Calculation and application of the anterior surface area of a model human cornea

The macroscopic anterior surface area was calculated for three models of the average human cornea. Two models, a general ellipsoid and a rotational ellipse (rotationally symmetric ellipsoid) gave a surface area of 132 mm2, while a spherical model gave 126 mm2. A general ellipsoidal model having the maximum radius horizontal (with-the-rule corneal astigmatism) has less surface area than a rotational ellipse with the same horizontal radius. For a corneal sagittal height of 2.59 mm, the surface area of an ellipsoidal cornea equals -19.2Q + 16.3R -0.476 which specifies a rotational ellipse (radius R, asphericity Q) of equal surface area. In a cornea with the maximum radius vertical (against-the-rule corneal astigmatism), the ellipsoid has slightly more surface area than a rotational ellipse with the same horizontal radius of curvature. For a given horizontal radius of curvature, the sphere has the lowest surface area. For a corneal sagittal height s of 2.59 mm, the sphere underestimates by 8% the surface area of a rotational ellipse with asphericity -0.5. The anterior corneal surface area of a rotational ellipse model, radius R, asphericity Q is given by 2 pi Rs- 19.2Q. In all three models, the surface area increases with horizontal radius of curvature. In the rotational ellipse model, the rate of increase (slope) is independent of asphericity, and the slope found in with-the-rule astigmatism is less than the slope found with against-the-rule astigmatism. The calculated surface area predicts a precorneal tear volume of 0.86 microliter for a 6.5 micron tear thickness. The apparent, or plane projected are of an epithelial lesion underestimates the curved surface area with a percentage error that increases rapidly with lesion diameter. For a 12 mm diameter lesion on a rotational ellipse model, the apparent area underestimates the surface area by 18%. The average posterior corneal surface in human is not spherical but imitates the anterior surface, and has an area of 137 mm2 or 3.8% greater than the anterior area.     

Determinants of Posterior Corneal Biometric Measurements in a Multi-Ethnic Asian Population

Purpose

To describe the corneal and anterior segment determinants of posterior corneal arc length (PCAL) and posterior corneal curvature (PCC).

Methods

Cross-sectional, population-based study of 1069 subjects (1069 eyes) aged 40–80 years, from three major Asian ethnic groups. All underwent anterior segment optical coherence tomography imaging and analysis with Zhongshan Angle Assessment Program. Our main outcome measures were determinants of PCAL and PCC using adjusted, multivariate linear regression analysis, adjusted for confounders to obtain the estimated marginal means (EMM) with standard error (SE).

Results

The overall mean (± SD) of PCC was: 6.51±0.39 mm; and PCAL was: 12.52±0.59 mm. Malays had a relatively longer PCAL (EMM = 12.74 mm, SE = 0.04 mm) than Chinese (EMM = 12.48 mm, SE = 0.03 mm, P<0.001), and Indians (EMM = 12.42 mm, SE = 0.03 mm, P<0.001). Anterior segment parameters had weak-moderate correlations with PCAL, which included: anterior chamber depth (ACD) (r = 0.55, P<0.001), PCC (r = 0.27, P<0.001), anterior corneal curvature (ACC) (r = 0.14, P<0.001) and central corneal thickness (CCT) (r = −0.07, P = 0.023). In multivariate analysis, anterior segment parameters explained only 37.6% of the variance of PCAL, with ACD being the most important determinant (partial R²  = 0.300; P<0.001). The determinants of PCC included ACC, PCAL and CCT (explaining 72.1% variation of PCC), with ACC being the most important determinant (partial R²  = 0.683; P<0.001).

Conclusion

There was moderate correlation of PCAL with ACD, but anterior segment parameters accounted for only a small proportion of the variation in PCAL. The significant differences in PCAL and PCC amongst different Asian ethnic groups suggests that there is a need to consider this factor when planning for anterior segment surgeries such as endothelial keratoplasty.     

