Medial Triangle Research Articles

삼각형의 Expansion Mandart Inellipse에 대한 연구

This study was based on the research results conducted as an R&E project for gifted students with financial support from the Korea Foundation for the Advancement of Science and Creativity. This study investigates the Expansion Mandart Inellipse of a triangle, defined in terms of the concepts of the inscribed circle and the circumscribed circle, as opposed to the Mandart Inellipse defined in terms of the inscribed ellipse and circumscribed ellipse of the triangle. Through this study, the following results were obtained: Firstly, the existence and uniqueness of the Expansion Mandart Inellipse of a triangle were established. Secondly, a condition was discovered wherein the area of the inscribed circle of the triangle and the corresponding Expansion Mandart Inellipse are equal. Thirdly, regarding the intersection of the inscribed circle of the triangle and the Expansion Mandart Inellipse corresponding to it, it was found that a triangle with the three intersection points as vertices is similar to the medial triangle of the original triangle, with one of the intersection points being the center of similarity. Research like this, which extend mathematical concepts into more generalized domains, are expected to contribute to the advancement of mathematics.

Another Simple Proof of Heron’s Formula

Summary We give a proof of Heron’s formula using the Pythagorean theorem, via the medial triangle.

Iterated Medial Triangle Subdivision in Surfaces of Constant Curvature

Consider a geodesic triangle on a surface of constant curvature and subdivide it recursively into four triangles by joining the midpoints of its edges. We show the existence of a uniform delta >0 such that, at any step of the subdivision, all the triangle angles lie in the interval (delta ,pi -delta ). Additionally, we exhibit stabilising behaviours for both angles and lengths as this subdivision progresses.

Clinical Significance of Ankle Arthroscopy in the Diagnosis of Type B Ankle Fracture Associated with the Distal Tibiofibular Syndesmosis Injury

Category:Arthroscopy, TraumaIntroduction/Purpose:To investigate clinical significance of ankle arthroscopy in the diagnosis of type B ankle fracture associated with the distal tibiofibular syndesmosis injury.Methods:From February 2014 to December 2016, the authors diagnosed and treated 35 cases of type B ankle fractures. including 23 males and 12 females; with an average age of (43.05±12.480) years.Each patient underwent preoperative assessment: according to the patient’s clinical manifestations and imaging examination, and before the operation and after internal fixation of ankle fracture, the Cotton test and the external rotation test were done in the C arm X-ray, the initial diagnosis whether there is the distal tibiofibular syndesmosis injury.When the Cotton test and the external rotation test was used, Ankle arthroscopy was used to observe and evaluate whether there is the distal tibiofibular syndesmosis injury.For patients with the distal tibiofibular syndesmosis injury, In addition to the internal fixation of the ankle fracture, the TightRope was used to repair the injury. And observation of repair effect by ankle arthroscopy.Results:After internal fixation of ankle fracture, the Cotton test and the external rotation test was performed under the C arm X-ray, there were no the distal tibiofibular syndesmosis injury in 22 patients. Preoperative CT showed 6 cases of combined the distal tibiofibular syndesmosis injury, Preoperative MRI showed 13 cases of combined the distal tibiofibular syndesmosis injury. Ankle arthroscopy confirmed 11 cases of combined the distal tibiofibular syndesmosis injury. The sensitivity of ankle arthroscopy and MRI diagnosis combined with the distal tibiofibular syndesmosis injury was higher than that of CT sensitivity(P<0.05). The sensitivity of ankle arthroscopy for the diagnosis of the distal tibiofibular syndesmosis injury was weaker than that of MRI in the diagnosis of the distal tibiofibular syndesmosis injury (P<0.05). MRI diagnosis of the distal tibiofibular syndesmosis injury can be false positive.Conclusion:Ankle arthroscopy can directly observe the medial triangle ligament of the ankle, the distal tibiofibular syndesmosis injury, which provides the basis for correct diagnosis and treatment of Type B ankle fracture with the distal tibiofibular syndesmosis injury. And it can evaluate the stability of ankle after repairing the distal tibiofibular syndesmosis injury.

