Quantitative morphology of the equine laminar junction in relation to capsule shape in the forehoof of Standardbreds and Thoroughbreds

REASONS FOR PERFORMING STUDY: Differences in hoof morphology have largely been underappreciated in the literature until recently, and it is these that hold the key to interpreting functional adaptation in the hoof. HYPOTHESES: Primary laminar morphology correlates with hoof capsule shape; and breeds with different hoof shapes and loadings show different patterns of correlation. METHODS: Seventeen measurements of capsule shape and 3 of primary epidermal laminae (PEL) morphology (spacing, orientation and curvature) were made on right and left front hooves from 27 Standardbred and 25 Thoroughbred horses, and tested for breed differences. Three laminar variables (spacing, orientation and curvature) were measured on each hoof for samples of 25 PEL in 5 circumferential and 4 proximodistal locations. Pairwise correlations of capsular and laminar measurements were compared within breeds. Significant correlations were mapped onto the 20 sampling sites. RESULTS: Capsule shape differed significantly between breeds in 7 measurements and in a multivariate test. Between breeds, PEL differed in orientation and spacing primarily at the medial quarters and heels, and in curvature at both quarters (P<0.05). Significant correlations between several pairs of capsule and laminar variables were found at sample locations that differed markedly between breeds. CONCLUSIONS: Laminar morphology, hoof capsule shape and correlations between them differ between Standardbreds and Thoroughbreds. These results support the concept that remodelling of PEL is, at least in part, stimulated and directed by varying stress or strain levels in the laminar junction. POTENTIAL RELEVANCE: Understanding the biological responses of hoof tissues to stress should add to the ability to prevent lameness involving the hoof and maintain its health.     

Evaluation of changes in architecture of the stratum internum of the hoof wall from fetal, newborn, and yearling horses

OBJECTIVE: To evaluate morphologic changes of the stratum internum of hooves from near-term fetal, newborn, and yearling horses. ANIMALS: Feet from 27 near-term equine fetuses, 19 newborn foals, and 8 yearlings. PROCEDURES: Primary epidermal laminae (PEL) of the stratum internum were examined for evidence of architectural changes. RESULTS: In near-term fetuses, the PEL had a homogeneous appearance and symmetric distribution around the hoof wall with no significant differences in PEL density between the toe and quarters. However after birth, branched laminae at the toe formed within the first few weeks, which significantly increased PEL density at the toe, compared with the quarters. In yearlings, morphology of the PEL differed from that in younger foals and the PEL density was significantly greater at the toe than the quarters. The PEL density at the toe and medial and lateral quarters was significantly different from each other, as these PEL densities appeared to have been associated with conformation. No significant differences in PEL densities between forefeet and hind feet were detected in any group. CONCLUSIONS AND CLINICAL RELEVANCE: Findings indicate that the stratum internum of the inner hoof wall undergoes several morphologic changes shortly after birth. The PEL become branched with a greater PEL density at the toe than the quarters. In an asymmetric foot, more PEL were associated with the sloping side than the steep side of the foot. Findings suggested that PEL growth may also occur by bifurcation as well as by mitosis from the coronet and that wall stress may be associated with increased PEL density.     

Density and morphologic features of primary epidermal laminae in the feet of three-year-old racing Quarter Horses

OBJECTIVE: To quantify the density of primary epidermal laminae (PELs) around the solar circumference and evaluate the relationship between regional PEL density and hoof capsule morphology in horses. SAMPLE POPULATION: Forefeet from nine 3-year-old Quarter Horse cadavers. PROCEDURES: Data pertaining to gross features of hoof morphology and PEL variables, including number, density, and distribution patterns around the perimeter of the hoof wall and number of bar PELs, were collected. Tissues of the laminar junction were examined histologically. RESULTS: No significant differences were found between left and right forefeet with respect to gross hoof morphologic measurements. Mean +/- SD number of PELs, including those at the bars of the hoof, was 551 +/- 30. Primary epidermal laminar density in the toe was significantly higher, compared with that in the quarter and heel regions, and was higher on the lateral aspect of the foot, compared with the medial aspect. Feet were significantly wider on the lateral aspect of the foot, compared with the medial aspect, as measured across the widest point of the solar surface. Histologic examination revealed atypical laminar morphology at the toe. CONCLUSIONS AND CLINICAL RELEVANCE: Variations were detected in PEL density and morphology around the solar circumference of hooves from 3-year-old racing Quarter Horses. A better understanding of relationships between laminar density, laminar morphology, and gross morphology of the hoof capsule in different populations of horses may aid practitioners in diagnosis and treatment of disease involving the hoof wall in horses.     

