肉食恐龙咬合力系列2：肌肉重建

                               
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上图的第三个就是肉食牛龙：
       aIC Internal carotid artery mPSTp m. pseudotemporalis profundus

aMN Mandibular artery mPSTs m. pseudotemporalis superficialis

asp ascending process of pterygoid mPTd m. pterygoideus dorsalis

aST stapedial artery mPTv m. pterygoideus ventralis

cot cotyle n,aIM internal mandibular nerve and

artery

cr crest nCID nerve to constrictor internus

dorsalis muscles

ect ectopterygoid pal palatine

ept epipterygoid pt pterygoid

lig ligament qj quadratojugal

ls laterosphenoid; qu quadrate

mAMEM m. adductor mandibulae externus

medialis

ri rictus

mAMEP m. adductor mandibulae externus

profundus

sh surangular shelf

mAMES m. adductor mandibulae externus

superficialis

tcr tensor crest

mAMP m. adductor mandibulae posterior V1 ophthalmic nerve

mDM m. depressor mandibulae V2 maxillary nerve

mLPt m. levator pterygoideus     V3 maxillary nerve

mPPt m. protractor pterygoideus  VIIhy hyomandibular ramus of facial

nerve

VIIpal palatine ramus of facial nerve

再补充一张：                                 登录/注册后可看大图 图片里面连霸王龙MOR 008的都有 Osteological correlates of the mandible. Scale bar equals 1cm. A, Thescelosaurus (ROM 3587; left, lateral view); B, Edmontosaurus (CMN 2289; right, medial view); C, indet. hadrosaur (ROM 1949; left, lateral view);D, Leptoceratops (CMN 8889; left, lateral view); E, Centrosaurus (ROM 767; left, lateral view); F, Stegosaurus(CM 41681; right, medial view); G, Panoplosaurus (ROM 1215; right, medial view); H, Plateosaurus (AMNH 6810; right, medial view); I, Camarasaurus (CM 11378; right, medial view); J, Dromaeosaurus (AMNH 5356; left, lateral view); K, Tyrannosaurus (MOR 008, right, medial view); L, Caenognathus (ROM 8776; left, lateral view).                                 登录/注册后可看大图 Fig. 5. Muscle attachments, trigeminal nerves, and arteries of the braincases of select dinosaurs in left, lateral view. A, Triceratops; B, Brachylophosaurus; C, Tyrannosaurus 楼上第一章图片的最下面的C号，就是霸王龙，braincase接连颌骨肌肉，神经和动脉 C, Nanotyrannus: right, conservative, ventral mandibular attachment of m. pterygoideus ventralis; left, osteological correlates suggest a jugal attachment of the muscle; D, Soft-tissue anatomy of the medial portion of the mandible of the theropod Tyrannosaurus. 下面的图片底下的C是Nanotyrannus，D是霸王龙. 现在看看脆弱异特龙; 脆弱异特龙的咬合力计算来之标本MOR 693，大艾尔，是一个亚成年个体                                   登录/注册后可看大图 a, Lateral view. b, Dorsal view. aof, antorbital fenestra; co, occipital condyle; ec, ectopterygoid; en, external naris; fr, frontal; j, jugal; lac, lacrimal; ltf, lower temporal fenestra; m, maxilla; mf, maxillary fenestra; n, nasal; or, orbit; pal, palatine; par, parietal; pfr, prefrontal; pm, premaxilla; po, postorbital; popr, paraoccipital process; ps, parasphenoid; pt, pterygoid; q, quadrate; qj, quadratojugal; soc, supraoccipital; sq, squamosal; stf, supratemporal fenestra. Scale bar, 10 cm. c, Meshed finite element model of Allosaurus fragilis in oblique view. d, Meshed finite element model in lateral view. Black stars, position of constraint; thick black arrows, line and direction of muscular force; thinner black arrows and 'bite', point of bite force; grey arrow, line and direction of condylar force; cond, point of condylar force; M.ap (F1), M. adductor posterior; M.ame (F2), M. adductor mandibulae externus superficialis, medius, profundus and M. pseudotemporalis; M.pt (F3), M. pterygoideus group;d1, moment arm of muscle F1; d2, moment arm of muscle F2; d3, moment arm of muscle F3. 亚成年异特龙的头骨比成年个体狭窄；下图是成年异特龙的头骨，还有一张我拍摄美国博物馆四楼成年异特龙的图片，是比较宽的                                 登录/注册后可看大图                                 登录/注册后可看大图 Stress distribution and vector plots for the skull of Allosaurus fragilis during a maximum impact bite without adductor muscle contraction (mode D). a, Stress distribution and magnitude plot for principal stress 1, lateral view. Colour scale bar indicates areas of high tension or compression. b, Stress distribution and magnitude plot for principal stress 3, lateral view. See colour scale bar for areas of high tension or compression. c, Stylized plot showing stress vector direction, lateral view. d, Stylized stress vector plot, dorsal view.                                 登录/注册后可看大图                                 登录/注册后可看大图 [size=0.83em]2010-9-8 23:55 上传 下载附件 [size=0.83em](33.21 KB) Rayfiled只计算了Jaw Adductor的对亚成年异特龙的作用，看2楼可以发现Jaw adductor的虽然是主力之一但并不是提供咬合力的唯一肌肉： 假设异特龙是温血，那么Jaw adductor；表格1（第二章图），异特龙的分布分别在左右上颌骨的第3.4.5号共6颗牙齿的静态咬合力 2147.88N，末端左右双牙静态咬合力3572.56N，大概比狮子末端左右双臼齿的静态咬力小，但是比狮虎犬齿（大个体大约2000N)的静态咬力大。 假设在有肌肉反作用和髁骨限制的情况下，头骨安全承受咬力18747N，在完全没有限制的情况下咬合力可达55447N,当然这个数据没有意义。 在有有肌肉反作用和髁骨限制的情况下，亚成年异特龙可能可以依靠颈部辅助肌肉的力量达到更高的动态咬力，或者直接用头部冲撞对方，咬的时候把部分体重和冲击力带入（clashing bite）的情况下可以达到18747N的咬力。 这个才是肉食牛龙的头骨                                 登录/注册后可看大图

