyramid volume, as well as exposure of sellar and parasellar areas. Statistical analyses were performed with Friedman's tests and Nemenyi's procedure. Hemisphenoidotomy provided limited exposure of the sellar area and a small working volume. Atransrostral approach was necessary to expose the entire sella. Exposure of lateral parasellar areas required superior turbinectomy or posterior ethmoidectomy. The differences between each of the modules was statistically significant. The present study validates, from an anatomic point of view, a modular classification of endoscopic endonasal transsphenoidal approaches to the sellar region.

Introducing a simple method of maxillary sinus volume assessment based on linear dimensions

Measuring sinus volume in a general practice clinic is a complex and time-consuming procedure, requiring experience in the use of radiological methods In the presented research, the automatically estimated maxillary sinus volume was compared with maxillary sinus volume assessed with mathematical formulas used to calculate the volume of spheres and pyramids. The starting point for the statistical analysis were specific measurements of the sinuses. We wanted to discover which geometric shape has the volume that is nearest to the automatically estimated volume.The study was performed using samples of CT scans of pediatric patients age 1–17. The dimensions (maximal width, maximal height, maximal length) were used for manual calculations. For the automatic volume calculation, the CT Image Segmentation algorithm (Syngo Via for Oncology, Siemens) was used. Pearson’s correlation coefficient was applied to analyse the interrelationship between automatically and manually calculated volume of maxillary sinus. It was statistically established that the “sphere”, “pyramid” and “mean” manually calculated maxillary sinus volume were accurate and strongly correlated with the automatically estimated maxillary sinus volume. The volume of the sphere corresponds better with the automatic measurements than the volume of the pyramid. The variations are significant and they were made reliable with the application of a statistical test. It is quick and easy to calculate the maxillary sinus volume based on its linear dimensions instead of applying advanced software. The manual method for maxillary sinus volume calculation requires three linear measurements of the sinus (length, width, and height) and can be recommended if the automatically estimated volume cannot be obtained.

각뿔의 부피 구하기에 대한 수학사적 고찰

The effort to find the volume of pyramids has been done by mathematicians for a long time, and many trial-and-error calculations and proofs give various perspectives and educational material. In the early days, finding the volume of pyramids was mainly studied by calculating the volume of triangular pyramids or quadrangular pyramids by cutting and the relationship between pyramids. Thereafter, methods based on infinite, infinitesimal, limit, etc. appeared, but the research topic was still about them. The purpose of this study is to examine the four themes appearing the mathematics history in terms of methodology, and to think about its implications from the viewpoint of improving the professionalism of the teachers.

Stereological investigation of the CA1 pyramidal cell layer in untreated and lithium-treated 3xTg-AD and wild-type mice

Pyramidal neuron loss in the hippocampal CA1 region is a very early hallmark of Alzheimer disease (AD). Lithium might be a therapeutic strategy for AD due to its neuroprotective and neurotrophic properties. This study used modern stereological techniques to investigate possible CA1 pyramidal neuron loss in 11-month-old triple transgenic AD (3xTg-AD) mice, and also the effects of therapeutic and subtherapeutic lithium doses on the number and density of CA1 pyramidal neurons and volume of CA1 pyramidal layer in 3xTg-AD and wild-type mice treated from 3 to 11 months of age. 3xTg-AD mice displayed CA1 pyramidal layer atrophy that is likely due to reduced neuronal volume because of the absence of neuronal loss. Both lithium treatments of 3xTg-AD mice, which already expressed AD-like pathology, had no effect on CA1 atrophy. However, lithium treatment of wild-type mice, at low (subtherapeutic) doses, induced a significant increase in total CA1 pyramidal neuron number that led to a significant increase in total CA1 pyramidal layer volume. The lithium-induced increase in CA1 neuron number is highly consistent with previous evidence that adult neurogenesis can be exogenously induced in the CA1 pyramidal layer with impact on total CA1 neuron number, thus raising the possibility of the chronic use of low-dose lithium as a strategy to help compensate for neuronal loss in CA1 and perhaps other typically non-neurogenic brain regions in various neurological diseases. With regard to AD, low-dose lithium intervention must be initiated as early as possible in the course of neuropathology for beneficial effects to occur.