In Vitro Assessment of the Equine Hoof Wall Strains in Flat Weight Bearing and After Heel Elevation

Horseshoeing is a common practice, but effects on the hoof wall are poorly understood. Strain gauges were used to document and compare hoof behavior in vitro during flat weight bearing and after artificial heel elevation. Ten front limbs of Thoroughbred race horses, shod with conventional flat shoes, were used. Eight strain gauges were symmetrically distributed around the toe, quarters, and heels. Each limb was mounted to a testing machine (Kratos K5002; Kratos Dynamômetros, Ltda., Cotia-SP-Brazil) and subjected to a load equivalent to 30% of the donor's body weight. Strains (μ) were acquired by means of a computerized system and the results compared using Friedman and Wilcoxon statistical tests. There was greater strain variation when the heels were elevated. Compression predominated during flat weight bearing, with a tendency to horizontal traction after heel elevation. The changes in strain caused by heel elevation were not always symmetrical. Elevation of the heels tensed the toe and the medial quarter horizontally, increased load at the posterior portion of the hoof capsule, and hindered its expansion.     

Geometric symmetry of the solar surface of hooves of thoroughbred racehorses

OBJECTIVE: To define a 3-dimensional (3-D) coordinate system with clear definitions of origins and axes relative to hoof anatomic features and determine whether solar surfaces of Thoroughbred racehorse hooves have geometric asymmetry in the mediolateral and dorsopalmar directions. SAMPLE POPULATION: Left forelimb hooves from 20 Thoroughbred racehorse cadavers. PROCEDURE: A right-handed 3-D coordinate axes system centered on the collateral sulci was defined for the left front hoof. Orthogonal distances of anatomic features from the dorsopalmar axis and the plane coincident with the ground were measured and compared between medial and lateral sides and between dorsal and palmar regions of the hoof. RESULTS: The hoof was wider and had a greater radius laterally than medially. The most distal part of the lateral bar of the frog was further from the dorsopalmar axis than that of the medial bar. Overall, mediolateral asymmetries in depth were not observed. The sole at the perimeter was deeper medially in the dorsal part of the hoof and laterally in the palmar part, with depth overall being greater palmarly than dorsally. Most features had dorsopalmar asymmetry. CONCLUSIONS AND CLINICAL RELEVANCE: When the angle bisected by the collateral sulci is used to determine the dorsopalmar axis of the hoof, most central structures (bars and collateral sulci) have mediolateral symmetry. However, the hoof wall and sole have some mediolateral asymmetries and most structures have dorsopalmar asymmetry. These findings may assist the development of devices for attachment to hooves and studies of the interaction of hooves with bearing surfaces.     

A Cross-Sectional Survey of Forelimb Hoof Conformation and the Prevalence of Flat Feet in a Cohort of Thoroughbred Racehorses in New Zealand

Racehorses in New Zealand predominantly train counter clockwise. This training pattern has been associated with between forelimb differences in bone mineral density profile and asymmetrical limb loading after training. At present, there is limited data on the hoof conformation of these racehorses. Distal forelimb and digital hoof conformation data were collected from 75 Thoroughbred racehorses (2–5 years old) from two training yards. Digital conformation was subjectively graded, and multiple hoof measurements were made with a modified tire gauge (sole and sulci depth) and from digital photographs. All the horses were shod by two registered master farriers within a median of 15 (interquartile range [IQR], 1–25) days before measurement. There were few distal limb conformation abnormalities scored. Most (62/75) horses presented with some deviation from normal hoof parameters, with 2 (IQR, 1–3) abnormalities reported per horse. The most common hoof abnormality was uneven sulci, which was identified in 43 horses and 59 affected hooves, followed by higher medial hoof wall height in 38 horses and 53 affected hooves. Many of the linear and hoof angle measurements and their ratios were within the bounds reported within the literature and indicative of a balanced foot. The length and width measurements increased with horse age. The dorsal hoof wall (DHW) length:heel length ratios were consistently less than 3:1, and the absolute difference between toe and heel angle was generally greater than 5°. Between limb hoof variation was identified for a number of the morphologic measurements including frog length and sole length and the ratio of sole width:sole length. Flat feet (lack of concave solar surface) were identified in 21/75 (28%) horses and in 28/150 (19%) forelimb hoofs. More horses had a flat left foot (10/75) than right foot (4/75), but seven horses had both feet classified as being flat. Flat feet had 2.4 (1.1–5.6, P = .036) greater odds of presenting with uneven sulci. These data indicate that uneven sulci depth and flatter hooves with may be a typical presentation of Thoroughbred feet. Asymmetry in measurements between limb may reflect the greater loading of the left forelimb when race training counter clockwise.     

