Sesamoid bones in horses are small, nodular bones embedded within tendons, typically located in areas subjected to high mechanical stress. In equines, the primary sesamoid bones of interest are the proximal sesamoid bones, found at the back of the fetlock joint, and the distal sesamoid bone, commonly known as the navicular bone, located within the hoof. These bones function to protect tendons, reduce friction, and enhance the mechanical advantage of tendons during locomotion. The health and integrity of sesamoid bones are essential for normal limb function, and they are often examined in cases of lameness or injury. This page compiles peer-reviewed research studies and scholarly articles that explore the anatomy, physiological role, and pathologies associated with sesamoid bones in horses.
Swerczek TW, Donahue JM, Hunt RJ.Scedosporium prolificans was associated with arthritis and degenerative osteomyelitis in a 6-year-old Thoroughbred racehorse. The horse was suspected to have an inflammatory lesion of the interosseous tendon, but treatment had resulted in only a minimal response. Shortly after diagnostic arthrocentesis of the left metacarpophalangeal joint was performed, the joint became severely swollen, and radiography of the area revealed lysis of the distal end of the third metacarpal bone, the proximal sesamoid bones, and the proximal end of the proximal phalanx. The horse did not respond to treatment and...
Cornelissen BP, van Weeren PR, Ederveen AG, Barneveld A.Bone mineral density (BMD) and cross-sectional area (CSA), measured using peripheral quantitative computed tomography, were determined in the left third metacarpal bone (MCIII) and left medial proximal sesamoid bone (psb) in 3 differently exercised groups of foals. Group(box) (n = 14) was confined to a box stall from birth to age 5 months, Group(training) (n = 14) was kept in similar box stalls but additionally given a daily exercise programme consisting of an increasing number of gallop sprints and Group(pasture) (n = 15) remained at pasture. At 5 months of age, 8 foals from each group were r...
Woodie JB, Ruggles AJ, Litsky AS.To evaluate 2 methods of midbody proximal sesamoid bone repair--fixation by a screw placed in lag fashion and circumferential wire fixation--by comparing yield load and the adjacent soft-tissue strain during monotonic loading. Methods: Experimental study. Methods: 10 paired equine cadaver forelimbs from race-trained horses. Methods: A transverse midbody osteotomy of the medial proximal sesamoid bone (PSB) was created. The osteotomy was repaired with a 4.5-mm cortex bone screw placed in lag fashion or a 1.25-mm circumferential wire. The limbs were instrumented with differential variable relucta...
Southwood LL, McIlwraith CW.To determine the outcome of horses with basal fractures of the proximal sesamoid bone from which a fracture fragment involving a portion of the base of the bone was removed arthroscopically and to determine whether fragment size was associated with outcome. Methods: Retrospective study. Methods: 26 horses. Methods: Dorsopalmar and axial-abaxial lengths of the fracture fragment were measured on the dorsopalmar and mediolateral radiographic views, respectively, and percentage of the base of the sesamoid bone involved was estimated. Fractures were classified as grade 1 ( 25% but < 100% of the ...
Frean SP, Gettinby G, May SA, Lees P.Proteoglycan (PG) release, in response to recombinant human interleukin-1beta (rh-IL-1beta), was measured in cartilage explants obtained from the equine distal sesamoid bone (navicular bone). Fibrocartilage from the surface of the navicular bone apposing the deep digital flexor tendon and hyaline cartilage from the surface of the navicular bone articulating with the middle phalanx were labelled with 35SO4. Hyaline cartilage from the distal metacarpus was used as a control tissue. Following radiolabel incorporation, the three cartilage types were treated with rh-IL-1beta (100 U/mL) in the prese...
Chiba S, Kanematsu S, Murakami K, Satoh A, Asahina M, Numakunai S, Goryo M, Ohshima K, Okada K.Serum parathyroid hormone (PTH) and calcitonin (CT) levels in fractured racehorses were measured by radioimmunoassay. Racehorses with fracture of large bone such as the radius, third metacarpus, third carpus, digital bone or tibia, showed normal PTH level and elevated CT level in the serum. Serum PTH level was slightly higher in racehorses with sesamoid bone fracture compared to that of healthy racehorses, but not statistically significant. Moreover, serum CT level of racehorses with sesamoid bone fracture was significantly higher than that of healthy racehorses. Racehorses with sesamoid bone ...