Rhinoplastie standard de réduction

Most patients who consult a surgeon for rhinoplasty do not want a radical change in their nose. They seek a reduction in the volume of the nasal pyramid and correction of a precise element that they judge to be ungainly--most often an osteocartilaginous hump. The procedure that we qualify as "standard" will eliminate the osteocartilaginous hump, decrease the dimensions of the septum and reduce the size of the alar crus of the alar cartilage. Although the required technical maneuvers are simple, their sequence must be coherent with a few basic rules that are simple but rarely explained in order to avoid defects linked to excessive, or on the contrary, insufficient corrections.

Pyramidal neurons of the prefrontal cortex in post-stroke, vascular and other ageing-related dementias.

Dementia associated with cerebrovascular disease is common. It has been reported that ∼30% of elderly patients who survive stroke develop delayed dementia (post-stroke dementia), with most cases being diagnosed as vascular dementia. The pathological substrates associated with post-stroke or vascular dementia are poorly understood, particularly those associated with executive dysfunction. Three separate yet interconnecting circuits control executive function within the frontal lobe involving the dorsolateral prefrontal cortex, anterior cingulate cortex and the orbitofrontal cortex. We used stereological methods, along with immunohistological and related cell morphometric analysis, to examine densities and volumes of pyramidal neurons of the dorsolateral prefrontal cortex, anterior cingulate cortex and orbitofrontal cortex in the frontal lobe from a total of 90 elderly subjects (age range 71-98 years). Post-mortem brain tissues from post-stroke dementia and post-stroke patients with no dementia were derived from our prospective Cognitive Function After Stroke study. We also examined, in parallel, samples from ageing controls and similar age subjects pathologically diagnosed with Alzheimer's disease, mixed Alzheimer's disease and vascular dementia, and vascular dementia. We found pyramidal cell volumes in layers III and V in the dorsolateral prefrontal cortex of post-stroke and vascular dementia and, of mixed and Alzheimer's disease subjects to be reduced by 30-40% compared to post-stroke patients with no dementia and controls. There were no significant changes in neuronal volumes in either the anterior cingulate or orbitofrontal cortices. Remarkably, pyramidal neurons within the orbitofrontal cortex were also found to be smaller in size when compared to those in the other two neocortical regions. To relate the cell changes to cognitive function, we noted significant correlations between neuronal volumes and total CAMCOG, orientation and memory scores and clinical dementia ratings. Total estimated neuronal densities were not significantly changed between patients with post-stroke dementia and post-stroke patients with no dementia groups or ageing controls in any of the three frontal regions. In further morphometric analysis of the dorsolateral prefrontal cortex, we showed that neither diffuse cerebral atrophy nor neocortical thickness explained the selective neuronal volume effects. We also noted that neurofilament protein SMI31 immunoreactivity was increased in post-stroke and vascular dementia compared with post-stroke patients with no dementia and correlated with decreased neuronal volumes in subjects with post-stroke dementia and vascular dementia. Our findings suggest selective regional pyramidal cell atrophy in the dorsolateral prefrontal cortex-rather than neuronal density changes per se-are associated with dementia and executive dysfunction in post-stroke dementia and vascular dementia. The changes in dorsolateral prefrontal cortex pyramidal cells were not associated with neurofibrillary pathology suggesting there is a vascular basis for the observed highly selective neuronal atrophy.

Antagomirs targeting microRNA-134 increase hippocampal pyramidal neuron spine volume in vivo and protect against pilocarpine-induced status epilepticus.

Emerging data support roles for microRNA (miRNA) in the pathogenesis of various neurologic disorders including epilepsy. MicroRNA-134 (miR-134) is enriched in dendrites of hippocampal neurons, where it negatively regulates spine volume. Recent work identified upregulation of miR-134 in experimental and human epilepsy. Targeting miR-134 in vivo using antagomirs had potent anticonvulsant effects against kainic acid-induced seizures and was associated with a reduction in dendritic spine number. In the present study, we measured dendritic spine volume in mice injected with miR-134-targeting antagomirs and tested effects of the antagomirs on status epilepticus triggered by the cholinergic agonist pilocarpine. Morphometric analysis of over 6,400 dendritic spines in Lucifer yellow-injected CA3 pyramidal neurons revealed increased spine volume in mice given antagomirs compared to controls that received a scrambled sequence. Treatment of mice with miR-134 antagomirs did not alter performance in a behavioral test (novel object location). Status epilepticus induced by pilocarpine was associated with upregulation of miR-134 within the hippocampus of mice. Pretreatment of mice with miR-134 antagomirs reduced the proportion of animals that developed status epilepticus following pilocarpine and increased animal survival. In antagomir-treated mice that did develop status epilepticus, seizure onset was delayed and total seizure power was reduced. These studies provide in vivo evidence that miR-134 regulates spine volume in the hippocampus and validation of the seizure-suppressive effects of miR-134 antagomirs in a model with a different triggering mechanism, indicating broad conservation of anticonvulsant effects.