Light and electron microscopy of keratinization in the laminar epidermis of the equine hoof with reference to laminitis

The laminar epidermis (epidermis parietis) of hooves from 14 clinically normal horses, 6 months to 15 years old, was examined by light and electron microscopy and immunofluorescence to measure the contributions of this region to the formation of the hoof wall. By their progressive keratinization to form primary epidermal laminae, the secondary epidermal laminae ultimately contributed about 20% of the thickness of the hoof wall (as revealed in the white line [zona alba]). The keratinized, primary epidermal laminae were developed to a height of 4 mm during their proximodistal-course, much of this obscured because of their basal portion being embedded in the cap horn epidermis. From evaluation of structural changes accompanying keratinogenesis in the cell and determination of the contribution of the laminar epidermis to the formation of laminar horn, cap horn, connecting horn, terminal horn, and the white line, we concluded that the sterile bed concept of a nongerminative role for the secondary epidermal laminae is no longer tenable.     

Effects of barefoot trimming on hoof morphology

Objective To monitor changes in hoof morphology in response to barefoot trimming. Methods Seven horses were trimmed every 6 weeks according to barefoot trimming principles, which involved levelling the hoof to live sole, lowering the heels, bevelling the toe and rounding the peripheral wall, while leaving the sole, frog and bars intact. A 4‐month period was allowed to lower the heels sufficiently to achieve a hoof shape representative of the barefoot trim. This was regarded as the starting point for morphological adaptations in response to maintenance of the trim. Hoof morphology was measured from lateral, dorsal and solar view photographs and lateromedial radiographs taken at 0, 4 and 16 months. Changes from 0 to 4 months represented differences between a natural hoof shape and the trim, while changes from 4 to 16 months represented adaptive effects during hoof growth. Results Establishment of the barefoot trim involved significant shortening of the toe, heel and medial and lateral walls, with increases in angulation at the toe, medial and lateral walls, but not at the heel. Maintenance of the trim resulted in a palmar/plantar migration of the heels, with increases in support length, heel angle and solar angle of the distal phalanx (P3). Conclusions Bevelling the toe and engaging the frog and bars in the weight‐bearing function of the foot resulted in elevation of the heel angle and solar angle of P3. These changes may be beneficial in treating under‐run heels and negative solar plane angulation of P3.     

Effect of dietary biotin supplement on equine hoof horn growth rate and hardness.

Over a 10-month period, 24 randomly selected riding horses were fed various amounts of biotin. Statistically significant improvements in growth rates and hardness of hooves were produced by biotin supplementation. Greater growth rates and hardness were achieved at a daily dose of 15 mg than at 7.5 mg. Increased hoof hardness was greatest in the hoof quarters and toe. No ring formation occurred in hooves of horses fed biotin intermittently.     

Analysis of strain and stress in the equine hoof capsule using finite element methods: comparison with principal strains recorded in vivo

Finite-element (FE) methods have great potential in equine biomechanics in evaluating mechanical stresses and strains in tissues deep within the hoof. In this study, we critically assessed that potential by comparing results of FE analyses of capsular strain with in vivo data. Nine FE models were developed, corresponding to the shape of hooves for which in vivo principal strain data are available. Each model had the wall, laminar junction, sole and distal phalanx (PIII). In a first loading condition (LC1), force is distributed uniformly to the bearing surface of the wall to determine reaction forces and moment on PIII. These reaction forces were subsequently applied to PIII in loading condition 2 (LC2) to simulate loading via the skeleton. Magnitude of the force resultant was equivalent to the vertical force on the hoof at midstance. Principal compressive strains epsilon2 were calculated at the locations of 5 rosette gauges on the real hooves and are compared with the in vivo strains at midstance. FE strains were from 16 to 221% of comparable in vivo values, averaging 104%. All models in this, and reports by other workers, show predominance of stress and strain at the toe to a greater extent than in the real hoof. The primary conclusion is that FE modelling of strain in the hoof capsule or deeper tissues of individual horses should not be attempted without corroborating experimental data.     

