Article

Defining the medial-lateral axis of an anatomical femur coordinate system using freehand 3D ultrasound imaging

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Abstract

Hip rotation from gait analysis informs clinical decisions regarding correct of femoral torsional deformities. However, it is among the least repeatable due to discrepancies in determining the medial-lateral axis of the femur. Conventional or functional calibration methods may be used to define the axis but there is no benchmark to evaluate these methods. Freehand 3D ultrasound, the coupling of ultrasound with 3D motion capture, may provide such a benchmark.We measured the accuracy in vitro and repeatability in vivo of determining the femur condylar axis from freehand 3D ultrasound. The condylar axis provided the reference medial-lateral axis of the femur and was used to evaluate one conventional method and three functional calibration methods, applied to three calibration movements. Ten healthy subjects (20 limbs) underwent 3D gait analysis and freehand 3D ultrasound. The functional calibration methods were a transformation technique, a geometrical method and a method that minimises variance of knee varus-valgus kinematics (DynaKAD). The conventional method used markers over the femoral epicondyles. The condylar axis determined by ultrasound showed good accuracy in vitro, 1.6° (SD: 0.3°) and good repeatability in vivo, 0.2° (RSMD: 2.3°). The DynaKAD method applied to the walking calibration movement determined the medial-lateral axis closest to the ultrasound reference. The average angular difference in the transverse plane was 3.1° (SD: 6.1°). Freehand 3D ultrasound offers an accurate, non-invasive and relatively fast method to locate the medial-lateral axis of the femur for gait analysis.

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... Recognizing that the body-fixed axes must coincide with the functional axes to obtain clinically meaningful tibiofemoral kinematics, methods to locate the functional axes are of interest. Because a detailed review of these methods is not the purpose of this paper and because such reviews and/or comparisons of methods have been provided by other papers (Ehrig et al., 2007;MacWilliams, 2008;Passmore and Sangeux, 2016;Schache et al., 2006), an overview of available methods will be described here and appropriate papers cited. Aside from conventional methods which place external markers over the medial and lateral femoral epicondyles or attach a knee alignment device to the femoral epicondyles, all other methods to locate the functional axes impose a movement of the knee, measure the resulting motion by various means, and analyze the resulting motion to determine the functional axes. ...
... A second difficulty with using video-based motion tracking of skin-mounted markers concerns the soft tissue artifact. For video-based tracking of skin-mounted markers, several validation studies using various functional methods concluded that the Dyna-KAD method of analysis (Baker et al., 1999) gives a medial-lateral femoral axis which best approximates the functional FE axis (Passmore and Sangeux, 2016;Sauret et al., 2016;Schache et al., 2006). Although the DynaKAD method was best for approximating the functional FE axis, nevertheless the variability in the mediallateral axis generated by the DynaKAD method was relatively large exceeding 15° (Passmore and Sangeux, 2016;Sauret et al., 2016). ...
... For video-based tracking of skin-mounted markers, several validation studies using various functional methods concluded that the Dyna-KAD method of analysis (Baker et al., 1999) gives a medial-lateral femoral axis which best approximates the functional FE axis (Passmore and Sangeux, 2016;Sauret et al., 2016;Schache et al., 2006). Although the DynaKAD method was best for approximating the functional FE axis, nevertheless the variability in the mediallateral axis generated by the DynaKAD method was relatively large exceeding 15° (Passmore and Sangeux, 2016;Sauret et al., 2016). This variability is undesirable because misalignment of the medial-lateral axis with the functional FE axis will introduce kinematic crosstalk errors as noted above. ...
Article
The relative rigid body motions between the femur and the tibia (termed tibiofemoral kinematics) during flexion activities can provide an objective measure of knee function. Physiologic tibiofemoral kinematics are defined as the six relative rigid body motions expressed in a joint coordinate system where the motions about and along the axes conform to clinical definitions and are free from kinematic crosstalk errors. To obtain physiologic tibiofemoral kinematics, coordinate systems must meet certain requirements which neither have been explicitly stated nor in fact satisfied in any previous publication known to the author. Starting with the joint coordinate system of Grood and Suntay (Grood and Suntay, 1983) where motions conform to clinical definitions, the body-fixed axes must correspond to the functional (i.e. actual) axes in flexion-extension and internal-external axial rotation and both functional axes must be body-fixed throughout knee flexion to avoid kinematic crosstalk errors in rotations. To avoid kinematic crosstalk errors in translations, the origins of the femoral and tibial Cartesian coordinate systems, which serve as stepping stones for computing translations, must lie on the body-fixed functional axes. Neither the paper by Grood and Suntay nor the ISB recommendation (Wu et al., 2002) which adopted the joint coordinate system of Grood and Suntay explains these requirements. Indeed meeting these requirements conflicts with the ISB recommendation thus indicating the need for revision to this recommendation. Future studies where physiologic tibiofemoral kinematics are of interest should be guided by the requirements described herein.
... Functional calibration offers an alternative to determine the medio-lateral axis for gait analysis (Passmore and Sangeux, 2016). Contrary to conventional models, functional calibration does not rely on bony landmarks but uses the movement of the tibia with respect to the femur to determine the knee axis, which is used as a proxy for the medio-lateral axis of the femur either explicitly e.g. ...
... Recent studies have provided results on functional calibration accuracy in healthy subjects with respect to an anatomical medio-lateral axis defined from freehand 3D ultrasound (Passmore and Sangeux, 2016) or from bi-plane x-ray imaging (Sauret et al., 2016). However, the results of these studies could not differentiate between the impact of the underlying knee model and the impact of STA at the thigh and shank segments. ...