Geometry of human ribs pertinent to orthopedic chest-wall reconstruction

Orthopedic reconstruction of blunt chest trauma can aid restoration of pulmonary function to reduce the mortality associated with serial rib fractures and flail chest injuries. Contemporary chest wall reconstruction requires contouring of generic plates to the complex surface geometry of ribs. This study established a biometric foundation to generate specialized, anatomically contoured osteosynthesis hardware for rib fracture fixation. On human cadaveric ribs three through nine, the surface geometry pertinent to anatomically conforming osteosynthesis plates was characterized by quantifying the apparent rib curvature C(A), the longitudinal twist alpha(LT) along the diaphysis, and the unrolled curvature C(U). In addition, the rib cross-sectional geometry pertinent to intramedullary fixation strategies was characterized in terms of cross-section height, width, area, and cortex thickness. The rib surface exhibited a curvature C(A) ranging from 3.8 m(-1) in the anteromedial section of rib seven to 17.3 m(-1) in the posterior section of rib three. All ribs had in common a longitudinal twist alpha(LT), ranging from 41-60 degrees. The unrolled curvature C(U) decreased gradually from ribs three to five, and increased gradually with reversed orientation from rib six to nine. The cross-sectional area remained constant along the rib diaphysis. However, the medullary canal increased in size from 29.9 mm(2) posteriorly to 41.2 mm(2) in anterior rib segments. Results of this biometric rib characterization describe a novel strategy for intraoperative plate contouring and provide a foundation for the development of specialized rib osteosynthesis strategies.     

Effect of the intra-abdominal pressure and the center of segmental body mass on the lumbar spine mechanics - a computational parametric study

Determination of physiological loads in human lumbar spine is critical for understanding the mechanisms of lumbar diseases and for designing surgical treatments. Computational models have been used widely to estimate the physiological loads of the spine during simulated functional activities. However, various assumptions on physiological factors such as the intra-abdominal pressure (IAP), centers of mass (COMs) of the upper body and lumbar segments, and vertebral centers of rotation (CORs) have been made in modeling techniques. Systematic knowledge of how these assumptions will affect the predicted spinal biomechanics is important for improving the simulation accuracy. In this paper, we developed a 3D subject-specific numerical model of the lumbosacral spine including T12 and 90 muscles. The effects of the IAP magnitude and COMs locations on the COR of each motion segment and on the joint/muscle forces were investigated using a global convergence optimization procedure when the subject was in a weight bearing standing position. The data indicated that the line connecting the CORs showed a smaller curvature than the lordosis of the lumbar spine in standing posture when the IAP was 0?kPa and the COMs were 10?mm anterior to the geometric center of the T12 vertebra. Increasing the IAP from 0 kPa to 10 kPa shifted the location of CORs toward the posterior direction (from 1.4?±?8.9 mm anterior to intervertebral disc (IVD) centers to 40.5?±?3.1 mm posterior to the IVD centers) and reduced the average joint force (from 0.78?±?0.11 Body weight (BW) to 0.31?±?0.07 BW) and overall muscle force (from 349.3?±?57.7 N to 221.5?±?84.2 N). Anterior movement of the COMs from -30 mm to 70 mm relative to the geometric center of T12 vertebra caused an anterior shift of the CORs (from 25.1?±?8.3 mm posterior to IVD centers to 7.8?±?6.2 mm anterior to IVD centers) and increases of average joint forces (from 0.78?±?0.1 BW to 0.93?±?0.1 BW) and muscle force (from 348.9?±?47.7 N to 452.9?±?58.6 N). Therefore, it is important to consider the IAP and correct COMs in order to accurately simulate human spine biomechanics. The method and results of this study could be useful for designing prevention strategies of spinal injuries and recurrences, and for enhancing rehabilitation efficiency.     

颈前路“杂交式”与颈后路治疗多节段脊髓型颈椎病的临床比较

目的:比较颈前路"杂交式"减压融合与颈后路全椎板减压侧块内固定术治疗多节段脊髓型颈椎病的临床特点。方法:选择36例行"杂交式"颈前路治疗及33例行颈后路全椎板减压侧块内固定术治疗的多节段脊髓型颈椎病患者,观察两组患者手术前后一般资料、出血量、手术时间、颈椎生理曲度、JOA评分及并发症的发生情况。结果:两组患者术前的一般资料包括年龄(颈前路组:56.23±7.64岁,颈后路组:55.76±8.18岁)、性别(颈前路组:22男/14女,颈后路组:20男/13女)、颈椎生理曲度D值(颈前路组:7.41±3.14,颈后路组:8.19±2.74)、JOA评分(颈前路组:9.08±1.09分,颈后路组:8.82±1.26分)、病程(颈前路组:17.24±7.36月,颈后路组:15.75±5.78月)和受累节段(颈前路组:3.11±0.26个,颈后路组:3.24±0.39个)比较差异均无统计学意义(P0.05)。与颈后路相比,颈前路的术中出血量(颈前路组:221.79±178.02 mL,颈后路组:483.07±434.25 mL)更少,差异有统计学意义(P0.05),手术时间(颈前路组:196.54±51.88 min,颈后路组:175.12±54.93 min)更长,但差异无统计学意义(P0.05)。随着时间的延长,颈前路组患者颈椎生理曲度和JOA评分逐渐增大,而颈后路组患者椎生理曲度减少,JOA评分逐渐增大,差异有统计学意义(P0.05)。颈前路组出现植骨未融合、声音嘶哑和脑脊漏液,颈后路组发生轴性疼痛和C5神经根麻痹,但两组患者并发症的发生率比较差异无统计学意义(颈前路组:13.89%,颈后路组:12.12%)(P0.05)。结论:颈前路"杂交式"减压融合与颈后路全椎板减压侧块内固定术在治疗多节段脊髓型颈椎病上各有优点,临床根据患者的情况而采取合适的治疗方式。     