MORPHOLOGICAL TRANSFORMATIONS OF TUBULAR STRUCTURES OF THE FETUSES HEPATODUODENAL LIGAMENT

The components of the hepatoduodenal ligament play an important role in the process of digestion. Calculi in the common bile duct are found in 10-15% of individuals suffering from chronic calculous cholecystitis, and obstruction of bile ducts is found in 59,1-67,4% of cases. The objective of the study was to investigate peculiarities of component morphogenesis of the hepatoduodenal ligament during the perinatal period of human ontogenesis, individual and age anatomical variability, spatial-temporal transformations, and anatomical-histological peculiarities of its structures. To achieve the stated purposes the following complex of methods was used: macroscopic – for visual detection of the state of the hepatoduodenal ligament components, vascular injection – to study peculiarities and variants of angioarchitectonics of the arterial components of the hepatoduodenal ligament, statistical – to determine peculiarities of morphological transformations of the components and adjacent structures of the hepatoduodenal ligament at different periods of prenatal and postnatal periods of human ontogenesis. According to the results of the study several accessory triangles of the hepatoduodenal ligament were found and described. The common bile duct, the common hepatic duct, cystic duct, left and right hepatic ducts, hepatic portal vein, common hepatic artery, right gastric artery, hepatic artery proper, right, left and accessory branches of the hepatic artery proper are permanent components of the ligament forming a number of combinations-crossings between themselves. Meanwhile, we have determined certain regularities of the formed pattern including minimum 5 permanent triangles to be distinguished: Calot’s triangle or "superior lateral triangle", "superior medial triangle", "inferior medial triangle", "inferior lateral triangle", "central space of the hepatoduodenal ligament".

The 16-Year Evolution of Proximal Modular Stem Design – Eliminating Failure of Modular Junction

Background: The complexity of hip reconstruction has been and continues to be a perplexing problem with restoring leg length, femoral offset, joint stability and overall hip implant fixation. These were contributing factors that lead to the development of a novel proximal femoral component design “Apex Modular Stem” (Omni, Raynham, MA). The basic stem geometry features a straight stem with a metaphyseal fit and fill cone, a medial triangle and a modular neck junction that allows for version and offset adjustment.In recent years, there has been great concern with the use of modularity in total hip arthroplasty. The goals of this study are (1) to identify complications with the use of a proximal modular design and (2) demonstrated factors that have eliminated those complications.Methods: This is a retrospective study of a single surgeon series (Design A and Design B) of using the same cementless stem and proximal modular neck body (Apex Modular Stem and Omni Mod Hip Stem) from 2000 to 2016 totaling 2,125 stems. 483 stems were the Design A and 1,642 stems, were of the Design B style.Results: Design A, 483 stems were implanted between 2000 and 2004. 31 alignment pins sheared resulting in a revision rate of 6.4%. Design B, 1,642 stems have been implanted between 2004 and 2016 all by the same surgeon, with no failures of the modular junction.Conclusion: All implant devices entail a multitude of risks and benefits. The Apex Modular Stem (Design A), provided excellent fixation, minimal risk of modular junction corrosion, and simple control of anteversion and femoral offset. The limitation was found to be the risk of the alignment pin shearing (6.4%). The pin was enlarged to make it 225% stronger in torsional resistance, and in a subsequent series of over 1,600 femoral stems in a single surgeon series, there were no pin failures over a 12 year duration.

Euler and triangle geometry

There is a very easy way to produce the Euler line, using transformational arguments. Given a triangle ABC, let AʹBʹ'C be the medial triangle, whose vertices are the midpoints of the sides. These two triangles are homothetic: they are similar and corresponding sides are parallel, and the centroid, G, is their centre of similitude. Alternatively, we say that AʹBʹC can be mapped to ABC by means of an enlargement, centre G, with scale factor –2.