... We used data from three consecutive strides in the centre of the walking trial (Passmore and Sangeux, 2016). The Cardan angles for the movement of the femur, tibia and knee (i.e. ...
Article
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Functional calibration methods were devised to improve repeatability and accuracy of the knee flexion-extension axis, which is used to define the medio-lateral axis of the femur coordinate system in gait analysis. Repeatability of functional calibration methods has been studied extensively in healthy individuals, but not accuracy in the absence of a benchmark knee axis. We captured bi-plane fluoroscopy data of the knee joint in 19 subjects with unilateral total knee arthroplasty during treadmill walking. The prosthesis provided a benchmark knee axis to evaluate the functional calibration methods. Stereo-photogrammetry data of thigh and shank marker clusters were captured simultaneously to investigate the effect of soft tissue artefact (STA). Three methods were tested, the Axis Transformation Technique (ATT) finds the best single fixed axis of rotation, 2DofKnee finds the axis that minimises knee varus-valgus and trajAJC finds the axis perpendicular to the trajectory, in the transverse plane of the femur, of a point located on the longitudinal axis of the tibia. Using fluoroscopy data, functional axes formed an angle of less than 2° in the transverse plane with the benchmark axis. True internal-external range of movement was correlated with decreased accuracy for ATT, while varus-valgus range of movement was correlated with decreased accuracy for 2DofKnee and trajAJC. STA had negative impact on accuracy and variability. Using stereo-photogrammetry data, the accuracy of 2DofKnee was 1.7°(SD: 5.1°), smaller than ATT 2.9°(SD: 5.1°) but not to trajAJC 1.7°(SD: 5.2°). Our results confirm that of previous studies, which utilised the femur condylar axis as reference.
... • A technique called DynaKAD has been proposed to define the thigh rotation offset by minimising the varus-valgus movement during the walking trial. Other techniques have been used suggested to define this from functional calibration trials (Schwartz and Rozumalski 2005;Sauret et al. 2016;Passmore and Sangeux 2016). • VCM and PiG introduced an angular offset along the tibia such that knee rotation is defined as being zero during a static trial when the KAD is used and the orientation of the ankle joint axis is defined by a measurement of tibial torsion made during the physical exam (rather than the tibial wand marker). ...
... Accuracy. Whilst the CGM has been subjected to several studies to investigate its repeatability there have been very few studies of its accuracy and those have focussed on very specific issues such as the location of the hip joint centre location Peters et al. 2012;Sangeux et al. 2011) and orientation of the knee flexion axis (Sauret et al. 2016;Passmore and Sangeux 2016) in standing. The model is intended to track the movements of the bones and there have been no studies performed to establish how accurately it can do this. ...
... Future versions should be adequately validated in line with a modern understanding of clinical best practice. At a minimum this should include evidence of reproducibility of results but it would also be useful to have accuracy established with reference to a variety of static and dynamic imaging techniques such as 3-d ultrasound (Peters et al. 2010;Hicks and Richards 2005;Passmore and Sangeux 2016), low intensity biplanar x-rays Sangeux et al. 2014;Sauret et al. 2016) or fluoroscopy (Tsai et al. 2009;Akbarshahi et al. 2010). There should also be publication of benchmark data with which services can compare their own to ensure consistency (Pinzone et al. 2014) and streamlined processed for conducting in-house repeatability studies would also be extremely useful. ...
Chapter
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The Conventional Gait Model (CGM) is a generic name for a family of closely related and very widely used biomechanical models for gait analysis. After describing its history, the core attributes of the model are described followed by evaluation of its strengths and weaknesses. An analysis of the current and future requirements for practical biomechanical models for clinical and other gait analysis purposes which have been rigorously calibrated suggests that the CGM is better suited for this purpose than any other currently available model. Modifications are required, however, and a number are proposed.
... However, the precision of hip rotation kinematics has raised concerns because it is one of the least repeatable parameters in clinical gait analysis (McGinley et al., 2009;Schache et al., 2006;Schwartz et al., 2004). The lack of repeatability in hip rotation kinematics is primarily attributed to difficulty in determining the secondary axis used to define the femoral coordinate system (Passmore and Sangeux, 2016;Schache et al., 2006). This secondary axis directly affects the medial-lateral axis of the femoral coordinate system which is formed orthogonal to the primary axis (knee joint centre (KJC) to hip joint centre (HJC)) and the cross product of the primary and secondary axes. ...
... Validation has largely been limited to evaluation on synthetic data, mechanical models and cadaver simulations (Cereatti et al., 2009;Chang and Pollard, 2007;Ehrig et al., 2007;MacWilliams, 2008). More recent studies have evaluated their performance in vivo but this has been limited to typically developing adults (Passmore and Sangeux, 2016;Sauret et al., 2016) and older adults post total knee arthroplasty (Sangeux et al., 2017). ...
... In vivo evaluation used either freehand 3D ultrasound imaging or biplanar radiographs (Passmore and Sangeux, 2016;Sauret et al., 2016). Both methods define a bone fixed coordinate system registered with respect to the skin markers during a static standing pose. ...