Effects of toe angle on hoof growth and contraction in the horse

The effects of toe angle on the growth of the unshod hooves of mature horses were measured over 126 days. The hooves of 4 horses were trimmed long in the toe and short in the heel (“LT”), with toe angles of 40° for the forelimb and 50° for the hind limb hooves; 4 others were trimmed short in the toe and long in the heel (“ST”), with toe angles of 50° for the forelimb and 55° for the hind limb hooves. Growth of the hoof wall at the toe ranged between .19 and .28 mm/day, and was slowest in the forelimb hooves trimmed ST. After 126 days, the hooves trimmed LT were 7% smaller in width than they had been at day 0. Narrowing of the hoof walls and frogs was accompanied by deformation of the angles of the walls (bending outward of their weightbearing surfaces). Frog lengths and sole areas were not affected by toe angle. Regardless of trimming method, all forelimb hooves tended to return to a toe angle of 45° between trimmings, while all hind limb hooves tended toward toe angles of 52° to 53°. The soles of all hooves were basically circular in shape, although the hooves trimmed LT tended to be skewed to the left, as viewed from above, after 126 days.     

The effect of flat horseshoes, raised heels and lowered heels on the biomechanics of the equine hoof assessed by finite element analysis (FEA)

The biomechanical effects of lowering and raising the heels were studied using a finite element (FE) computer model of the equine hoof capsule consisting of 18,635 finite elements. A static load of 3000 N was distributed to nodes of the inner hoof wall (80%) according to the suspension of the coffin bone, 20% loaded sole and frog. When loaded the FE hoof capsules showed the following deformations: the proximal dorsal wall moves back, the quarters flare to the side and sole and frog perform a downward movement. Stresses are high in the material surrounding the quarter nails, in the heels and in the proximal dorsal wall. Three types of horseshoes were simulated, a regular shoe with flat branches, a shoe with 5 degrees raised heels and a shoe with 5 degrees lowered heels. Raising the heels resulted in significantly (P < 0.05) low stress and displacement values. The lowered heels model calculated highest stress and displacement values and the results of the FE model with the regular horseshoe were found in between.     

Associations between hoof shape and the position of the frontal plane ground reaction force vector in walking horses

AIMS: To determine the frontal plane position of the ground reaction force vector at its centre of pressure under the hoof of walking horses, and its projection through the distal limb joints, and to relate this to hoof geometric measurements.

METHODS: Reflective markers were glued to the forelimb hooves and skin of 26 horses, over palpable landmarks representing centres of the coffin, fetlock and carpal joints, and the dorsal toe at its most distal point. A 4-camera kinematic system recorded the position of these markers as the horse walked in hand across a force platform, to generate a frontal plane representation of the ground reaction force vector passing between the markers at the joints. The position of the vector was calculated as the relative distance between the lateral (0%) and medial (100%) markers at each joint. Digital photos were taken of the hoof in frontal and sagittal views to determine hoof geometric measurements. Associations between these and the position of the force vector at each joint were examined using Pearson correlation coefficients.

RESULTS: Mean vector position for both forelimbs at the toe, coffin, fetlock and carpal joint was 50.1 (SD 8.9), 53.0 (SD 9.2), 54.6 (SD 11.4) and 50.5 (SD17.3)%, respectively, of the distance between the lateral and medial sides of the joint in the frontal plane. Across all four joints, the vector position was slightly more medial (2–4%) for the right than left limb (p>0.05). Medial hoof wall angle was correlated (p<0.05) with force vector position at the fetlock (r=?0.402) and carpal (r=?0.317) joints; lateral hoof wall angle with vector position at the toe (r=0.288) and carpal (r=?0.34) joint, and medial hoof wall height with vector position at the fetlock (r=?0.306) and carpal (r=?0.303) joints.