Neuron Volumes in Hippocampal Subfields in Delayed Poststroke and Aging-Related Dementias

Hippocampal atrophy is widely recognized in Alzheimer disease (AD). Whether neurons within hippocampal subfields are similarly affected in other aging-related dementias, particularly after stroke, remains an open question. We investigated hippocampal CA3 and CA4 pyramidal neuron volumes and densities using 3-dimensional stereologic techniques in postmortem samples from a total of 67 subjects: poststoke demented (PSD; n = 11), nondemented stroke survivors (PSND) and PSD patients from the CogFAST (Cognitive Function After Stroke) cohort (n = 13), elderly controls (n = 12), and subjects diagnosed as having vascular dementia (n = 11), AD (n = 10), and mixed AD and vascular dementia (n = 10). We found that CA3 and CA4 neuron volumes were reduced in PSD samples compared with those in PSND samples. The CA3 and CA4 neuron volumes were positively correlated with poststroke global cognitive function but were not associated with the burden of AD pathology. There were no differences in total neuron densities in either subfield in any of the groups studied. Our results indicate that selective reductions in CA4 and to a lesser extent CA3 neuron volumes may be related to post stroke cognitive impairment and aging-related dementias. These data suggest that CA4 neurons are vulnerable to disease processes and support our previous finding that a reduction in hippocampal neuron volume predominantly reflects vascular mechanisms as contributing to dementia after stroke.

Young Investigator Award session - Basic Science: 11/12/2013, 12:45-13:45 * Location: Manisa

Young Investigator Award session - Basic Science: 11/12/2013, 12:45-13:45 * Location: Manisa

Improved three-dimensional localization algorithm based on volume-test scan for wireless sensor networks

Aiming at the ‘in-to-out error’ and ‘out-to-in error’ caused by boundary effect in approximate point-in-triangulation test three dimension (APIT-3D) algorithm for wireless sensor networks (WSNs), which leads a bad location precession, this paper proposes an improved APIT-3D scheme based on volume-test, named volume test approximate point-in-triangulation test three-dimension (VT-APIT-3D) algorithm. By adding the advantage of comparing to the volume of the triangular pyramids in process of point-in-triangulation test (PIT) during APIT-3D, the unknown node can be accurately determined whether it is in the testing triangular pyramid or not. This method can remove the probability of the ‘in-to-out error’ and ‘out-to-in error’ in APIT-3D. Finally, the simulation results confirm that the proposed scheme has great advantage in aspects of localization accuracy in comparison with original APIT-3D scheme and relational scheme respectively.

Decreased pyramidal neuron size in Brodmann areas 44 and 45 in patients with autism

Autism is a neurodevelopmental disorder characterized by deficits in social interaction and social communication, as well as by the presence of repetitive and stereotyped behaviors and interests. Brodmann areas 44 and 45 in the inferior frontal cortex, which are involved in language processing, imitation function, and sociality processing networks, have been implicated in this complex disorder. Using a stereologic approach, this study aims to explore the presence of neuropathological differences in areas 44 and 45 in patients with autism compared to age- and hemisphere-matched controls. Based on previous evidence in the fusiform gyrus, we expected to find a decrease in the number and size of pyramidal neurons as well as an increase in volume of layers III, V, and VI in patients with autism. We observed significantly smaller pyramidal neurons in patients with autism compared to controls, although there was no difference in pyramidal neuron numbers or layer volumes. The reduced pyramidal neuron size suggests that a certain degree of dysfunction of areas 44 and 45 plays a role in the pathology of autism. Our results also support previous studies that have shown specific cellular neuropathology in autism with regionally specific reduction in neuron size, and provide further evidence for the possible involvement of the mirror neuron system, as well as impairment of neuronal networks relevant to communication and social behaviors, in this disorder.