Brama PA, Tekoppele JM, Bank RA, Karssenberg D, Barneveld A, van Weeren PR.The aim of this study was to evaluate topographical differences in the biochemical composition of the extracellular matrix of articular cartilage of the normal equine fetlock joint. Water content, DNA content, glycosaminoglycan (GAG) content and a number of characteristics of the collagen network (total collagen content, levels of hydroxylysine- (Hyl) and the crosslink hydroxylysylpyridinoline, (HP) of articular cartilage in the proximal 1st phalanx (P1), distal 3rd metacarpal bone (MC), and proximal sesamoid bones (PSB) were determined in the left and right fetlock joint of 6 mature horses (a...
Ehrlich PJ, Dohoo IR, O'Callaghan MW.To document anatomic patterns of scintigraphic uptake and related orthopedic disease associated with racing activity in Standardbred horses. Methods: Retrospective study. Methods: 64 Standardbred horses evaluated for lameness. Methods: Medical records at the time of discharge were reviewed, and information regarding signalment; history; results of lameness examination, scintigraphy, and radiography; diagnosis; and treatment were obtained. Results: 274 areas of increased radiopharmaceutical uptake were identified. Scintigrams of 218 limbs (106 forelimbs, 112 hind limbs) were available for revie...
Wilson DA, Keegan KG, Carson WL.This study compared the mechanical properties of the normal intact suspensory apparatus and two methods of fixation for repair of transverse, midbody fractures of the proximal sesamoid bones of adult horses: transfixation wiring (TW) and screws placed in lag fashion (LS). Methods: An in vitro, paired study using equine cadaver limbs mounted in a loading apparatus was used to test the mechanical properties of TW and LS. Methods: Seventeen paired (13 repaired, 4 normal) equine cadaver limbs consisting of the suspensory apparatus third metacarpal bone, and first and second phalanges. Methods: The...
Bouré L, Marcoux M, Laverty S, Lepage OM.To develop a technique for arthroscopic excision of apical sesamoid fracture fragments using electrocautery probes. Methods: A total of 18 Standardbred horses. Methods: Arthroscopic removal of apical sesamoid fracture fragments using both hook and loop electrocautery probes was performed on 18 Standardbred horses. The fracture fragments were approached using either an ipsilateral (3) or contralateral (15) arthroscopic triangulation technique. Distension of the metacarpo- (metatarso)-phalangeal joints was achieved using a 1.5% glycine solution. Under arthroscopic guidance, both the suspensory a...
Woodie JB, Ruggles AJ, Bertone AL, Hardy J, Schneider RK.To determine whether fracture fragment dimensions, suspensory ligament damage, and racing status at the time of injury were associated with outcome in Standardbred horses with apical fracture of the proximal sesamoid bone. Methods: Retrospective study. Methods: 43 Standardbred racehorses. Methods: Medical records, racing records, and radiographs were reviewed, and ultrasonographic findings were scored. Measurements of the fractured portion of the proximal sesamoid bone were made. Results: Seventy-four percent (32/43) of horses were pacers, and 26% (11/43) were trotters. Statistical differences...
Harkins JD, Mundy GD, Woods WE, Lehner A, Karpiesiuk W, Rees WA, Dirikolu L, Bass S, Carter WG, Boyles J, Tobin T.Lidocaine is a local anaesthetic agent that is widely used in equine medicine. It is also an Association of Racing Commissioners International (ARCI) Class 2 foreign substance that may cause regulators to impose substantial penalties if residues are identified in post race urine samples. Therefore, an analytical/pharmacological database was developed for this drug. Using our abaxial sesamoid local anaesthetic model, the highest no-effect dose (HNED) for the local anaesthetic effect of lidocaine was determined to be 4 mg. Using enzyme-linked immunosorbent assay (ELISA) screening, administration...
Cornelissen BP, Buma P, Rijkenhuizen AB, Barneveld A.To localize and determine relative frequency of occurrence of calcitonin gene-related peptide (CGRP) and substance P (SP) fibers in the proximal sesamoid bones (PSB) and adjacent structures in sound horses. Methods: 4 foals and 3 adult horses. Methods: Medial PSB and adjacent ligaments of both forelimbs were collected, flushed, and fixed in buffered 4% formalin. The left PSB were cut into 5 longitudinal, sagittally oriented slabs, and the right PSB were cut into 5 transverse slabs. After decalcification in EDTA, slices were transferred to a 30% sucrose solution, deep frozen, sectioned (80 micr...
