Impact of lumbar spine posture on thoracic spine motion and muscle activation patterns

Complex motion during standing is typical in daily living and requires movement of both the thoracic and lumbar spine; however, the effects of lumbar spine posture on thoracic spine motion patterns remain unclear. Thirteen males moved to six positions involving different lumbar (neutral and flexed) and thoracic (flexed and twisted) posture combinations. The thoracic spine was partitioned into three segments and the range of motion from each posture was calculated. Electromyographical data were collected from eight muscles bilaterally. Results showed that with a flexed lumbar spine, the lower-thoracic region had 14.83° and 15.61° more flexion than the upper- and mid-thoracic regions, respectively. A flexed lumbar spine significantly reduced the mid-thoracic axial twist angle by 5.21° compared to maximum twist in the mid-thoracic region. Functional differences emerged across muscles, as low back musculature was greatest in maintaining flexed lumbar postures, while thoracic erector spinae and abdominals showed bilateral differences with greater activations to the ipsilateral side. Combined postures have been previously identified as potential injury modulators and bilateral muscle patterns can have an effect on loading pathways. Overall, changes in thoracic motion were modified by lumbar spine posture, highlighting the importance of considering a multi-segmented approach when analyzing trunk motion.     

Exploring the geometric and mechanical characteristics of the spine musculature to provide rotational stiffness to two spine joints in the neutral posture

Joint stiffness is inherently linked to both performance and injury. Muscular activation is the predominant provider of stiffness to the lumbar spine, and is essential to ensure optimal spine performance. The purpose of the current paper was to examine the potential of the trunk muscles to provide rotational joint stiffness at two spine joints in the neutral posture, and to demonstrate the sensitivity of this stiffening potential to various muscle orientation and stiffness assumptions. Two separate anatomical models were utilized to analyze the muscular contributions to the 3-dimensional rotational stiffness about each of the L1-L2 and L4-L5 spine joints. Total muscular stiffening potentials, for both joints in each anatomical model, were found to be highest about the global lateral bend axis, and lowest about the global axial twist axis. The stiffening potential was found to depend highly on both the assumed muscle stiffness coefficient (q value) and the moment arm of the muscle about the joint in question. Analyses of spine stiffness were found to be greatly affected by both the anatomical representation of the surrounding musculature and the selection of the q value in the determination of muscular stiffness. Inappropriate choices of either of these factors could lead to errors in stiffness and subsequently stability estimates, and in the interpretation and possible clinical recommendations stemming from such estimates.     

Three-dimensional angular kinematics of the lumbar spine and pelvis during running

The objective of this study were to: (i) describe the typical three-dimensional (3D) angular kinematics of the lumbar spine and pelvis during running and; (ii) assess whether the movements of the lumbar spine and pelvis during running are coordinated. A cohort of 20 non-injured male runners who usually ran >20 km/week were voluntarily recruited. All trials were conducted on a treadmill at a running speed of 4.0 m/second. Reflective markers were placed over anatomical landmarks of the thoraco-lumbar spine and pelvis. Data were captured using a VICON motion analysis system. The lumbar spine and pelvis both displayed complex 3D angular kinematic patterns during running. High correlations were found for the comparisons of flexion-extension of the lumbar spine with anterior-posterior tilt of the pelvis (r=-0.84) and lateral bend of the lumbar spine with obliquity of the pelvis (r=-0.75). However, a poor correlation was found for the comparison of axial rotation of the lumbar spine with axial rotation of the pelvis (r=0.37). A phase difference of 21% of the running cycle was evident between axial rotation of the lumbar spine and pelvis. The identified coordinated kinematic patterns of the lumbar spine and pelvis during running serve as a basis for future investigations exploring the relationship between atypical kinematic patterns and injury.     