Changing the convexity and concavity of nasal cartilages and cartilage grafts with horizontal mattress sutures: part I. Experimental results

Prior studies indicated that horizontal mattress sutures can control the curvature of a convex lateral crus. This study undertook to ascertain the ideal spacing for mattress sutures, determine what effect they have on the subsequent strength of the cartilage, and compare that to the resultant strength after scoring procedures used to control curvature. Curved fresh cadaver septa of various thicknesses (0.5, 1, and 1.5 mm) were used. The ideal spacing (gap between suture purchases) for the mattress suture was sought in 15 specimens. The consequent change in stiffness (modulus) of the cartilage was measured in nine other specimens before and after suture placement and after scoring. If the spacing was too large, instability resulted. If it was too small, curvature correction could not be obtained. An ideal mattress spacing (6 to 8 mm for 0.5-mm specimens and 8 to 10 mm for 1.5-mm specimens) removed most curvature and provided stability. The mattress suture increased the stiffness (modulus) above normal and far above that when the curvature was removed by scoring. The mean composite modulus before suturing was 4.6 MPa. After ideally spaced sutures, it was 6.2 MPa, a 35 percent increase in stiffness. After scoring to improve curvature, it was 2.4 MPa, a 48 percent reduction in stiffness (p = 0.02, Wilcoxon signed rank test). The horizontal mattress suture technique corrects cartilage curvature if the appropriate spacing is used. The corrected cartilage is stiffer/stronger than normal cartilage and much stiffer/stronger than if scored.     

Reconstruction of the STS 14 (Australopithecus africanus) pelvis

The study reports a reconstruction of the sacrum in STS 14 based on extrapolation from the measurements of the first two sacral vertebrae of STS 14 and of the angle formed by the anterior surfaces of their vertebral bodies. Reconstruction is based on comparisons of, and extrapolation from, sacra of Pan troglodytes, Homo sapiens, and Australopithecus afarensis. The reconstructed sacrum has an anterior sacral curvature of 39°. The two ossa coxae were also completed by mirror imaging of one side by the other. With the pelvis completely reconstructed, the pelvic dimensions for the antero-posterior (AP) diameters of the pelvic inlet, midpelvis, and pelvic outlet are 85, 68, and 69 mm and the corresponding transverse (TR) diameters are 109, 88, and 103 mm, respectively. The posterior sagittal diameters in the three pelvic planes are small compared to the anterior sagittal diameters. This analysis indicates that the STS 14 pelvis is platypelloid in the three pelvic planes; i.e., all the AP diameters are smaller than the corresponding TR diameters. This makes the STS 14 pelvis similar to that to Al 288-1, save for a less pronounced degree of platypelloidy at the inlet in the former. © 1995 Wiley-Liss, Inc.     

Growth related changes to functional parameters in the bovine lens.