Southwood LL, Trotter GW, McIlwraith CW.To determine the outcome of horses after arthroscopic removal of abaxial fracture fragments of the proximal sesamoid bone and association of fracture grade with outcome. Methods: Retrospective study. Methods: 47 horses. Methods: Information obtained from dorsopalmar and dorsoplantar radiographic views of metacarpophalangeal and metatarsophalangeal joints was used to classify fractures as grade 1 ( 25 mm long) and type 1 (abaxial) and type 2 (apical-abaxial). Outcome was determined by whether the horse returned to its intended use, raced in the same class or higher (racehorses), or performed sa...
Cornelissen BP.Sesamoiditis is characterized clinically by repeated lameness and radiologically by changes in the proximal sesamoid bones. This thesis, which was defended in June 1997, investigated two characteristics of sesamoiditis, namely the arterial blood supply and the innervation of the proximal sesamoid bones, in order to gain more insight into the etiopathogenesis of sesamoiditis. Experiments with patient material showed that the proximal sesamoid bones have an enormous arterial reserve, due in part to the formation of an arterial shift. Moreover, the sesamoid bones have their own sensory innervatio...
Chan CC, Munroe GA.Chronic septic tenosynovitis with concurrent, associated focal osteomyelitis of the lateral proximal sesamoid bone was diagnosed in a seven-year-old thoroughbred gelding. Surgical management of this case consisted of open annular ligament desmotomy and curettage of the affected sesamoid. Following lavage of the digital sheath the incisional wound was closed but a 2 cm gap was left distally to allow for postoperative open drainage. The distal limb was bandaged and the horse treated with antibiotics and non-steroidal anti-inflammatories. Sepsis resolved and the horse made a gradual return to ful...
Martinelli MJ, Kuriashkin IV, Carragher BO, Clarkson RB, Baker GJ.Magnetic resonance imaging was used to examine the equine metacarpophalangeal joint. Thirty-two saggital images generated by partial volume imaging were transferred to a computer for three-dimensional reconstruction and analysis. All the tissues constituting the metacarpophalangeal joint were readily identified. The most significant increase finding regarded the soft tissues on the palmar aspect of the metacarpophalangeal joint and their interactions with the proximal sesamoid bones. The equine metacarpophalangeal joint has not previously been evaluated using 3-dimensional imaging software.
Stiglhuber A, Breit S, König HE.The equine fetlock joint cavity shows ten pouches. The dorsal recess, which is oriented to the proximal side, is separated from those three pouches, which show to the distal direction, by several capsular folds. These folds are documented by means of sagittal sections through the fetlock joint. A medial/lateral recess is covered by the deep part of the collateral ligament of the fetlock joint. The collateral ligaments as well as the sesamoidean collateral ligaments are closely connected with the joint capsule, from which two capsular folds are separated. Between the part of the sesamoidean col...
Denoix JM, Busoni V, Olalla MJ.Normal and abnormal ultrasonographic images are presented of the proximal scutum (proximal sesamoid bones and palmar ligament) in the horse. Comparison between anatomical sections, MRI (magnetic resonance imaging) and ultrasound scans enabled the authors to establish the normal ultrasonographic anatomy of the palmar fetlock. Nine cases of proximal scutum injuries were identified ultrasonographically, of which 4 are illustrated. On normal limbs, the facies flexoria of the proximal sesamoid bones appeared as a thin and regular hyperechoic line and the palmar ligament was regularly echogenic. Les...
Cornelissen BP, Rijkenhuizen AB, Barneveld A.The sesamoidean nerve branches from the palmar nerve and runs towards the proximal sesamoid bone. To study the structures innervated by this nerve, a technique for blocking it was developed. The effect of this nerve block was determined in ponies with an induced lameness located in the lateral proximal sesamoid bone (5 ponies) or in the distal part of the lateral branch of the suspensory ligament (5 ponies), and in 10 horses with clinical sesamoidosis. A lameness provoked by the implantation of an expansion plug in the proximal sesamoid bone could, to a large extent, be anaesthetized by a sesa...