Article
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Hip rotation during gait is a major indicator for femoral derotation osteotomy. However, repeatability of hip rotation is poor because of discrepancies in determining the medial-lateral axis of the femur. Combining 3D gait analysis with medical imaging allows in vivo evaluation of current clinical methods. We used the condylar axis, identified from low dose biplanar radiographs (EOS imaging Inc), as our reference to evaluate conventional, functional calibration and freehand 3D ultrasound methods to define the medial-lateral axis in children with lower-limb torsional deformities.Twenty participants underwent 3D gait analysis accompanied by freehand 3D ultrasound and biplanar radiographs. The condylar axis identified from biplanar radiographs provided the reference method used to construct the femoral coordinate system. This was used to evaluate a conventional, two functional calibration methods (axis transformation technique and 2DoFKnee) and freehand 3D ultrasound. We measured reliability of 3D localisation of skin markers and anatomical landmarks from the biplanar radiographs.Localisation of skin markers (SD 0.4 mm) and anatomical landmarks (SD 1.3 mm) from the biplanar radiographs were reliable, leading to a precision of 1° for the condylar axis after registration in the motion capture system. The freehand 3D ultrasound produced similar results to the biplanar radiographs reference, with internal hip rotation during gait of 18° and 19° respectively. The conventional and functional calibration methods were predominantly external compared to the reference, with average hip rotation of 4-6° internal.Freehand 3D ultrasound and biplanar radiographs provide reliable means to define the medial-lateral axis of femur for gait analysis, and aid clinical interpretation in children with torsional deformities.
... The latter has been identified as the largest source of extrinsic variability between measurements [7,8]. Multiple methods have been proposed to correct this source of errors such as: palpation methods [9], real-time feedback methods [10,11], external devices [12,13], fusion with static 3D medical imaging [14,15] and dynamic 3D imaging such as bi-plane fluoroscopy [16,17]. ...
... This method could potentially remove the extrinsic variability due to external marker misplacement but it will not address the issue of soft tissue artefacts. To our knowledge, bi-plane X-rays has only been used as a gold standard to validate marker-based methods that identify anatomical landmarks [14,20,21] but its potential to reduce the variability due to external marker misplacements has not been assessed yet. ...
... Thus, skin markers taped on the lateral side of the patients are often not visible. An alternative would be to use a different markerset or a different imaging technique such as 3D ultrasound [14]. ...
Article
Full-text available
In clinical gait analysis, measurement errors impede the reliability and repeatability of the measurements. This extrinsic variability can potentially mislead the clinical interpretation of the analysis and should thus be minimised. Skin marker misplacement has been identified as the largest source of extrinsic variability between measurements. The goal of this study was to test whether the fusion of motion capture and 3D medical imaging could reduce extrinsic variability due to skin marker misplacement. The fusion method consists in using anatomical landmarks identified with 3D medical imaging to correct marker misplacements. To assess the reduction of variability accountable to the fusion method, skin marker misplacements were voluntarily introduced in the measurement of the pelvis and hip kinematics during gait for two patients scheduled for unilateral hip arthroplasty and two patients that underwent unilateral hip arthroplasty. The root mean square deviation was reduced by -78 ± 15% and the range of variability by -80 ± 16% for the pelvis and hip kinematics in average. These results showed that the fusion method could significantly reduce the extrinsic variability due to skin marker misplacement and thus increase the reliability and repeatability of motion capture measurements. However, the identification of anatomical landmarks via medical imaging is a new source of extrinsic variability that should be assessed before considering the fusion method for clinical applications.
... Thirteen out of the 31 papers explicitly named calibration movements of which five reported calibration from gait trials [22][23][24][25][26]. A few studies [25][26][27][28] additionally compared knee flexion, walking, squatting, and stair climbing as calibration movements. ...
... Thirteen out of the 31 papers explicitly named calibration movements of which five reported calibration from gait trials [22][23][24][25][26]. A few studies [25][26][27][28] additionally compared knee flexion, walking, squatting, and stair climbing as calibration movements. Out of the studies investigating and discussing several functional calibration motions [11,25,27,28], squatting was shown to bring less knee varus-valgus variability when compared to walking and knee flexion [11], while walking [25] and passive knee flexion-extension [27] were in turn described as the methods yielding the results closest to the gold standard in use, ultrasound or biplanar radiographs, respectively, when compared to other calibration movements (walking vs flexion and squats [25], passive vs active flexion-extension and walking [27]). ...
... A few studies [25][26][27][28] additionally compared knee flexion, walking, squatting, and stair climbing as calibration movements. Out of the studies investigating and discussing several functional calibration motions [11,25,27,28], squatting was shown to bring less knee varus-valgus variability when compared to walking and knee flexion [11], while walking [25] and passive knee flexion-extension [27] were in turn described as the methods yielding the results closest to the gold standard in use, ultrasound or biplanar radiographs, respectively, when compared to other calibration movements (walking vs flexion and squats [25], passive vs active flexion-extension and walking [27]). ...