Dimensions, volumes and protein contents were measured for bovine lenses with wet weights ranging from 0.17-3.07 g (2 months gestation to 19 years post-natal). All increase in a non-linear fashion. The lens becomes flatter with age due to a more rapid increase in the equatorial plane, but the ratio of anterior to posterior sagittal distances remains constant (1.19). The radius of curvature increases from 4.9 to 15 for the anterior surface and from 4.4 to 13 for the posterior. Protein content increases more rapidly than volume resulting in an increased average protein concentration from around 18% in the early prenatal lens to nearly 50% in the 19 year old. Total protein content (TPC) was found to be related to wet weight (We) according to the equation, TPC = 0.3We1.33. It is suggested that TPC is a better parameter for describing growth than wet weight or age. The refractive index, in the equatorial plane, increases towards the centre, from 1.38 at the edge of the lens. The maximum index, in the centre, increases with lens size up to 1.474 in the largest lens studied. This corresponds to a protein concentration of 70%. In all lenses, refractive index and protein concentration gradients were superimposable when plotted from the outside towards the centre. The optical performance of the lenses was assessed by measuring the back focal length which increases gradually from 24 to 51.5 mm over the 0.17 to 3.07 g size range. This was attributed to the increased radii of curvature.     

A methodology for quantifying seated lumbar curvatures

To understand the role seating plays in the support of posture and spinal articulation, it is necessary to study the interface between a human and the seat. However, a method to quantify lumbar curvature in commercially available unmodified seats does not currently exist. This work sought to determine if the lumbar curvature for normal ranges of seated posture could be documented by using body landmarks located on the anterior portion of the body. The development of such a methodology will allow researchers to evaluate spinal articulation of a seated subject while in standard, commercially available seats and chairs. Anterior measurements of boney landmarks were used to quantify the relative positions of the ribcage and pelvis while simultaneous posterior measurements were made of lumbar curvature. The relationship between the anterior and the posterior measures was compared. The predictive capacity of this approach was evaluated by determining linear and second-order regressions for each of the four postures across all subjects and conducting a leave-one-out cross validation. The relationships between the anterior and posterior measures were approximated by linear and second-order polynomial regressions (r(2?) = 0.829, 0.935 respectively) across all postures. The quantitative analysis showed that openness had a significant relationship with lumbar curvature, and a first-order regression was superior to a second-order regression. Average standard errors in the prediction were 5.9° for the maximum kyphotic posture, 9.9° for the comfortable posture, 12.8° for the straight and tall, and 22.2° for the maximum lordotic posture. These results show predictions of lumbar curvature are possible in seated postures by using a motion capture system and anterior measures. This method of lumbar curvature prediction shows potential for use in the assessment of seated spinal curvatures and the corresponding design of seating to accommodate those curvatures; however, additional inputs will be necessary to better predict the postures as lordosis is increased.     

Intramural mechanics of the human tongue in association with physiological deformations

Contraction of the tongue musculature during speech and swallowing is associated with characteristic patterns of tissue deformation. In order to quantify local deformation (strain) in the human tongue, we used a non-invasive NMR tagging technique that represents tissue as discrete deforming elements. Subjects were studied with a fast gradient echo pulse sequence (TR,TE 2.3/0.8 ms, slice thickness 10 mm, and effective spatial resolution 1.3x1.3 mm). Individual elements were defined by selectively supersaturating bands of magnetic spills in resting tongue tissue along the antero-posterior and superior inferior directions of the mid-sagittal plane, resulting in a rectilinear square grid. Axial and shear strains relative to the rest condition were determined for each clement and represented by two-dimensional surface strain maps. During forward protrusion, the anterior tongue underwent positive antero posterior strain (elongation) (maximum 200%) and symmetrical negative medial lateral and superior inferior strain (contraction). During sagittal curl directed to the hard palate, the tongue exhibited positive asymmetrical antero posterior strain (maximum 160%) that increased radially as a function of distance from the center of curvature (r = 0.9216, p<0.0005), and commensurate negative strain in the medial lateral direction. Similarly, the magnitude of anterior posterior strain during left-directed tongue curl was proportional to the distance from the curved inner surface (r = O.8978, p<0.0005). We conclude that the regulation of tongue position for the motions studied was related to regional activation of the intrinsic lingual musculature.     

Anterior femoral curvature: Its probable basis and utility as a criterion of racial assessment

Stewart ('62) and Walensky ('65) indicated that while the metrical expression of anterior femoral curvature alone will not always differentiate between Whites, American Negroes, and North American Indians, it was very useful as a racial criterion in combination with observed traits such as torsion, pilastry, and cross-sectional shape. Seven additional North American Indian groups reported here, representing both pre-Columbian and post-contact times, upheld the observation that anterior femoral curvature is a useful feature of racial assessment for Negroes, Whites and North American Indians. However, two South American groups studied (Ecuador and Peru) were only slightly more curved than American Negroes, and were less curved than Whites and North American Indians. The metrical expression of anterior femoral curvature therefore is not a useful feature of racial assessment for separating these two South American Indian groups from Whites and American Negroes. Femora of American Negro and White individuals with low ponderal indices were found to be less bowed than the norms for their race; individuals with high ponderal indices were more bowed than the norm for their race. The assumed genetic basis for expression of anterior femoral curvature suggested by Stewart ('62) and Walensky ('65) seems to be a feature of human plastic response to body weight rather than to temporal, clinal, postural or equestrian influences.     