CONCLUSION: The position of the two-dimensional frontal plane ground reaction force vector at the toe, and at the fetlock and carpal joints was associated with hoof shape. Mediolateral hoof balance has been shown in vitro to affect articular forces, which may be a factor in development of joint disease. The effect of hoof shape needs to be evaluated at faster gaits to determine the potential for joint injury in the presence of larger forces.     

Laminar epidermal hyperplasia and hyperkeratosis in an equine hoof

A 6-year-old Canadian Warmblood gelding was presented for suspicion of keratoma growth, based on a history of recurring abscesses in the right front foot. Radiographic examination and computed tomography identified 2 bilaterally symmetrical, laminar epidermal ingrowths adhered to the hoof wall at the level of the lateral and medial heels.     

A preliminary study into the correlation of stiffness of the laminar junction of the equine hoof with the length density of its secondary lamellae

Reason for performing study: The relationship between mechanical behaviour and microscopic structure of the laminar junction of equine hooves under testing conditions requires elucidation. Objectives: To determine mechanical parameters and 2D length density of profiles of secondary lamellae of the laminar junction in the dermal region and to assess possible correlations. Methods: Specimens (25 samples in total) of the laminar junction were taken from front, quarter and heel parts from 3 equine hooves and exposed to a uniaxial tensile test until rupture to obtain Young's moduli of elasticity, ultimate stress and strain. Neighbouring specimens to those used for the biomechanical experiment were processed histologically to assess the length density of laminar junction basement membrane using stereological grids. Results: The estimated median (interquartile range) length density of the laminar junction basement membrane was 0.024 (0.020–0.027)/µm. Young's modulus of elasticity was 0.15 (0.11–0.35) MPa in the small deformation region, and 7.58 (6.14–8.68) MPa in the linear region was. The ultimate stress was 1.67 (1.41–2.67) MPa, and the ultimate strain was 0.50 (0.38–0.70). The Young's modulus of elasticity in the region of small deformations has a moderate correlation with the length density of the laminar junction basement membrane. Conclusions: As with most soft biological tissues, the laminar junction has a nonlinear mechanical behaviour. Within the range of small deformations, which correspond to physiological loading of the laminar junction, a higher length density of the laminar junction basement membrane is correlated with a higher resistance of the laminar junction against high stresses transmitted from the distal phalanx to the hoof wall. Potential relevance: The condition of the laminar junction apparatus may be easily quantified as the length density of profiles of secondary dermal lamellae. This quantification provides a simple tool that could be used for comparing the proneness of the various parts of the laminar junction to initial stages of laminitis.     

Evaluation using hoof wall strain gauges of a therapeutic shoe and a hoof cast with a heel wedge as potential supportive therapy for horses with laminitis

OBJECTIVE: To evaluate using strain gauges, a hoof cast with heel wedge, and a therapeutic shoe with unsupported toe for their effectiveness in redistribution of load from the dorsal hoof wall. STUDY DESIGN: In vitro biomechanical study. SAMPLE POPULATION: Twenty forelimb specimens. METHODS: Rosette strain gauges were placed on the dorsal and lateral hoof wall of 20 normal shaped hooves. Limbs were loaded vertically using a tensile testing machine with a 1 Hz sinusoidally cycling load up to 3000 N during 15 seconds. Mean values of principal strain and direction at 2500 N load were calculated for 3 experimental conditions (unshod, therapeutic shoe with unsupported toe, and hoof cast with heel elevation) and tested by ANOVA (P<.05). RESULTS: Vertical limb loading in an unshod hoof leads to a biaxial compression of the dorsal wall with high longitudinal compression (epsilon2 = -1515 microm/m). Principal strain at the dorsal wall (epsilon2) was decreased by 23% with the therapeutic shoe and by 59% with the hoof cast. On the lateral hoof wall principal strain was unchanged with the shoe, but increased by 34% with the cast. CONCLUSIONS: Strain measurements indicate unloading of the dorsal hoof wall by both methods with the cast being more effective than the shoe. CLINICAL RELEVANCE: The hoof cast with wedge offers substantial unloading of the dorsal wall, but increases load on the quarter. Therefore a hoof cast would likely be most helpful in acute laminitis when palmar structures can still bear load. The therapeutic shoe offers rehabilitation and regrowth of the dorsal wall without increased load on the quarter wall.     