Article
Background Attempts to improve protocol standards of marker-based clinical gait analysis (CGA) have been one of the main focuses of research to enhance robustness and reliability outcomes since the 1990s. Determining joint centers and axes constitutes an important aspect of those protocols. Although the hip joint is more prominent in such studies, knee joint center (KJC) and axis (KJA) directly affect all outcomes. Research question What recommendations arise from the study of the scientific literature for determining knee joint parameters (KJP) for protocols of CGA? Methods A systematic, electronic search was conducted on November 2018 using three databases with the keyword combination (“functional approach” OR “functional method” OR “functional calibration”) AND (“hip joint” OR “knee joint” OR “ankle joint”) and analyzed by four reviewers. Given the existence of a recent review about the hip joint and the lack of material about the ankle joint, only papers about the knee joint were kept. The references cited in the selected papers were also screened in the final round of the search for these publications. The quality of the selected papers was assessed and aspects regarding accuracy, repeatability, and feasibility were thoroughly considered to allow for a comparison between studies. Technical aspects, such as marker set choice, KJP determination techniques, demographics, and functional movements, were also included. Results Thirty-one papers were included and on average received a rating of about 75% according to the quality scale used. The results showed that functional methods are superior or equivalent to predictive methods to estimate the KJA, while a regression method was slightly better for KJC prediction. Significance Calibration methods should be applied to CGA whenever feasibility is reached. No study to date has focused on evaluating the in vivo RoM required to obtain reliable and repeatable results and future work should aim in this direction.
... This information is particularly critical when planning surgical procedures such as derotation osteotomies [42]. We have used freehand 3D ultrasound imaging to determine the medial-lateral axis of an anatomical based femur coordinate system [43]. The mediallateral axis was defined using the condylar axis. ...
... Many studies have used this technique to measure muscle fibre lengths, pennation angles, muscle thickness and tendon strains in isolated muscles during static and dynamic movements [15,57]. Adapted from Passmore and Sangeux [43] Due to their relatively superficial location, the ankle plantar-flexor muscles, consisting of the soleus, medial gastrocnemius and lateral gastrocnemius, are the most frequently imaged muscles in the body. The ankle plantar-flexors connect to the Achilles tendon, which is known to be important for efficient movement and optimal performance due to its ability to store substantial amounts of elastic strain energy. ...
Article
Full-text available
Ultrasound imaging is relatively inexpensive, does not involve ionising radiation, and requires much shorter scan times compared with other imaging modalities such as magnetic resonance imaging and computed tomography. These advantages make it an appealing option in both clinical and research settings. Computational models of the human musculoskeletal system are used for a wide range of applications in biomechanics, from studies of muscle function during locomotion to pre-operative planning of orthopaedic surgeries. The integration of ultrasound imaging with musculoskeletal modelling has the potential to create new opportunities in the study of human movement science. Subject-specific measures of muscle–tendon properties and bone geometry obtained from ultrasound imaging are now being used in conjunction with detailed models of the musculoskeletal system to better understand muscle–tendon function during normal and pathological movement. This approach also allows more rigorous validation studies to be performed to quantify the accuracy of musculoskeletal modelling predictions. We have been using ultrasound imaging to create subject-specific models of the human musculoskeletal system for the purpose of simulating normal and pathological gait. This review describes our experiences in using ultrasound imaging to measure muscle–tendon architecture and bone geometry in vivo. Recent studies focused on integrating ultrasound imaging and musculoskeletal modelling to determine muscle–tendon function in human walking and running are also described.
... The ATT functional method was more external (average mean: 12°, average SD: 5.5°) than the reference BPR-based TCA. Overall, our results were in agreement with a recent study using 3D freehand ultrasound (rather than BPR) to locate the TCA axis [29]. ...
... Hence, EOS biplanar radiographs or an alternative medical image based technology (e.g. 3D freehand ultrasound, [29]) may still be required when major surgical decision, such as derotational osteotomies, depend on the reliable orientation of the frontal plane of the femur and accurate hip rotation kinematics. ...
Article
Full-text available
Accurate calibration of the medio-lateral axis of the femur is crucial for clinical decision making based on gait analysis. This study proposes a protocol utilizing biplanar radiographs to provide a reference medio-lateral axis based on the anatomy of the femur. The biplanar radiographs allowed 3D modelling of the bones of the lower limbs and the markers used for motion capture, in the standing posture. A comprehensive analysis was performed and results from biplanar radiographs were reliable for 3D marker localization (±0.35 mm) and for 3D localization of the anatomical landmarks (±1 mm), leading to a precision of 1° for the orientation of the condylar axis of the femur and a 95% confidence interval of ±3° after registration with motion capture data. The anatomical condylar axis was compared to a conventional, marker-based, axis and three functional calibration techniques (axis transformation, geometric axis fit and DynaKAD). Results for the conventional method show an average difference with the condylar axis of 15° (SD: 6°). Results indicate DynaKAD functional axis was the closest to the anatomical condylar axis, mean: 1° (SD: 5°) when applied to passive knee flexion movement. However, the range of the results exceeded 15° for all methods. Hence, the use of biplanar radiographs, or an alternative imaging technique, may be required to locate the medio-lateral axis of the femur reliably prior to clinical decision making for femur derotational osteotomies.
... A validation analysis on ground truth objects by means of US-PaP was previously performed and had excellent accuracy (Cenni et al. 2016b). The same method has also been applied to improve the precision of participant-specific modeling of the human musculoskeletal system in 3-D gait (Passmore and Sangeux 2016). This approach reduces the processing time, as only the linear distances between the relevant anatomic landmarks need to be calculated. ...
... Another advantage of the US-PaP method is that it is not limited to extracting MG MTU lengths. A variation of this method was to improve the precision of participant-specific modeling of the human musculoskeletal system in 3-D gait analysis (Passmore and Sangeux 2016). Furthermore, an ongoing investigation in our research unit is using the US-PaP method to identify anatomic landmarks as reference points while tracking the MG MTJ during passive ankle motion ( Bar-on et al. 2016;Cenni et al. 2016a). ...