The lateral triangle of the groin

The lateral triangle (LT) of the groin is an area that includes the deep inguinal ring (DIR), and the tissues immediately lateral to it. It is vulnerable to develop recurrent indirect inguinal and interstitial hernias. An interstitial hernia is one in which the sac burrows through or between muscular layers. One typically presents as a palpable bulge at the lateral aspect of a prior inguinal incision; and it becomes more evident when the patient does a Valsalva maneuver. A review was done of our personal, single-center, four-year, series of recurrent inguinal hernia repairs. It showed that preference for a new site of recurrent hernia occurred when many open and laparoscopic mesh-repairs failed. Lateral failure following open-mesh repair (OMR) was related to using mesh to plug or cover the defect(s) of a primary or a recurrent hernia. Failure of laparoscopic hernia repair (LHR) typically was due to inadequate coverage lateral to the DIR. In a consecutive series of 3216 inguinal hernias repaired by the authors, 2768 were primary hernias, and 452 were 1X-4X recurrent hernias. Mesh had been used in groups of 28 prior LHR, and 20 prior OMR. The location of recurrences following any of the classical anterior open non-mesh repairs, i.e. Bassini, Halsted, McVay, Shouldice (ONMR), OMR, and LHR is compared. Based on our findings, we conclude that muscular weakness in the LT of the groin, coupled with mesh placed in the medial triangle of the groin, is the major cause of interstitial recurrent inguinal hernias.

Characterizations of the Medial Triangle: 10588

Characterizations of the Medial Triangle: 10588

Juxta-dural ring aneurysmの分類と治療法

Surgical treatment of internal carotid artery aneurysms around the carotid siphon is an art that is described elaborately in this paper. The surgical approach to the aneurysms in this region, is as follows: 1) A fronto-temporal approach with the patient in a 45° semi-sitting position to decrease venous pressure. 2) A Dolenc's approach cutting a part of the dura mater of the superior orbital fissure to facilitate removal of the anterior clinoid process and unroofing of the optic canal. 3) Opening of the medial triangle followed by transection of the optic canal dural sheath. Carotid siphon aneurysms can be divided into 3 groups anatomically: aneurysms of the ophthalmic segment (C2), those of the clinoid segment (C3), and those of the horizontal segment (C4). We present 34 cases of aneurysms arising from the C2 or C2/3 segment, 15 cases arising from the C3 or C3/4 segment, and 11 cases arising from the C4 segment. Anatomic localization of the aneurysms was established preoperatively by angiography and three-dimensional CT imaging. Small aneurysms of the ophthalmic segment projecting inferomedially can be clipped using a contralateral approach via the prechiasmatic root.Aneurysms of the ophthalmic segment projecting superiorly can be clipped following resection of the anterior clinoid process. The clinoid process should be resected intradurally with direct visualization of the aneurysms. Straight side-angled clips are suitable for these aneurysms. Carotid cave aneurysms, which include aneurysms of the ophthalmic segment oriented inferomedially and of the clinoid segment projecting postero-medially, can be clipped using curved fenestrated clips via Dolenc's extradural approach. For accurate clipping, opening of the medial triangle and full mobilization of the IC at the clinoid segment and optic nerve by unroofing the optic canal are required.Aneurysms of the horizontal portion are clipped after full exposure of the artery in the cavernous sinus only when the aneurysms are large and symptomatic. We used the fronto-temporal and Dolenc's approaches and applied fenestrated clips to aneurysms oriented postero-medially and straight or oblique clips to aneurysms projecting antero-laterally. Out of 52 aneurysms that underwent surgical clipping, 46 resulted in good post-operative recovery. There were 3 deaths secondary to complications of vasospasm and 3 cases with postoperative visual loss. We highlight the classification of these aneurysms and the surgical techniques we had employed.

Microsurgical anatomy of the cavernous sinus.