Evolution of the flagellar waveform of ram spermatozoa in relation to the degree of epididymal maturation.

Motility and flagellar movement of ram spermatozoa along the epididymis were analysed in vitro. From the caput to the cauda of the epididymis, the percentage of motile and progressive spermatozoa increases. No flagellar bending was observed in spermatozoa from the testis or the epididymal anterior caput. When spermatozoa reached the distal caput of the epididymis, a static curvature, associated with an initiation of the flagellar beating, appeared on the flagella. This curvature normally disappeared during epididymal transit. Its disappearance was associated with an increase in the flagellar beat efficiency. Our results suggest that the initiation of motility is related to two mechanisms involving: (1) the presence of a transient static curvature, and (2) the establishment of a symmetric regular beating of the flagellum.     

Late pleistocene human femoral diaphyseal curvature

Anterior femoral curvature is a consistent characteristic of Pleistocene and recent humans, although variation exists in the degree of curvature among individuals and across populations. In particular, one group, the Neandertals, has been characterized for a century as having marked femoral curvature. To evaluate the degree of anterior femoral curvature in both Neandertals and other Late Pleistocene humans, their curvature subtenses and proximodistal positions were evaluated in the context of recent human variation. Recent human comparisons show little relationship between subtense (absolute curvature) and femoral length, suggesting that an index that incorporates subtense relative to the length of the femur is inappropriate for between-group assessments. Neandertals were statistically indistinguishable from Middle or earlier Upper Paleolithic modern humans in the degree of absolute curvature, all of whom had greater curvature on average than all later humans. Additionally, Neandertals and Qafzeh-Skhul early modern humans had a more distal point of maximum curvature than any other group. Curvature was not strongly correlated with functional considerations including body mass estimates, surrogate variables for body size, proximal femoral articular orientation, or knee anteroposterior dimensions. The functional role of femoral anterior curvature is unknown; however, the general decrease in curvature subtense closely parallels the between-group changes in inferred levels of mobility from femoral diaphyseal robusticity and shape, suggesting that femoral curvature may reflect mobility levels and patterns among Late Pleistocene and recent humans.     

MECHANICAL PROPERTIES WITHIN THE GROWTH ZONE OF CORN ROOTS INVESTIGATED BY BENDING EXPERIMENTS I. PRELIMINARY OBSERVATIONS

Bending experiments were performed to analyze mechanical properties within the apical 15 mm of the primary root of corn, Zea mays. Force required to maintain a root in a bent shape declined with the logarithm of time, indicating significant stress relaxation. Spatial distributions of local curvature, strain due to bending, and geometrical moment of inertia were calculated from digitized photographs of mechanically bent roots during and after imposition of a bending moment. When roots were bent to nonuniform curvature (maximum K = 3 cm^–1 at the location 8 mm from the root tip), “irreversible” curvature (residual curvature 4 hr after release of the bending moment) was approximately 44% of initial curvature. This percentage of irreversible curvature (and associated bending strain) was uniform throughout the growth zone. When roots were bent to uniform curvature of either 1 cm^–1 or 1.67 cm^–1, “springback” curvature (residual curvature after two minutes of bending) varied from 60% of initial curvature in the apical regions (at 4 mm) to 85% of initial curvature at the base of the growth zone. The results are consistent with a model in which total strain is proportional to stress, and irreversible strain at a particular location is proportional to total strain at the same location.     

Hierarchical processing of tactile shape in the human brain

It is not known exactly which cortical areas compute somatosensory representations of shape. This was investigated using positron emission tomography and cytoarchitectonic mapping. Volunteers discriminated shapes by passive or active touch, brush velocity, edge length, curvature, and roughness. Discrimination of shape by active touch, as opposed to passive touch, activated the right anterior lobe of cerebellum only. Areas 3b and 1 were activated by all stimuli. Area 2 was activated with preference for surface curvature changes and shape stimuli. The anterior part of the supramarginal gyrus (ASM) and the cortex lining the intraparietal sulcus (IPA) were activated by active and passive shape discrimination, but not by other mechanical stimuli. We suggest, based on these findings, that somatosensory representations of shape are computed by areas 3b, 1, 2, IPA, and ASM in this hierarchical fashion.     