Article
A clinically feasible method to reliably estimate muscle-tendon unit (MTU) lengths could provide essential diagnostic and treatment planning information. A 3-D freehand ultrasound (3-DfUS) method was previously validated for extracting in vivo medial gastrocnemius (MG) lengths, although the processing time can be considered substantial for the clinical environment. This investigation analyzed a quicker and simpler method using the US transducer as a spatial pointer (US-PaP), where the within-session reliability of extracting the muscle-tendon unit (MTU) and tendon lengths are estimated. MG MTU lengths were extracted in a group of 14 healthy adults using both 3-DfUS and US-PaP. Two consecutive acquisitions were performed per participant, and the data processed by two researchers independently. The intra-class correlation coefficients were above 0.97, and the standard error of measurements below 3.6 mm (1.5%). This investigation proposes that the simplified US-PaP method is a viable alternative for estimating MG MTU lengths.
... All participants underwent 3D gait analysis consisting of a static standing calibration and walking at the self-selected speed. Passive reflective markers were attached to each participant's lower-limbs according to the plug-in-gait marker set [23] with additional thigh and shank markers used to enhance segment tracking [24]. A ten-camera video motion capture system (Vicon TX 160, UK) recorded marker positions at 100 Hz. ...
... Hip joint centre locations were estimated using regression equations reported by Harrington et al. (2007) [29]. The condylar axis was approximated using the 2DoFKnee functional calibration [18,24,30] while the bimalleolar axis was defined using markers placed over the medial and lateral malleoli. We also modified the knee varus-valgus angle in the generic model to match that measured for the subjects during static calibration determined from the skin markers. ...
Article
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Torsional deformities of the femur and tibia are associated with gait impairments and joint pain. Several studies have investigated these gait deviations in children with cerebral palsy. However, relatively little is known about gait deviations in children with idiopathic torsion and debate ensues about the management of these patients. Research question: What are the effects of idiopathic increased femoral neck anteversion and external tibial torsion on lower-limb kinematics, kinetics and joint loading during gait in children and adolescents. Patient-specific musculoskeletal models were created for 12 children/adolescents (mean age of 14 years) with torsional deformities using low-dose biplane radiographic imaging and 3D gait analysis. Comparisons of joint motion and net joint torques during gait were made to an age-matched control group with no torsional deformities. The effects of torsional deformities on muscle and joint contact forces were investigated using two personalised musculoskeletal models: one with normal torsion and another with patient-specific torsion. Femoral neck anteversion and external tibial torsion for the patients were (mean ± SD) 38° ± 9° and 40° ± 10°, respectively. Patients had increased internal hip rotation and external knee rotation as well as increased pelvic tilt during gait. Additionally, the efficacy of the plantarflexor-knee extension mechanism was diminished. Hip joint contact force was higher in the model with patient-specific torsion. The mediolateral component of the patellofemoral joint contact force was also increased despite the magnitude of the resultant patellofemoral contact force being unchanged. It has been previously established that idiopathic lower-limb torsional deformities alter gait kinematics. However, this study also showed that loading of the hip and patellofemoral joints are increased. This is an important insight for the clinical management of these patients and highlights that idiopathic lower-limb torsional deformities are not a purely cosmetic issue.
... Children underwent a 3DGA, carried out by experienced physiotherapists and biomedical engineers, according to the standardized protocols of Baker (2013) [21] with quality control. Skin mounted reflective markers were applied to the child's lower limbs according to the conventional gait model marker set with the knee axis defined using a knee alignment device [22,23] and additional thigh and shank markers to enhance segment tracking [24]. The 3DGA consisted of a static standing calibration and walking barefoot for a minimum of 5 walks at a self-selected speed along a 10-metre walkway. ...
... The 3DGA consisted of a static standing calibration and walking barefoot for a minimum of 5 walks at a self-selected speed along a 10-metre walkway. Kinematics and kinetics were calculated in Nexus 2 (Vicon, Oxford Metrics, UK) using Plug-in-Gait with the following modifications; Pelvic kinematics were calculated according to Baker (2001) [25] using the rotation, obliquity, tilt sequence to decompose the joint kinematics, the position of the thigh and shank segments were tracked using a clusters of skin markers instead of a single lateral marker on the segment [24,26]. The most representative stride was selected and the data from the selected limb with higher FNA was used for analysis [27]. ...
Article
Background Torsional deformities of the lower limbs in children and adolescents are a common cause of in-toeing gait and cause gait deviations. The purpose of this study was to examine the relationship of children and adolescents with suspected Idiopathic Torsional Deformities(ITD) and pain, gait function, activity and participation. Methods A retrospective review of all children and adolescents who attended our Centre over a 5-year period for evaluation of the effect of ITD. All children completed three-dimensional gait analysis(3DGA), standardized physical examination, medical imaging and the Pediatric Outcomes Data Collection Instrument(PODCI). Statistical analysis was completed using two sample t-tests, Pearson’s Correlation and linear regression. Results Fifty children and adolescents, 40 females and 10 males with a mean age of 13.3 years were included. Children reported a high prevalence of pain(86%), had increased internal hip rotation(p = 0.002) and decreased external hip rotation(p < 0.001) on physical examination when compared to published normative data. Medical imaging showed a mean(SD) femoral neck anteversion(FNA) of 38°(13°) and external tibial torsion(ETT) of 39°(12°). Mean(SD) PODCI score was 32(16), indicating these children are functioning below their typically developing peers. The 3DGA kinematics show deviations from typical data including hip rotation, foot progression, pelvic tilt, hip flexion and knee extension. Observed mild kinetic deviations were within typical limits. The relationship between FNA and gait parameters, FNA and PODCI and gait and PODCI were weak. Significance These children and adolescents have altered gait and experience pain leading to impaired function and diminished participation. Therefore, ITD is not purely a cosmetic issue.