Lillich JD, Ruggles AJ, Gabel AA, Bramlage LR, Schneider RK.Medical records of 17 horses in which a distal sesamoid bone fracture was diagnosed between 1982 and 1992 were reviewed. There were 8 Standardbreds, 6 Quarter Horses, 2 Thoroughbreds, and 1 Arabian. Mean age was 4.7 years. A forelimb was affected in 15 horses, and a hind limb was affected in 2. All horses were lame, and most were grade III/V lame at the trot. In all horses, the diagnosis was confirmed by means of radiography. Five horses were treated with stall rest alone; 5 underwent neurectomy; 4 were treated with stall rest and corrective shoeing; and 1 was treated with stall rest and exter...
Dyson SJ, Denoix JM.The palmar (plantar) aspect of the pastern is an anatomically complex area and an understanding of this is a prerequisite for accurate diagnosis of injuries in this area. The gross and normal ultrasonographic anatomy are described, and injuries of the superficial and deep digital flexor tendons and the digital flexor tendon sheath, the distal sesamoidean ligaments, and the palmar ligaments of the proximal interphalangeal joint are discussed.
Dyson SJ, Arthur RM, Palmer SE, Richardson D.The gross and functional anatomy of the suspensory ligament (SL) and its ultrasonographic variability are described. Injuries of the suspensory apparatus are divided into lesions confined to the proximal one third of the metacarpus or metatarsus (proximal suspensory desmitis and avulsion fractures), lesions of the body, and branch lesions. Complete breakdown injuries are also discussed. In view of the close association of the SL, the second, third, and fourth metacarpal or metatarsal bones, and the proximal sesamoid bones, associated bony lesions are also considered.
Trumble TN, Arnoczky SP, Stick JA, Stickle RL.The blood supply to the proximal sesamoid bone of the equine forelimb was examined in 18 cadaver limbs from adult horses, using x-ray computed tomography and a tissue-clearing (Spalteholz) technique. Results of the study indicated that the proximal sesamoid bones were supplied by multiple branches of the medial and lateral palmar digital arteries, which entered the proximal half of the bones on their non-articular, abaxial surface. After entering the bone, the vessels traverse dorsally, axially, and distally, arborizing into several smaller branches that appear to supply the entire bone. The m...
Honnas CM, Crabill MR, Mackie JT, Yarbrough TB, Schumacher J.Six horses with septic navicular bursitis or distal sesamoid osteomyelitis were treated by means of surgical debridement and lavage, followed by packing of the wound created in the bottom of the foot with an autogenous cancellous bone graft. Two horses were euthanatized, one 18 months after surgery because of complications in the contralateral support limb, and one 68 days after surgery because of continuing severe lameness. Four horses were alive 9, 16, 21, and 42 months after surgery. One horse was used as a broodmare and did not have observable lameness. Two horses were being ridden. The re...
Parente EJ, Nunamaker DM.Six forelimb specimens from three adult horses had the fetlock joint fused by application of a dorsal plate and by a screw placed in lag fashion through the metacarpus to each proximal sesamoid bone. Five specimens were instrumented on the central dorsal surface of the plate with a single rosette strain gage, and the plate of the sixth specimen was instrumented with four longitudinally oriented single-axis strain gages. The specimens were loaded axially in compression to 4,000 N in a cast (test 1), in a cast with a heel block (test 2), and uncast (test 3). The principal angle of strain in all ...
Bowker RM, Rockershouser SJ, Linder K, Vex KB, Sonea IM, Caron JP.The innervation of the navicular bone (os sesamoideum distale) and its suspensory ligaments (ligamenta sesamoidea collateralia) (CSL) or proximal suspensory ligament and the ligamentum sesamoideum distale impar or the distal sesamoidean impar ligament (DS-impar ligament) was examined using combined anatomical techniques of silver impregnation and immunocytochemistry. Silver impregnation studies revealed an abundance of nerve fibres present in both the CSL and DS-impar ligament with the latter having relatively more nerve fibres. These silver-impregnated nerves coursed parallel to and were asso...