A clinical and anatomical study of the location of the mental foramen in adult Chinese mandibles

One hundred mandibles of adult Chinese cadavers of both sexes without missing teeth, alveolar bone resorption and malposition of teeth were studied. The anatomical location of each mandibular mental foramen was measured by using a combination of three previous methods. Our results showed that the location of the mental foramen below the apex of the lower second premolar (relation IV: 58.98%) was the most common. On average, the distance between the most anterior portion of the anterior border of the mental foramen and the mandibular symphysis was 28.06 mm, between the most anterior portion of the anterior border of the mental foramen and the posterior border of the ramus 74.14 mm, between the inferior border of the mental foramen and the lower border of the mandibular body 14.70 mm, between the superior border of the mental foramen and the bottom of the lower second premolar socket 2.50 mm. The distance across the mental foramen between the alveolar crest and the lower border of the mandibular body was 30.29 mm. Our results were compared with those of other investigators. The significance of identifying the anatomical location of the mental foramen in dental practice is discussed.     

Ostium of the collection stem of the anterior cardiac veins (vv. cardiacae anteriores) in the vena cava, inferior

In 1 of 150 studied cases, we found the collection stem of anterior cardiac veins that emptied into the inferior vena cava. This collection stem had eight tributaries: two right atrial veins, five anterior cardiac veins and a right marginal vein. The caliber of the collection stem was increasing gradually from its beginning (2.8 mm) to its orifice (4.5 mm). The orifice of the collection stem was in the inferior vena cava, at a distance of 10 mm from its ostial valve, and was itself provided with a semilunar valve.     

Cone Beam Computed Tomography Assessment of the Maxillary Incisive Canal and Foramen: Considerations of Anatomical Variations When Placing Immediate Implants

IntroductionThe maxillary incisive canal connects the roof of the oral cavity with the floor of nasal cavity and has the incisive and nasal foramina respectively at its two opposite ends. Its close proximity with the anterior incisors affects one’s ability to place immediate implants in ideal position.ObjectiveTo avoid causing complication, variations in their dimensions were studied.ResultsThe mean labiopalatal and mesiodistal measurements of the incisive foramen were 2.80mm and 3.49 mm respectively, while the labiopalatal width of the nasal foramen was 6.06mm. The incisive canal was 16.33mm long and 3.85 mm wide. The anterior maxillary bone has an average thickness of 7.63 mm. The dimensions of the incisive foramen and incisive canal, and anterior maxillary bone thickness demonstrated gender differences with males showing greater values. The anterior maxillary bone thickness was affected by age but this difference was not observed in canal dimensions. The majority of subjects have a funnel shape-like incisive canal with the broader opening located at its superior. They seem to have a longer slanted-curve canal with one channel at its middle portion and a narrower incisive foramen opening than those reported elsewhere.ConclusionsThis study found that gender is an important factor that affected the characteristics of the IC and the amount of bone anterior to it. Male generally had bigger IC and thicker anterior bone. In addition, the anterior maxillary bone thickness was affected by aging, where it becomes thinner with increased age even though the subjects were fully dentate.     

Analysis of growth patterns during gravitropic curvature in roots ofZea mays by use of a computer-based video digitizer

A computer-based video digitizer system is described which allows automated tracking of markers placed on a plant surface. The system uses customized software to calculate relative growth rates at selected positions along the plant surface and to determine rates of gravitropic curvature based on the changing pattern of distribution of the surface markers. The system was used to study the time course of gravitropic curvature and changes in relative growth rate along the upper and lower surface of horizontally-oriented roots of maize (Zea mays L.). The growing region of the root was found to extend from about 1 mm behind the tip to approximately 6 mm behind the tip. In vertically-oriented roots the relative growth rate was maximal at about 2.5 mm behind the tip and declined smoothly on either side of the maximum. Curvature was initiated approximately 30 min after horizontal orientation with maximal (50°) curvature being attained in 3 h. Analysis of surface extension patterns during the response indicated that curvature results from a reduction in growth rate along both the upper and lower surfaces with stronger reduction along the lower surface.