... Différentes études ont comparé les méthodes permettant d'obtenir l'axe de flexion extension du genou (Passmore & Sangeux, 2016;Sauret et al., 2016). Ils proposent de comparer quatre méthodes permettant d'obtenir l'axe de flexion/extension du genou avec une méthode de référence : la radiographie bi planaire EOS ou échographie. ...
Thesis
L’analyse du mouvement humain est un paramètre clé pour comprendre les différentes problématiques de la locomotion humaine. Qui plus est, il est nécessaire que ces analyses soient effectuées au plus proche de la locomotion réelle. L’essor de la miniaturisation des capteurs et des technologies sans fil a permis d’offrir la possibilité d’utiliser les centrales inertielles sur le terrain. Mais différentes problématiques existent encore pour obtenir la cinématique des membres inférieurs avec les centrales inertielles.La première étude de ce manuscrit aborde une comparaison des différents calibrages centrale-à-segment pour définir le passage entre l’orientation de la centrale inertielle et le segment sous-jacent. Nous avons mis en avant une méthode qui valide ces critères au mieux et ne demande que deux postures et un dispositif simple. Mais la cinématique obtenue reste entachée d’erreurs qui pourraient être dues à la présence d’artefacts de tissu mou.C’est pourquoi dans une seconde partie nous étudions la possibilité de diminuer ces effets par l’intermédiaire de l’optimisation multisegmentaire. Ainsi nous avons pu mettre en avant la nécessité de bien paramétrer le modèle derrière l’optimisation sans pour autant présenter un apport significatif. Enfin, en dernière partie, nous proposons d’appliquer la méthodologie de traitement de la cinématique articulaire sur une population pathologique, en collaboration avec le laboratoire de cinésiologie Willy Taillard des HUG et de l’Université de Genève. En conclusion cette thèse propose un processus méthodologique et des recommandations pour développer des analyses de la cinématique en milieu écologique avec des centrales inertielles.
... By using a FAR, frontal plane range of motion was reduced even presenting a reversal of the abduction motion, in both stance and swing phase. Excessive abduction angles during gait, especially those coinciding with peak knee flexion during the swing phase, have been shown to result from cross-talk [19,28]. Therefore, our results imply that the use of FAR effectively reduces cross-talk. ...
Article
Objective: This study, firstly, investigates the effect of using an anatomical versus a functional axis of rotation (FAR) on knee adduction moment (KAM) in healthy subjects and patients with knee osteoarthritis (KOA). Secondly, this study reports KAM for models with FAR calculated using weight-bearing and non-weight-bearing motion. Design: Three musculoskeletal models were created using OpenSim with different knee axis of rotation (AR): transepicondylar axis (TEA); FAR calculated based on SARA algorithm using a weight-bearing motion (wFAR) and a non-weight-bearing motion (nwFAR). KAM were calculated during gait in fifty-nine subjects (n=20 healthy, n=16 early OA, n=23 established OA) for all models and groups. Results: Significant differences between the three groups in the first peak KAM were found when TEA was used (p=0.038). However, these differences were no longer present when using FAR. In subjects with established OA, KAMs were significantly reduced when using nwFAR compared to TEA models but also compared to wFAR models. Conclusion: The presence of excessive KAM in subjects with established KOA showed to be dependent on the definition of the AR: anatomical versus functional. Therefore, caution should be accounted when comparing KAM in different studies on KOA patients. In patients with end-stage knee OA where increased passive knee laxity is likely to exist, the use of weight-bearing motions should be considered to avoid increased variability in the location and orientation of a FAR obtained from activities with only limited joint loading.
... It is therefore possible, that methods inherent to mDynaKAD may be trying to optimise for both the processes of cross-talk and STA. The results of this study are comparable to another study investigating differing calibration methods of similar activities namely gait, loaded flexion-extension (squat) and unloaded flexion-extension [33]. As stated previously, our study may have had higher levels of STA due to our population completing movements over a larger range. ...
Article
Background: “Dynamic knee valgus” has been identified as a risk factor for significant knee injuries, however, the limits and sources of error associated with existing 3D motion analysis methods have not been well established. Research question: What effect does the use of differing static and functional knee axis orientation methods have on the observed knee angle outputs for the activities of gait, overhead squatting and a hurdle step? Methods: A pre-existing dataset collected from one season (September 2015–May 2016) as part of a prospective observational longitudinal study was used. A secondary analysis of data for 24 male footballers, from a single British University football team, was conducted in order to evaluate the effect of static (conventional gait model) and dynamic (constrained and unconstrained mDynaKAD) methods on knee joint kinematics for flexion-extension and valgus-varus angles. Results: No single calibration method consistently achieved both the highest flexion and lowest valgus angle for all tests. The constrained and unconstrained mDynaKAD methods achieved superior alignment of the knee medio-lateral axis compared to the conventional gait model, when the movement activity served as its own calibration. The largest mean difference between methods for sagittal and coronal plane kinematics was less than 4⁰ and 14⁰ respectively. Cross-talk could not account for all variation within the results, highlighting that soft tissue artefact, associated with larger muscle volumes and movements, can influence kinematics results. Significance: When considering the trade-off between achieving maximum flexion and minimal valgus angle, the results indicate that the mDynaKAD methods performed best when the selected movement activity served as its own calibration method for all activities. Clinical decision making processes obtained through use of these methods should be considered in light of the model errors associated with cross-talk and effect of soft tissue artefact.