Shaffer SK, Sachs N, Garcia TC, Fyhrie DP, Stover SM.To assess the motion of the proximal sesamoid bones (PSBs) relative to the third metacarpal bone (MC3) of equine forelimbs during physiologic midstance loads. Methods: 8 musculoskeletally normal forelimbs (7 right and 1 left) from 8 adult equine cadavers. Methods: Each forelimb was harvested at the mid-radius level and mounted in a material testing system so the hoof could be moved in a dorsal direction while the radius and MC3 remained vertical. The PSBs were instrumented with 2 linear variable differential transformers to record movement between the 2 bones. The limb was sequentially loaded ...
Jackson M, Geyer H, Fürst A.This study concerns the vestigial metacarpal and metatarsal bones, so called splint bones. The soft tissues, which stabilize the splint bones were carefully examined. The palmar metacarpal/plantar metatarsal fascia, the metacarpal/metatarsal interosseous ligaments and the fibres, which exit distally from the splint bone, were examined in depth. Cadaveric distal limbs were collected from 5 slaughtered or euthanized horses. The legs were examined both, microscopically and macroscopically. The palmar metacarpal/plantar metatarsal fascia is a very stable structure, which connects the splint bone w...
Olive J, Videau M.Macroscopic studies have suggested a link between distal border synovial invaginations of the navicular bone and the distal interphalangeal joint. However, many practitioners consider that these invaginations are directly and solely related to navicular disease. The objective was to investigate the communication pattern of these synovial invaginations with the synovial compartments of the distal interphalangeal joint and the navicular bursa, using minimally invasive imaging techniques. Methods: In a prospective observational study, 10 cadaveric limbs with radiographically evident distal border...
Farfan M, Genton M, Rossignol F.To describe reliable minimally invasive procedures for (1) removing cartilage by joint distraction and articular drilling for equine metacarpophalangeal (MCP)/metatarsophalangeal (MTP) arthrodesis; (2) applying a palmar/plantar tension band without MCP/MTP joint luxation. Methods: Experimental study. Methods: Cadaveric equine limbs (n = 12). Methods: All limbs were used to evaluate the drilling technique. First the MCP/MTP joint was distracted with a 5.5-mm cortical screw. Then, through four stab incisions, articular cartilage was removed with a 4.5-mm drill. Six randomly chosen limbs were the...
MacDonald JL, Richter RA, Wimer CL.Ultrasonography is an established diagnostic test for evaluating horses with foot pain due to suspected podotrochlear apparatus pathology. However, variations from the previously reported normal appearance of the distal sesamoidean impar ligament have not always coincided with lameness. The objective of this prospective, cross-sectional, descriptive study was to characterize variations in the ultrasonographic appearance of the distal sesamoidean impar ligament in sound horses using the transcuneal approach. Transcuneal ultrasonography of the distal sesamoidean impar ligament was performed on s...
Kamm JL, Bramlage LR, Schnabel LV, Ruggles AJ, Embertson RM, Hopper SA.Analysis was performed to examine a method for refining the preoperative prognosis for horses that had surgery to remove apical fractures of the proximal sesamoid bones (PSBs). Objective: To determine if: 1) there was a difference in size or configuration of apical fractures between the different anatomical locations of the PSBs, which have been shown to affect the prognosis; and 2) the size or configuration could predict the prognosis for racehorses with these fractures. Methods: The study included 110 weanlings and yearlings and 56 training racehorses that underwent surgery to remove apical ...
Preston SA, Brown MP, Trumble TN, Chmielewski TL, Zimmel DN, Hernandez JA.To determine the effects of various presale radiographic findings for Thoroughbreds sold at a yearling sale on 2-year-old racing performance of those horses. Methods: 397 Thoroughbreds. Methods: Cohort study. Methods: Thoroughbreds offered for sale at a Thoroughbred sales facility in Kentucky were selected via a randomization procedure. Effects of various presale radiographic findings on the following measures of 2-year-old racing performance were determined: having started a race and having placed (ie, finished in first, second, or third place) in a race at least once, total amount of money e...
Guo L, Yu X, Thair A, Rideout A, Collins A, Wang ZJ, Hore M.The objective of this study was to develop a robust machine-learning approach for efficient detection and grading of sesamoiditis in horses using radiographs, specifically in data-limited conditions. Methods: A dataset of 255 dorsolateral-palmaromedial oblique (DLPMO) and dorsomedial-palmarolateral oblique (DMPLO) equine radiographs were retrospectively acquired from Hagyard Equine Medical Institute. These images were anonymized and classified into 3 categories of sesamoiditis severity (normal, mild, and moderate). Methods: This study was conducted from February 1, 2023, to August 31, 2023. Tw...