The cavernous sinuses of 50 adult cadavers were examined to investigate the relationships of the blood vessels and cranial nerves, important structures during surgery in this sinus. The first and second divisions of the fifth cranial nerve were embedded in the deep dural layer of the cavernous sinus and were supplied by the two main branches of the intracavernous carotid artery. The meningohypophyseal artery supplied the sixth cranial nerve in Dorello's canal and the third and fourth cranial nerves where they entered the dura. The inferolateral trunk supplied the third, fourth, fifth, and sixth cranial nerves. The size of the meningohypophyseal artery was usually inversely proportional to the size of the inferolateral trunk. The capsular artery did not supply the cranial nerves. The cavernous sinus can be approached through various routes: a) superior, through the anteromedial or medial triangle; b) lateral, through the paramedial, Parkinson's, anterolateral, and lateral triangles; c) inferior, through the posterolateral and posteromedial triangles; and d) from the inferomedial walls. The choice of surgical approach depends mainly on the location of the lesion to be treated.

Combined infratemporal epidural and medial triangle approachによる脳底動脈先端部動脈瘤の手術

Surgical techniques for a combined infratemporal epidural and medial triangle approach to basilar tip aneurysms consists of 1) an orbitozygomatic frontotemporal craniotomy, 2) an infratemporal epidural approach in order to expose the nerve sheathes of the IInd and Ist divisions of the trigeminal nerve and the medial half of the gasserian ganglion, 3) a pterional transsylvian approach for opening the superior wall of the cavernous sinus via the medial triangle and 4) unveiling the cavernous sinus medial to the IInd division of the trigeminal nerve.Seventeen cases of ruptured basilar tip aneurysms which were operated on via this orbitozygomatic infratemporal transcavernous approach were divided into three groups and the clinical features were reviewed. The fact that out of 4 cases in the early-operation group only one case showed good operative result seems to be attributed to the serious original Hunt and Kosnik Grade of the patients. All 3 cases with Hunt and Kosnik Grades I and II in the relatively early-stage operation group (operated on between Day 6 and Day 10) were good postoperatively. The operative result of 6 out of 8 cases with Grade I or II in the delayed-operation group was good. Conclusion: 1. This transcavernous approach seems to be the preferable approach to the basilar tip aneurysm in the early stage, with several advantages such as 1) wide exposure of the operative field, 2) the shortest possible distance with only slight retraction of the temporal tip with its dura mater, and 3) no division of the Sylvian vein and the spheno-parietal sinus running within the temporal dura propria. 2. Clipping of the basilar tip aneurysm being located either in higher or lower position can be performed successfully without retracting the carotid artery and its tributaries.

Homologous Point in the Medial Triangle

Homologous Point in the Medial Triangle

Homologous Point in the Medial Triangle

Homologous Point in the Medial Triangle

The Orthopolar Circle

Definition: ABC is a triangle; A′B′C′ is its medial triangle; L, M, N are the feet of the perpendiculars from A, B, C respectively on a straight line, σ1 σ2, σ3 are three circles having their centres at A′, B′, C′ respectively such that σ1 passes through M and N, σ2 through N and L, and σ3 through L and M Then it is readily seen that the radical axes of the three circles taken in pairs meet in a point W—the radical centre of the circles. Again, since L is a common point of σ2 and σ3, their radical axis is the line through L at right angles to their line of centres B′C′, and hence to BC. Hence the lines through L, M, N at right angles to BC, CA, AB respectively meet at W, which is said to be the orthopole of the line LMN The common radical circle of σ1, σ2, σ3 is called the Orthopolar circle of the line LMN. Let us consider a few applications of the properties of this circle and its centre.

The Modern Geometry of the Triangle

THE principal novelties in this tract are the chapters on the orthopole (with some original propositions by the author) and on orthogonal projection (mostly after Prof. Neuberg). A pretty theorem in the latter is that all equilateral triangles in a given plane project upon another plane into triangles having the same Brocard angle. The other four chapters discuss various kinds of coordinates, the Lemoine and Brocard points, pedal and anti-pedal triangles, the medial triangle, and the Simpson line. No reference is made to the Tucker circles, or to Kiepert's hyperbola; even the Brocard circle is unmentioned, so the tract is deficient, even as a summary of the most important parts of the subject. A rather irritating feature is that the symbol ∞ is used for two entirely different purposes; this might easily have been avoided. Perhaps the figures will be found as useful as anything in the tract, for although they are not particularly good, they are drawn so that the special points are far enough apart, which is not very easy to contrive when a student is drawing figures for himself.