... Regression methods were developed and the Harrington's method (Harrington et al., 2007) based on MRI imaging data was found the most reliable and usable for all populations (Sangeux, 2015). A fusion of kinematics and imaging data to improve the determination of joint centers, axis systems and the positioning of markers on anatomical points emerged as well (Assi et al., 2013;Passmore and Sangeux, 2016). Besides, markerless methods could be a relevant alternative. ...
Thesis
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The natural course of cerebral palsy (CP) can be modulated by treatments and therapies that are nowadays mostly decided on the basis of assessments performed in clinical settings, through the Clinical Gait Analysis. However, it is not clear whether gait assessments in clinics (capacity) are representative of daily-life behaviors (performance). The present thesis aimed at exploring the gap between gait assessed in the laboratory and in real life for children with CP, as compared to children with typical development. Inertial measurement units, including accelerometers and gyroscopes, were exploited as a solution to measure gait features in the children’s s daily life. The clinical results proved with objective and quantitative evidence the existence of a systematic gap between gait assessed in the laboratory and gait in real life, which could help clinicians to devise therapeutic plans better tailored to each child’s needs.
... Methods: Simultaneous bi-plane fluoroscopy and stereo-photogrammetry acquisitions of the knee joint were performed on 19 subjects with a knee prosthesis, and mean(SD) age, weight and height of 70(6)years, 80(14)kg and 168(9)cm respectively [3]. Data from fluoroscopy were obtained by tracking the movement of the femoral and tibial components of the prosthesis while data from stereo-photogrammetry were obtained from a thigh and shank marker clusters [4]. The thigh cluster included the lateral epicondyle marker, proximal and distal markers on the iliotibial band, proximal and distal markers on the anterior aspect of the thigh and a patella marker located immediately proximal to the patella. ...
Conference Paper
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Introduction: Soft tissue artefact (STA) is one of the main source of measurement error in gait analysis [1]. Thigh rotation is particularly affected by STA and contributes to inaccurate measurement of both hip and knee rotation kinematics. Wren et al. [2] proposed a model which used a skin marker located above the patella to better track rotation of the femur. However, the model has not been validated during dynamic activities because gold standard movement tracking technologies, such as bi-plane fluoroscopy, were not readily available. Research Question: Does the use of a patella marker improve the accuracy of femur rotation kinematics during walking? Methods: Simultaneous bi-plane fluoroscopy and stereo-photogrammetry acquisitions of the knee joint were performed on 19 subjects with a knee prosthesis, and mean(SD) age, weight and height of 70(6)years, 80(14)kg and 168(9)cm respectively [3]. Data from fluoroscopy were obtained by tracking the movement of the femoral and tibial components of the prosthesis while data from stereo-photogrammetry were obtained from a thigh and shank marker clusters [4]. The thigh cluster included the lateral epicondyle marker, proximal and distal markers on the iliotibial band, proximal and distal markers on the anterior aspect of the thigh and a patella marker located immediately proximal to the patella. The shank cluster included the two malleoli, proximal and distal markers on the tibia crest and a marker on the lateral aspect of the shank. For the thigh segment, the rotation was also calculated by using each individual marker and the longitudinal axis of the femur as provided by the fluoroscopy data. The accuracy of femur and tibia kinematics was expressed as the root mean square error compared to fluoroscopy data. Results: Mean(SD) accuracy for the femur in the sagittal, coronal and transverse plane was 3.3°(0.9°), 2.1°(1.1°) and 4.7°(2.1°) respectively and 1.1°(0.5°), 0.7°(0.3°) and 1.9°(0.7°) for the tibia. Accuracy for the femur in the transverse plane was best when using the patella marker: 3.5°(1.9°) and worst when using the proximal marker on the iliotibial band: 6.2°(2.2). Paired t-test between the accuracy of least square fit and patella marker rotation was not significant (p=0.08). Discussion: Our results confirm the effects of soft tissue artefact are most predominant on the thigh and affect rotation the most. Overall, markers located on the anterior aspect of the thigh were marginally better at tracking femur rotation than markers on the iliotibial band. The use of a patella marker improved rotation accuracy, albeit not significantly. It is important to note that the subjects in this study were older people with more loose skin around the patella region than what would be expected in other populations.
... A validated numerical optimization method to correct for any displacement of the thigh markers from the true femoral frontal plane were used [27][28][29]. This method is a functional approach in which the knee axis orientation is estimated based on the assumption of minimum variance in the frontal plane motion of the knee. ...