Spatial and temporal characteristics of the spine muscles activation during walking in patients with lumbar instability due to degenerative lumbar disk disease: Evaluation in pre-surgical setting

Our purpose was to investigate the spatial and temporal profile of the paraspinal muscle activation during gait in a group of 13 patients with lumbar instability (LI) in a pre-surgical setting compared to the results with those from both 13 healthy controls (HC) and a sample of 7 patients with failed back surgery syndrome (FBSS), which represents a chronic untreatable condition, in which the spine muscles function is expected to be widely impaired.Spatiotemporal gait parameters, trunk kinematics, and muscle activation were measured through a motion analysis system integrated with a surface EMG device. The bilateral paraspinal muscles (longissimus) at L3-L4, L4-L5, and L5-S1 levels and lumbar iliocostalis muscles were evaluated.Statistical analysis revealed significant differences between groups in the step length, step width, and trunk bending and rotation. As regard the EMG analysis, significant differences were found in the cross-correlation, full-width percentage and center of activation values between groups, for all muscles investigated.Patients with LI, showed preserved trunk movements compared to HC but a series of EMG abnormalities of the spinal muscles, in terms of left-right symmetry, top-down synchronization, and spatiotemporal activation and modulation compared to the HC group. In patients with LI some of such EMG abnormalities regarded mainly the segment involved by the instability and were strictly correlated to the pain perception. Conversely, in patients with FBSS the EMG abnormalities regarded all the spinal muscles, irrespective to the segment involved, and were correlated to the disease’s severity. Furthermore, patients with FBSS showed reduced lateral bending and rotation of the trunk and a reduced gait performance and balance.Our methodological approach to analyze the functional status of patients with LI due to spine disease with surgical indications, even in more complex conditions such as deformities, could allow to evaluate the biomechanics of the spine in the preoperative conditions and, in the future, to verify whether and which surgical procedure may either preserve or improve the spine muscle function during gait.     

Multi-segmental thoracic spine kinematics measured dynamically in the young and elderly during flexion

In contrast to the cervical and lumbar region, the normal kinematics of the thoracic spine have not been thoroughly investigated. The aim of this study was to characterize normal multi-segmental continuous motion of the whole thoracolumbar spine, during a flexion maneuver, in young and elderly subjects. Forty-two healthy volunteers were analyzed: 21 young (age = 27.00 ± 3.96) and 21 elderly (age = 70.1 ± 3.85). Spinal motion was recorded with a motion-capture system and analyzed using a 3rd order polynomial function to approximate spinal curvature throughout the motion sequence. The average motion profiles of the two age groups were characterized. Flexion timing of the thoracic region of the spine, as compared to the lumbar spine and hips, was found to be different in the two age groups (p = 0.011): a delayed/sequential motion type was observed in most of the young, whereas mostly a simultaneous motion pattern was observed in the elderly subjects. A similar trend was observed in flexion of the lower thoracic segments (p = 0.017). Differences between age groups were also found for regional and segmental displacements and velocities. The reported characterization of the thoracic spine kinematics may in the future support identification of abnormal movement or be used to improve biomechanical models of the spine.     

Lumbar spine coordination during axial trunk rotation in adolescents with and without right thoracic idiopathic scoliosis

Adolescent idiopathic scoliosis (AIS) is a complex deformity that often leads to loss of coordination and dynamic posture. However, there is a lack of understanding on inter-segmental coordination in AIS. The purpose of this study was to compare spinal range of motion (ROM), as well as the relations to coupling angles (CA) in the spinal region during trunk rotation, between AIS and control subjects. There were 14 subjects with right thoracic AIS and 18 control subjects who participated in the study. All subjects were asked to perform five repeated axial trunk rotations in standing while holding a bar. The outcome measures included ROM at the first thoracic spinous process (T1), the seventh thoracic spinous process (T7), the twelfth thoracic spinous process (T12), and the first sacrum spinous tubercle (S1) by the motion capture system. The CA in each spinal region (trunk, lumbar spine, and lower and upper thoraces) were analyzed while considering age and body mass index (BMI). The Cobb angle demonstrated positive moderate relationships with ROM at T7 (r = 0.62, p = 0.04) and the CA in the upper thorax (r = 0.69, p = 0.02) in the AIS group. There was no CA difference at the spinous processes between groups; however, the lumbar spine ROM significantly decreased in the AIS group (t = 2.40, p = 0.02). The BMI demonstrated moderate relationships on the lumbar spine (r = −0.67, p = 0.02) in the AIS group and the lower thorax (r = 0.59, p = 0.01) in the control group. The lumbar spine was significantly dissociated in the AIS group during trunk rotation, although the Cobb angle demonstrated positive relationships with ROM at T7. Collectively, the inter-segmental CA indicated that the AIS group compensated more independently to the right thoracic convexity.Mini abstractThe coordinated trunk rotations in the adolescent idiopathic scoliosis (AIS) group were compared with the control subjects. The lumbar spine motion was dissociated with the thorax in the AIS group and was negatively correlated with body mass index. Clinicians need to consider thorax convexity and dissociated lumbar motion for compensatory and rehabilitation strategies.     