Dockery A, Beasley B, Goldberg M, Aguirre G, Moorman VJ.To determine the dose effect of peri-neural liposomal bupivacaine (LB) in an induced forelimb lameness model. Methods: 12 clinically normal adult horses. Methods: A randomized cross-over design was performed with 1 limb receiving saline and the other LB: low dose (6), high dose (6). Lameness was induced in 1 forelimb using a frog-pressure model. In the lame limb, peri-neural injection of the palmar nerves at the proximal sesamoid bones was performed using saline, low dose LB (0.25 mg/kg) (LDLB), or high dose LB (0.5mg/kg) (HDLB) in random order with a 1-week washout period between treatments. ...
Bierau J, Rott P, Röcken M, Staszyk C.This study aimed to delineate the detailed anatomy of the metacarpophalangeal (MCP) and metatarsophalangeal (MTP) joints in healthy horses using cone beam computed tomography (CBCT). The fetlock region of 15 cadaveric forelimbs and 14 cadaveric hindlimbs from nine adult horses without orthopaedic disease underwent CBCT scanning. Additionally, arthrography CBCT scans were conducted following intra-articular injection of a radiopaque contrast medium containing blue epoxy resin dye. Subsequently, limbs were frozen and sectioned to visualize anatomical structures in sectional planes corresponding ...
Beck C, Hitchens PL, Whitton RC.Post-mortem studies have shown that fractures involving the metacarpophalangeal/metatarsophalangeal or fetlock joint are associated with focal areas of microdamage. Identification of computed tomography (CT) features consistent with microdamage and their association with fracture may aid in identification of horses at risk of fracture. Objective: To identify CT features associated with fracture of the metacarpophalangeal/metatarsophalangeal joint. Methods: Retrospective cohort study. Methods: Post-mortem CT images of 367 limbs from 157 Thoroughbred racehorses were graded for CT features. Multi...
Reesink HL.Foals are susceptible to many of the same types of fractures as adult horses, often secondary to external sources of trauma. In addition, some types of fractures are specific to foals and occur routinely in horses under 1 year of age. These foal-specific fractures may be due to the unique musculoskeletal properties of the developing animal and may present with distinct clinical signs. Treatment plans and prognoses are tailored specifically to young animals. Common fractures not affecting the long bones in foals are discussed in this article, including osteochondral fragmentation, proximal ses...
Dik KJ.Several clinical and radiological studies of the proximal sesamoid bones were done in eleven horses from the age of one month to three years. The X-ray findings were found to be inconstant. The number of nutrient canals visualized increased or decreased, and the bone structure gradually became more irregular. Bone deposits along the borders of the sesamoid bones usually did not become apparent until the second or third year of life. Particularly this growth of new bone was found to be a significant clinical feature. On the other hand, nutrient canals and irregular bone structures were also obs...
Meek DG, Dickinson EO.An illustrated approach to the medial aspect of the equine fetlock joint is described, whereby the collateral ligaments are transected. This approach is suggested as a possible technique for metatarsal or metacarpal bone fracture repair by retrograde pinning, arthrodesis of the fetlock joint and other joint and sesamoid bone surgery. The histological evidence of satisfactory healing is presented and the advantages and disadvantages are discussed.
Greet TR.The case histories of three young thoroughbred racehorses with displaced lateral condylar fractures combined with an axial fracture of the lateral sesamoid bone are described. In two cases the condylar fracture was repaired surgically but both horses developed severe degenerative joint disease and remained lame. The third horse was destroyed humanely. It is important that axial fractures of the sesamoid bone are recognised so that a poorer prognosis can be given for treatment of condylar fractures in racing thoroughbreds.
Palmieri G, Sanna L, Asole A, Farina V, Bo Minelli L.The origin and course of the collateral sesamoidean (suspensory navicular) ligament of the horse and ass and its attachment to the distal sesamoid bone were studied by means of dissection. Particular attention was given to the topographic relations between this ligament and the deep digital flexor tendon. Numerous sensitive nerve endings are present in this anatomical district. The free and encapsulated nerve endings, displayed by impregnating techniques, are mostly concentrated in the ligament tract connected to the above-named tendon and close to its attachment to the distal sesamoid angle. ...