楼上下两图：第一张图是Distribution patterns of maximum (A) and minimum (B) principal stresses on the cranium of Carnotaurus sastrei during bilateral static bite at the posteriormost teeth.
末端双牙静态咬力时头骨承受的压力

第二张图：Distribution patterns of maximum (A) and minimum (B) principal stresses on the cranium of Carnotaurus sastrei when a dorsally directed force (2,485 N) is applied to the central teeth; an inactive adductor musculature is considered.
在中部三颗牙齿受到2485N反作用力时头骨受压情况

                               
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Left half of the cranium of Carnotaurus sastrei shown across a section coincident with the distal end of the frontal horn. The FE model shows the distribution of maximum (A) and minimum (B) principal stresses produced during a hypothetical head-butting contest.
肉食牛龙之间互相用头部撞击时头骨后端的受压图

                               
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三组肌肉（仅指半边头骨）的力量; MPT也有相当大的作用的，甚至超过了TRM.

这是用1号方案计算的，作者还加了一个二号方案：
Model 2 also took into account other uncertain features related to the MPt, as unequivocal evidence of the size and orientation of its anterior portion was not found. Such uncertain features are its cross-sectional area (assumed 10% greater than the area measured for model 1), and the direction of its line of action (taken as 16° higher). The actual bite force, condylar force and peak stresses developed during a muscle-driven bite lie somewhere within the range of values calculated for both the initial and the alternative models. This provided a basic sensitivity analysis whereby we were able to determine the extent to which our conclusions depend on the muscle restoration and muscle architecture we adopted.