Gaze,head and eye movements during somersaults with full twists

Somersaults with or without twists are the most important elements in sports such as gymnastics or trampolining. Moreover, to perform elements with the highest possible difficulty gymnasts should show good form and execution during the flight phase. In order to ensure perfect body control and a safe landing, gaze behavior has been proven to be crucial for athletes to orientate in the air. As eye movement and head movement are closely coordinated, both must be examined while investigating gaze behavior. The aim of the current study is to analyze athletes' head motion and gaze behavior during somersaults with full twists. 15 skilled trampoline gymnasts performed back straight somersaults with a full twist (back full) on the trampoline. Eye movement and head movement were recorded using a portable eye-tracking device and a motion capture suit. The results indicate that gymnasts use the trampoline bed as a fixation point for orientation and control the back full, whereas the fixation onsets for athletes of a better performance class occur significantly later. A strong coordination between gymnasts' eye movement and head movement could be determined: stabilizing the gaze during the fixation period, the eyes move in combination with the head against the twisted somersault direction to counteract the whole body rotation. Although no significant differences could be found between the performance classes with regard to the maximum axial head rotations and maximum head extensions, there seems to be a trend that less skilled gymnasts need orientation as early as possible resulting in greater head rotation angles but a poorer execution.     

Spinal kinematics during gait in healthy individuals across different age groups

Most studies investigating trunk kinematics have not provided adequate quantification of spinal motion, resulting in a limited understanding of the healthy spine’s biomechanical behavior during gait. This study aimed at assessing spinal motion during gait in adolescents, adults and older individuals.Fourteen adolescents (10–18 years), 13 adults (19–35 years) and 15 older individuals (≥65 years) were included. Using a previously validated enhanced optical motion capture approach, sagittal and frontal plane spinal curvature angles and general trunk kinematics were measured during shod walking at a self-selected normal speed.Postural differences indicated that lumbar lordosis and thoracic kyphosis increase throughout adolescence and reach their peak in adulthood. The absence of excessive thoracic kyphosis in older individuals could be explained by a previously reported subdivision in those who develop excessive kyphosis and those who maintain their curve. Furthermore, adults displayed increased lumbar spine range of motion as compared to the adolescents, whereas the increased values in older individuals were found to be related to higher gait speeds. This dataset on the age-related kinematics of the healthy spine can serve as a basis for understanding pathological deviations and monitoring rehabilitation progression.     

Relationship between the movements of the lumbar spine and hip

Movements of the lumbar spine and hips were measured in 20 healthy subjects using an electromagnetic tracking device. Movement sensors were attached to the L1 spinous process, the sacrum and the thighs. Each subject was requested to perform the following movements of the trunk: forward and backward bending, lateral bending and twisting. The ratio of the maximum magnitude of spine movement to that of the hip was determined. Angle-angle plot and cross-correlation were used to examine the relationship between the movements of the spine and hip. It was shown that during forward and backward bending of the trunk, the overall contributions of the lumbar spine and hip were similar, but the spine had a greater contribution to the early stage of the movement. Lateral bending of the trunk was found to be primarily accomplished by movement of the spine, whereas the hips were the predominate sources of movement for twisting. Moreover, it was shown that in the sagittal and horizontal planes, the movement patterns of the spine and hip were in phase, whereas in the coronal plane, the spine generally moved earlier than the hips. It is concluded that clinical examination of the back should include kinematic measures of both the lumbar spine and hips.     