Photoelastic stress analysis of strain patterns in equine hooves after four-point trimming

OBJECTIVE: To evaluate changes in strain patterns in normal equine hooves following 4-point trimming, using photoelastic stress analysis. SAMPLE POPULATION: 15 equine front limbs with normal hoof configuration. PROCEDURE: Limbs were disarticulated at the carpometacarpal joint. Weight-bearing surfaces of each hoof were trimmed level to ensure 100% ground contact. Hoof walls were coated with a custom-made strain-sensitive plastic, and limbs were loaded to a third of body weight. Using a polariscope, strain distribution, magnitudes, and directions were evaluated in level hooves as well as before and after standardized 4-point trimming. Repeated-measures ANOVA was used to compare strain magnitudes and directions before and after trimming. RESULTS: In leveled specimens, strain fields were symmetrically distributed above the heels and at quarter-toe junctions along a line between the middle and distal thirds of the hoof wall. After 4-point trimming, strain epicenters localized above the contact points, whereas strain magnitudes significantly increased by approximately 50%. Decreasing contact area by 50% resulted in an additional significant increase (32%) in strain magnitude. Trimming did not have a significant effect on strain orientations. CONCLUSION AND CLINICAL RELEVANCE: This study documents that 4-point trimming results in strain concentration above the hoof contact points and that strain magnitude is dependent on contact area.     

The effect of hoof angle variations on dorsal lamellar load in the equine hoof

Reasons for performing study: In the treatment of laminitis it is believed that reducing tension in the deep digital flexor tendon by raising the palmar angle of the hoof can reduce the load on the dorsal lamellae, allowing them to heal or prevent further damage. Objective: To determine the effect of alterations in hoof angle on the load in the dorsal laminar junction. Methods: Biomechanical finite element models of equine hooves were created with palmar angles of the distal phalanx varying from 0–15°. Tissue material relations accounting for anisotropy and the effect of moisture were used. Loading conditions simulating the stages in the stance where the vertical ground reaction force, midstance joint moment and breakover joint moment were maximal, were applied to the models. The loads were adjusted to account for the reduction in joint moment caused by increasing the palmar angle. Models were compared using the stored elastic energy, an indication of load, which was sampled in the dorsal laminar junction. Results: For all loading cases, increasing the palmar angle increased the stored elastic energy in the dorsal laminar junction. The stored elastic energy near the proximal laminar junction border for a palmar angle of 15° was between 1.3 and 3.8 times that for a palmar angle of 0°. Stored elastic energy at the distal laminar junction border was small in all cases. For the breakover case, stored elastic energy at the proximal border also increased with increasing palmar angle. Conclusions and potential relevance: The models in this study predict that raising the palmar angle increases the load on the dorsal laminar junction. Therefore, hoof care interventions that raise the palmar angle in order to reduce the dorsal lamellae load may not achieve this outcome. See also correspondence by Redden See also correspondence by Curtis     

Effect of biotin supplementation on hoof health and ceramide composition in dairy cattle

The effect of biotin supplementation on various foot lesions and hoof ceramide composition of toe (wall) and sole portions of hooves was studied in crossbred dairy cattle. Biotin supplementation was done for five months in 14 cattle at a farm and the other 14 animals kept as control. A significant decline was observed in heel erosions and sole avulsions along with total disappearance of white line fissures and double soles in the biotin supplemented cattle resulting in decrease in the overall disease score. Thin layer chromatographs of the hoof lipids revealed 11 types of ceramides in sole lipids and 6 types of ceramides in toe (wall) lipids. The ceramides were typed and identified according to their Rf values. A qualitative increase in the density of thin layer chromatographs of sole lipids was observed in biotin supplemented cattle whereas a non-significant difference in density of thin layer chromatographs of toe lipids was observed after supplementation of biotin.     

奶牛蹄部不同部位温度在跛行诊断中的应用

为了确定应用手持式红外线测温仪筛选奶牛蹄部不同部位的温度用于奶牛跛行的诊断价值,本研究在奶牛修蹄前进行跛行评分,修蹄后用手持式红外线测温仪分别测量奶牛右后蹄系部、右后蹄外侧趾远轴侧蹄壁和右后蹄外侧趾蹄底三角区的温度,分析其与奶牛跛行程度的相关性,并绘制不同部位蹄部温度的ROC曲线,确定其诊断作用和最佳临界值.结果显示,...