也就是MPt部分的肌肉大小不确定，如果往上限计算（比1号重建方案）多10%，和发力的角度也会略有不同，高16度。实际咬力应该在方案1和方案2之间

Although the adductor muscles are of similar proportions in Carnotaurus and Allosaurus, the forces exerted by Carnotaurus are consistently lower. However, higher forces than those for Allosaurus can be estimated from model 2 for the MAMP and MPt of Carnotaurus, which are 1,066 and 5,079 N, respectively. The maximum bite force is exerted at the posteriormost teeth of Carnotaurus (3,341 N; Table 2). When we allow for muscle pinnation and the other features accounted for in model 2, the resultant maximum bite force (5,274 N) and condylar force (11,190 N) are 58% and 88% higher than those calculated for model 1, respectively. 使用方案2计算的结果就是（半边头部）MAMP的力量从444N增加到了1066N，而TRM的肌肉力量从2082N增加到了5079N，超过了脆弱异特龙，用方案1，末端双齿静态咬合力3341N，用方案2则高达5274N，超过了狮子的末端静态臼齿咬力（4168N）和鬣狗的动态末端臼齿咬力（4500N，实测结果）                                 登录/注册后可看大图 上图；头骨的作用力FB，和对应的髁骨反作用力 On the whole, the adductor musculature of Carnotaurus exerts a force of 8,503 N (model 1). As the bite force exerted at the anteriormost teeth is 1,959 N (Table 2), its mechanical advantage for this bite position is 0.230, which is higher than those in Allosaurus (0.160) and Caiman (0.225), as calculated from data published by Rayfield et al. (2001), and Sinclair and Alexander (1987). For a posterior bite, the feeding apparatus of Carnotaurus is also mechanically more advantageous (0.393) than those in Allosaurus (0.330) and Caiman (0.270). On the other hand, the condylar force (FA) in Carnotaurus is 2.61 times higher than its bite force (FB) at the central teeth (Table 2). This force ratio is nearly twice as large in Allosaurus, (4.86; after data published by Rayfield et al., 2001). A comparison with data for Caiman (reported by Sinclair and Alexander, 1987) shows even greater differences in terms of mechanical “waste”; condylar forces are 3.50 and 7,81 times higher than corresponding bite forces, for anterior bites in Carnotaurus and Caiman, respectively. Nonetheless, the difference is less substantial for posterior bites (1.78 and 3.08 times higher). These results show that, mechanically, the jaw design of Carnotaurus is at least 42% more efficient (less wasteful) than that observed in extant crocodilians such as Caiman. The bite force of Carnotaurus (model 1) appears to be comparatively weak in relation to those reported for other theropods and living carnivorous vertebrates (Table 3). A bite force computed from model 2 (5,274 N; see above) does not alter radically the conclusion extracted from this comparison, even though its consideration would make Carnotaurus a stronger biter than living lions and hyenas. 肉食牛龙的肌肉整体提供8503N（方案1）,前颌骨最前端牙齿咬力1959N，效率23%,高于亚成年脆弱异特龙的16%和凯门鳄的22.5%，末端牙齿同样效率更高，肉食牛龙39.3%，异特龙33%,凯门鳄27% 髁骨反作用力，肉食牛龙的中端牙齿效率更高，反作用力是咬力的2.61倍，而相比之下亚成年脆弱异特龙是4.86倍，而凯门鳄则是3.50~7.81倍（末端牙齿1.78~3.08倍）。当然这和肉食牛龙的头骨较短有关系，尽管如此，总体上肉食牛龙比凯门鳄的效率高42%。 Moreover, this case indicates that the cranium of Carnotaurus could have resisted a static tug of up to 45,464 N (or 38,520 N if model 2 is considered) before yielding. However, the actual force magnitude on which the cranium yields could be markedly reduced if the dynamic effect of tugging in life situations is taken into account. 肉食牛龙的头骨可以承受45464N（方案1）~38520N（方案2）的猎物静态拖扯的力道，当然真实生活中猎物会动态挣扎，头骨承受的力量明显不会达到38520N Meer's equation predicts a bilateral bite force of 66 kN, or about twelve times the maximum bite force calculated in the present study (model 2). Despite being the result of an extrapolation, the bite force predicted looks reliable enough as the largest animal in Meers' data sample (Alligator mississippiensis) has a mass nearly an order of magnitude less than that in a hypothetical Carnotaurus-sized predator. Nonetheless, it would not have been possible for a 1,500-kg Carnotaurus to attain such a bite force because of the constraint imposed by its unremarkable cranial strength (see below). Our stress results for model 1 (where a bite force of about 3.3 kN generates a tensile stress of 20 MPa) show that a bilateral bite force of only 22 kN (or even less if model 2 results are considered) should be enough to induce yielding in Carnotaurus cranium. 结论：Meer的肉食动物体重咬力比例公式，1500kg的一头肉食牛龙按照“所有肉食动物综合公式”可以达到66000N的“满嘴最高咬力”，而头骨的坚强度，即便肉食牛龙采用“撞击”咬力，也就是把冲撞力量带入咬合力也最多能达到22000N（方案1），按照方案2甚至更少（方案2重建的肌肉更多，限制也更多），如果咬力超过22000N,头骨就会损坏。 再稍微说一下Meer的公式（在第三系列，暴龙里面会做详细介绍）                                 登录/注册后可看大图                                 登录/注册后可看大图 假设肉食牛龙的体重1400—2600kg（Mazeeta,2004，和计算卡氏南方巨兽龙体重来之同一篇） LN（1400~2600）=7.244~7.8632， 如果按综合公式：EXP((7.244~7.8632)x0.9182+4.3829)= 58404.431~102587.6382N 明显过高； 如果使用鳄鱼公式：EXP((7.244~7.8632)x0.7848+5.3789)= 63842.20393~103776.1781N 还略高于所有动物公式。 如果使用哺乳动物公式：EXP((7.244~7.8632)x0.725+5.0308)= 29227.48898~45783.01157N 这个数据比较接近答案，Meer的陆生哺乳动物公式反而更加适合恐龙，毕竟恐龙是陆地生态系统的。肉食牛龙较低的咬力也许和它相对较小的头骨有关联。 亚成年异特龙大艾尔的体重下限估计900kg ，上限（3D激光模式计算）1500kg，最大撞击咬力（安全状态下）18500N左右，成年的宽头骨模式的大个体可能能达到25000N左右的撞击咬力吧？ Meer的公式其实问题很大，一开始综合公式的结果在现存陆生动物内都是低于鳄鱼，但是取量到后来竟然远远的超过了大型动物里面以咬力呈长的鳄鱼，明显有问题。 用综合公式，5300kg的霸王龙的咬合力竟然可达23500N，居然和80吨的巨齿鲨的动态上限（静态咬力上限190000N,我修改了一下论文的结果，因为巨齿的颌骨较白鲨为强） 实际上考虑到肉食恐龙的头骨比真鳄类的要脆弱，既是是擅长咬的恐龙的咬力也应该在哺乳动物公式和真鳄类公式之间。

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