两种术式治疗腰椎管狭窄症的疗效分析

探讨后路椎弓根螺钉系统固定、Cage加自体骨椎间融合(PLIF)与传统术式(开窗减压、半椎板切除、全椎板截骨回植)治疗腰椎管狭窄症的疗效差异。2006年6月～2008年8月,对85例腰椎管狭窄症患者行传统术式减压(A组38例)、PLIF治疗(B组47例)。术后随访16个月～43个月,平均23个月。采用JOA评分评估疗效并行统计学分析。结果A组有效率78.94%,B组有效率95.74%。A组与B组比较,B组疗效优于A组,差异有统计学意义。因此,后路椎弓根螺钉系统固定、Cage加自体骨椎间融合治疗腰椎管狭窄症的疗效优于传统术式。     

The limits of aerial and contact techniques for producing twist in reverse 1½ somersault dives

An angle-driven computer simulation model of aerial movement was used to determine the maximum amount of twist that can be produced in a reverse 1½ somersault dive from a three-metre springboard using various aerial and contact twisting techniques. The segmental inertia parameters of an elite springboard diver were used in the simulations and lower bounds were placed on the durations of arm and hip angle changes based on recorded performances of twisting somersaults. A limiting dive was identified as that producing the largest possible odd number of half twists. Simulations of the limiting dives were found using simulated annealing optimisation to produce the required amounts of somersault, tilt and twist after a flight time of 1.5 s. Additional optimisations were then run to seek solutions with the arms less adducted during the twisting phase. It was found that the upper limits ranged from 3½ to 5½ twists with arm abduction ranges lying between 8° and 23°. Similar results were obtained when the inertia parameters of two other springboard divers were used. It may be concluded that a reverse 1½ somersault dive using aerial asymmetrical arm and hip movements to produce 5½ twists is a realistic possibility. To accomplish this limiting dive the diver needs to be able to coordinate the timing of configurational changes with the progress of the twist with a precision of 10 ms or better.     

Reference values and functional descriptions of transverse plane spinal dynamics during gait based on surface topography

Spinal dynamics during gait have been of interest in research for many decades. Based on respective previous investigations, the pelvis is generally expected to be maximally forward rotated on the side of the reference leg at the beginning of each gait cycle and to reach its maximum counterrotation approximately at the end of the reference leg’s stance phase. The pelvic–upper-thoracic-spine coordination converges towards an anti-phase movement pattern in high velocities during ambulation. The vertebral bodies around the seventh thoracic vertebra are considered to be an area of transition during human ambulation where no or at least little rotary motion can be observed. The respective cranial and caudal vertebrae meanwhile are expected to rotate conversely around this spinal point of intersection. However, these previous assumptions are based on scarce existing research, whereby only isolated vertebrae have been analyzed contemporaneously. Due to huge methodological differences in data capturing approaches, the results are additionally hardly comparable to each other and involved measurement procedures are often not implementable in clinical routines. Furthermore, none of the above-mentioned methods provided reference data for spinal motion during gait based on an appropriate number of healthy participants. Hence, the aim of this study was to present such reference data for spinal rotary motion of every vertebral body from C7 down to L4 and the pelvis derived from surface topographic back shape analyses in a cohort of 201 healthy participants walking on a treadmill at a given walking speed of 5 km/h. Additionally, the spine‘s functional movement behavior during gait should be described in the transverse plane based on data derived from this noninvasive, clinically suitable measurement approach and, in conclusion, the results shall be compared against those of previous research findings derived from other measurement techniques. Contrary to the previous functional understanding, the area of the mid-thoracic spine was found to demonstrate the largest amplitude of rotary motion of all investigated vertebrae and revealed an approximately counterrotated movement behavior compared to the rotary motion of the pelvis. In both directions, spinal rotation during gait seemed to be initiated by the pelvis. The overlying vertebrae followed in succession in the sense of an ongoing movement. Therefore, the point of intersection was not statically located in a specific anatomical section of the spine. Instead, it was found to be dynamic, ascending from one vertebra to the next from caudal to cranial in dependence of the pelvis’s rotation initiation.     

Intersegmental dynamics of 3D upper arm and forearm longitudinal axis rotations during baseball pitching

The shoulder internal rotation (IR) and forearm pronation (PR) are important elements for baseball pitching, however, how rapid rotations of IR and PR are produced by muscular torques and inter-segmental forces is not clear. The aim of this study is to clarify how IR and PR angular velocities are maximized, depending on muscular torque and interactive torque effects, and gain a detailed knowledge about inter-segmental interaction within a multi-joint linked chain. The throwing movements of eight collegiate baseball pitchers were recorded by a motion capture system, and induced-acceleration analysis was used to assess the respective contributions of the muscular (MUS) and interactive torques associated with gyroscopic moment (GYR), and Coriolis (COR) and centrifugal forces (CEN) to maximum angular velocities of IR (MIRV) and PR (MPRV). The results showed that the contribution of MUS account for 98.0% of MIRV, while that contribution to MPRV was indicated as negative (−48.1%). It was shown that MPRV depends primarily on the interactive torques associated with GYR and CEN, but the effects of GYR, COR and CEN on MIRV are negligible. In conclusion, rapid PR motion during pitching is created by passive-effect, and is likely a natural movement which arises from 3D throwing movement. Applying the current analysis to IR and PR motions is helpful in providing the implications for improving performance and considering conditioning methods for pitchers.     