Tetrahedral silicon balloon for endoscopic skull base reconstruction

INTRODUCTION Advances in transnasal endoscopic approaches and the development of instrumentation and imaging technology have turned endoscopic endonasal surgery into the mainstay for treating inflammatory diseases and neoplasms involving the paranasal sinuses and skull base. The expanded endonasal approach (EEA) and its modifications provide access to the anterior skull base, planum, sphenoid, sella, clivus, cervical spine, and infratemporal fossa via the two nostrils. This approach enables endoscopic extradural and intradural tumor resection and skull base reconstruction in a single procedure. Technical advances in reconstruction methods and the development of vascularized locoregional flaps have improved our ability to seal the cranio-basal diaphragm after tumor extirpation. Use of a nasal septal flap (NSF) has reduced the rate of complications and allowed increasing numbers of patients with skull base neoplasms to undergo curative surgical resections by means of minimally invasive techniques. One drawback of this technique is the difficulty of stabilizing the multilayered reconstruction in place after its application. Currently, a 12-French Foley catheter latex balloon is used to support the multilayered reconstruction during the 1st week after surgery. The main disadvantages of this method are: 1) the balloon surface is spherical, thus providing inadequate support to the flat surfaces of the skull base; 2) decrease in the balloon’s volume due to frequent leaks may impair the support of the flap; 3) the latex balloon is weak and frequently bursts due to exposed bone chips; 4) inability to use this balloon in patients who are allergic to latex; and 5) it is inconvenient for patients because it interferes with their nasal breathing. An alternative support for skull base reconstruction that is free of these limitations is needed. In this report we describe a novel anatomically shaped graft stabilizer for endonasal skull base reconstruction.

Three-dimensional Echocardiography in Valvular Heart Disease

Recent technologic advances in 3-dimensional (3D) echocardiography, using parallel processing to scan a pyramidal volume, have allowed for a superior ability to describe valvular anatomy using both transthoracic and transesophageal echocardiography. Although still in evolution and at an early phase of adaptation with respect to its clinical application, 3D echocardiography has emerged as an important clinical tool in the assessment of valvular heart disease. Three-dimensional echocardiography provides unique perspectives of valvular structures by presenting "en face" views of valvular structures, allowing for a better understanding of the topographical aspects of pathology, and a refined definition of the spatial relationships of intracardiac structures. Three-dimensional echocardiography makes available indices not described by 2D echocardiography and has been demonstrated to be superior to 2D echocardiography in a variety of valvular disease scenarios. The information gained from 3D echocardiography has especially made an impact in guiding clinical decisions in the evaluation of mitral valve (MV) disease. The decision of early surgery in degenerative MV disease is based on the suitability of repair, and the suitability of repair is generally based on echocardiography. The superior understanding of MV anatomy afforded by 3D echocardiography has been shown to be quite valuable in this setting. This review will describe the contemporary use of 3D echocardiography in the assessment of valvular heart disease, including MV, aortic, tricuspid, and prosthetic valve abnormalities. This article illustrates how 3D echocardiography can complement current echocardiography techniques in the management of valvular heart disease.

Hippocampal Neuronal Atrophy and Cognitive Function in Delayed Poststroke and Aging-Related Dementias

We have previously shown delayed poststroke dementia in elderly (≥75 years old) stroke survivors is associated with medial temporal lobe atrophy; however, the basis of the structural and functional changes is unknown. Using 3-dimensional stereological methods, we quantified hippocampal pyramidal neuronal volumes and densities in a total of 95 postmortem samples from demented and nondemented poststroke survivors within our prospective Cognitive Function after Stroke study and subjects pathologically diagnosed with vascular dementia, Alzheimer disease, and mixed Alzheimer disease and vascular dementia syndrome. Hippocampal CA1 but not CA2 subfield neuron density was affected in poststroke, Alzheimer disease, vascular dementia, and mixed dementia groups relative to control subjects (P<0.05). Neuronal volume was reduced in the poststroke dementia relative to poststroke nondemented group in both CA1 and CA2, although there were no apparent differences in neuronal density. Poststroke nondemented neuronal volumes were similar to control subjects but greater than in all dementias (P<0.05). Neuronal volumes positively correlated with global cognitive function and memory function in both CA1 and CA2 in poststroke subjects (P<0.01). Degrees of neuronal atrophy and loss were similar in the poststroke dementia and vascular dementia groups. However, in the entorhinal cortex layer V, neuronal volumes were only impaired in the mixed and Alzheimer disease groups (P<0.05). Our results suggest hippocampal neuronal atrophy is an important substrate for dementia in both cerebrovascular and neurodegenerative disease.