Arm position influences the activation patterns of trunk muscles during trunk range-of-motion movements

To understand the activation patterns of the trunk musculature, it is also important to consider the implications of adjacent structures such as the upper limbs, and the muscles that act to move the arms. This study investigated the effects of arm positions on the activation patterns and co-activation of the trunk musculature and muscles that move the arm during trunk range-of-motion movements (maximum trunk axial twist, flexion, and lateral bend). Fifteen males and fifteen females, asymptomatic for low back pain, performed maximum trunk range-of-motion movements, with three arm positions for axial twist (loose, crossed, abducted) and two positions for flexion and lateral bend (loose, crossed). Electromyographical data were collected for eight muscles bilaterally, and activation signals were cross-correlated between trunk muscles and the muscles that move the arms (upper trapezius, latissimus dorsi). Results revealed consistently greater muscle co-activation (higher cross-correlation coefficients) between the trunk muscles and upper trapezius for the abducted arm position during maximum trunk axial twist, while results for the latissimus dorsi-trunk pairings were more dependent on the specific trunk muscles (either abdominal or back) and latissimus dorsi muscle (either right or left side), as well as the range-of-motion movement. The findings of this study contribute to the understanding of interactions between the upper limbs and trunk, and highlight the influence of arm positions on the trunk musculature. In addition, the comparison of the present results to those of individuals with back or shoulder conditions may ultimately aid in elucidating underlying mechanisms or contributing factors to those conditions.     

Walking breaks can reduce prolonged standing induced low back pain

Standing is commonly recommended to reduce sedentary behavior in the workplace; however, constrained prolonged standing has also been linked to musculoskeletal symptoms, such as low back pain (LBP). Light physical activity breaks, such as walking, may change lumbar spine posture enough to reduce LBP during standing. This study assessed the effectiveness of inserting 5-minute walking breaks every 25 min for reducing prolonged standing-induced LBP development. Nineteen participants completed two bouts of standing lasting 2 h – one with a 5-minute walking break every 25 min and one with no breaks. Pain measures were completed throughout the trial to categorize participants as pain developers (PDs) or non-pain developers (non-PDs). Lumbar region kinematics angle and range of motion were measured continuously. In standing, 58% (11/19) of participants were PDs, compared to just 26% when walking breaks were inserted. Seventy-three percent (8/11) were categorized as non-PDs with walking breaks. Median lumbar flexion increased during walking compared to standing. Lumbar region range of motion in the coronal and transverse planes also increased during walking. The intermittent lumbar flexion may help decrease LBP during prolonged standing. These results demonstrate that walking breaks may help promote lumbar movement and reduce prolonged standing-induced LBP.     

Spatial attention: different mechanisms for central and peripheral temporal precues?

The external noise paradigm (Z.-L. Lu & B. A. Dosher, 1998) was applied to investigate mechanisms of spatial attention in location precuing. Observers were precued or simultaneously cued to identify 1 of 4 pseudocharacters embedded in various amounts of external noise. The cues were either central or peripheral. Both central and peripheral precuing significantly reduced threshold in the presence of high external noise (16% and 17.5%). Only peripheral precuing significantly reduced threshold in the presence of low, or no, external noise (11%). A perceptual template model identified different mechanisms of attention for central and peripheral precuing, external noise exclusion for central precuing, and a combination of external noise exclusion and stimulus enhancement (or equivalently, internal additive noise reduction) for peripheral cuing.     

Consistency of vertebral motion and individual characteristics in gait sequences

Vertebral motion reveals complex patterns, which are not yet understood in detail. This applies to vertebral kinematics in general but also to specific motion tasks like gait. For gait analysis, most of existing publications focus on averaging characteristics of recorded motion signals. Instead, this paper aims at analyzing intra- and inter-individual variation specifically and elaborating motion parameters, which are consistent during gait cycles of particular persons. For this purpose, a study design was utilized, which collected motion data from 11 asymptomatic test persons walking at different speed levels (2, 3, and 4 km/h). Acquisition of data was performed using surface topography. The motion signals were preprocessed in order to separate average vertebral orientations (neutral profiles) from basic gait cycles. Subsequently, a k-means clustering technique was applied to figure out, whether a discrimination of test persons was possible based on the preprocessed motion signals. The paper shows that each test sequence could be assigned to the particular test person without additional prior information. In particular, the neutral profiles appeared to be highly consistent intra-individually (across the gait cycles as well as speed levels), but substantially different between test persons. A full discrimination of test persons was achieved using the neutral profiles with respect to flexion/extension data. Based on this, these signals can be considered as individual characteristics for the particular test persons.     

The coordinated movement of the spine and pelvis during running

Previous research into running has demonstrated consistent patterns in pelvic, lumbar and thoracic motions between different human runners. However, to date, there has been limited attempt to explain why observed coordination patterns emerge and how they may relate to centre of mass (CoM) motion. In this study, kinematic data were collected from the thorax, lumbar spine, pelvis and lower limbs during over ground running in n = 28 participants. These data was subsequently used to develop a theoretical understanding of the coordination of the spine and pelvis in all three body planes during the stance phase of running. In the sagittal plane, there appeared to be an antiphase coordinate pattern which may function to increase femoral inclination at toe off whilst minimising anterior–posterior accelerations of the CoM. In the medio-lateral direction, CoM motion appears to facilitate transition to the contralateral foot. However, an antiphase coordination pattern was also observed, most likely to minimise unnecessary accelerations of the CoM. In the transverse plane, motion of the pelvis was observed to lag slightly behind that of the thorax. However, it is possible that the close coupling between these two segments facilitates the thoracic rotation required to passively drive arm motion. This is the first study to provide a full biomechanical rationale for the coordination of the spine and pelvis during human running. This insight should help clinicians develop an improved understanding of how spinal and pelvic motions may contribute to, or result from, common running injuries.     

Coordination and timing of spine and hip joints during full body reaching tasks

Coupling of spine and hip joints during full body reaching tasks was investigated in 16 participants (8 male and 8 female) who performed reaching tasks at comfortable and fast-paced movement speeds to three targets located in a para-sagittal plane. The participants paused at target contact for 500ms and then returned to an upright posture. Three-dimensional joint motions of the spine and hip were recorded using an electromagnetic tracking device. We found an effect of movement phase (i.e., reach and return) on the onset timing of the spine and hip joints. For most target locations and movement speeds, spine motion onset preceded hip motion onset during the reaching phase of the movement task. In the reach phase, when averaged across all movement conditions, spine joint motion preceded hip joint motion by an average of 48.9ms. In contrast, in the return phase, hip joint motion preceded spine joint motion by an average of 63.0ms. Additionally, when participants were instructed to use either a knee flexion or knee extension strategy to perform the reaching tasks there was no effect of movement strategy on timing of the spine and hip. There was also no effect of target height on the spine-hip ratio, but as movement speed increased, the spine/hip ratio decreased for all target locations due primarily to an increase in hip joint excursion. The findings indicate clear differences in onset timing of the spine and hip joints during reaching tasks that necessitate some forward bending of the trunk and that onset timing is reversed for the return to an upright posture.     

The Fusion Frequency in Different Areas of the Visual Field: III. Foveal Fusion Frequency and the Light-Dark Ratio for Constant Retinal Illumination at Fusion

An investigation was performed, with the use of 60 male and female college students, to quantify the Chevreul pendulum illusory effect, the tendency of a small pendulum, when suspended from the hand and imaginatively concentrated upon, to oscillate seemingly of its own accord. By means of a time exposure photographic measurement technique, strong parametric influences of the pendulum's sinusoidal motion were isolated. It was found that the pendulum effect was enhanced when (a) attentional capacity remained undivided, (b) the amount of musculature used to suspend the pendulum was at a maximum, (c) oscillating visual and auditory external stimuli were present, and (d) females were Ss. In addition, the visual stimulus was found to be superior to its auditory counterpart. The relevance of ideomotor and visual capture interpretations of covert muscle processes in the pendulum illusion was discussed.