Article
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Background Functional gait is an integral part of life, allowing individuals to function within their environment and participate in activities of daily living. Gait assessment forms an essential part of a physical examination and can help screen for physical impairments. No three-dimensional (3D) gait analysis studies of children have been conducted in South Africa. South African gait analysis laboratory protocols and procedures may differ from laboratories in other countries, therefore a South African data base of normative values is required to make a valid assessment of South African children’s gait. The primary aim of this study is to describe joint kinematics and spatiotemporal parameters of gait in South African children to constitute a normative database and secondly to assess if there are age related differences in aforementioned gait parameters. MethodsA descriptive study was conducted. Twenty-eight typically developing children were conveniently sampled from the Cape Metropole in the Western Cape, South Africa. The 3D lower limb kinematics and spatiotemporal parameters of gait were analyzed. The lower limb Plug-in-Gait (PIG) marker placement was used. Participants walked bare foot at self-selected speed. Means and standard deviations (SD) were calculated for all spatiotemporal and kinematic outcomes. Children were sub-divided into two groups (Group A: 6–8 years and Group B: 9–10 years) for comparison. ResultsA significant difference between the two sub-groups for the normalized mean hip rotation minimum values (p = 0.036) was found. There was no significant difference between the sub-groups for any other kinematic parameter or when comparing the normalized spatiotemporal parameters. Conclusion The study’s findings concluded that normalized spatiotemporal parameters are similar between the two age groups and are consistent with the values of children from other countries. The joint kinematic values showed significant differences for hip rotation, indicating that older children had more external rotation than younger children.
... With advancement in medical imaging it is now feasible to incorporate accurate measures of femoral and tibial torsion in the clinical pathway [60][61][62] . ...
Article
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This position paper proposes a modeling pipeline to develop clinically relevant neuromusculoskeletal models to understand and treat complex neurological disorders. Although applicable to a variety of neurological conditions, we provide direct pipeline applicative examples in the context of cerebral palsy (CP). This paper highlights technologies in: (1) patient-specific segmental rigid body models developed from magnetic resonance imaging for use in inverse kinematics and inverse dynamics pipelines; (2) efficient population-based approaches to derive skeletal models and muscle origins/insertions that are useful for population statistics and consistent creation of continuum models; (3) continuum muscle descriptions to account for complex muscle architecture including spatially varying material properties with muscle wrapping; (4) muscle and tendon properties specific to CP; and (5) neural-based electromyography-informed methods for muscle force prediction. This represents a novel modeling pipeline that couples for the first time electromyography extracted features of disrupted neuromuscular behavior with advanced numerical methods for modeling CP-specific musculoskeletal morphology and function. The translation of such pipeline to the clinical level will provide a new class of biomarkers that objectively describe the neuromusculoskeletal determinants of pathological locomotion and complement current clinical assessment techniques, which often rely on subjective judgment. For further resources related to this article, please visit the WIREs website.
Article
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The Quantified Motion Analysis (QMA) has become in recent years a clinical examination whose understanding and improvement are being developed. Based on a three-dimensional projection of the body segments, the QMA must define these segments and their means of union, the axes and centers of articular rotation. Two main techniques exist: predictive estimation techniques and functional techniques which use a calibration movement to estimate the axes and centers of rotation. These latter techniques, known as functional, seem to show superiority in terms of reproducibility of the estimate of the axis of rotation of the knee, but no consensus exists. The same applies to the calibration movements used.
Article
Two-dimensional ultrasound (US) imaging has been successfully used in clinical applications as a low-cost, portable and non-invasive image modality for more than three decades. Recent advances in computer science and technology illustrate the promise of the 3-D US modality as a medical imaging technique that is comparable to other prevalent modalities and that overcomes certain drawbacks of 2-D US. This systematic review covers freehand 3-D US imaging between 1970 and 2017, highlighting the current trends in research fields, the research methods, the main limitations, the leading researchers, standard assessment criteria and clinical applications. Freehand 3-D US systems are more prevalent in the academic environment, whereas in clinical applications and industrial research, most studies have focused on 3-D US transducers and improvement of hardware performance. This topic is still an interesting active area for researchers, and there remain many unsolved problems to be addressed.
Article
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Musculoskeletal tissues respond to optimal mechanical signals (e.g., strains) through anabolic adaptations, while mechanical signals above and below optimal levels cause tissue catabolism. If an individual's physical behavior could be altered to generate optimal mechanical signaling to musculoskeletal tissues, then targeted strengthening and/or repair would be possible. We propose new bioinspired technologies to provide real-time biofeedback of relevant mechanical signals to guide training and rehabilitation. In this review we provide a description of how wearable devices may be used in conjunction with computational rigid-body and continuum models of musculoskeletal tissues to produce real-time estimates of localized tissue stresses and strains. It is proposed that these bioinspired technologies will facilitate a new approach to physical training that promotes tissue strengthening and/or repair through optimal tissue loading.
Article
Introduction Proximal tibial sarcoma resections result in a reconstructive challenge, necessitating joint and extensor mechanism reconstruction. The gait and functional outcomes for children reconstructed with a combination of megaprosthesis and pedicled fibular flap for extensor mechanism reconstruction, are presented. Methods Four patients, aged 11–18 years old, were available for comprehensive analysis. The proximal tibial osteosarcoma was resected, and the reconstructive technique involved a megaprosthesis for the knee joint, used in combination with a pedicled fibula flap as a biologic structure for reinsertion of the knee extensor mechanism. Outcomes were measured with three-dimensional gait analysis and patient questionnaires. Results Minor postoperative wound issues occurred in some patients, requiring debridement with skin grafting. One patient fractured their transferred fibula, requiring fixation. The follow up period ranged from 1.7 to 24 years postoperatively. The longevity and quality of reconstructions were strong, measured by both objective and patient-reported outcomes. All patients reported independent walking >500 m in the Functional Mobility Scale and rated their walking as a nine or 10 (out of 10) on the Functional Assessment Questionnaire. Knee society scoring revealed overall satisfaction rate of 75–80%. No patients required gait aids. The gait profile analysis revealed effective gait patterns, with patterns deviating 5.4–7° from “typical gait.” Deviations >6.5° are considered abnormal. Conclusion The long-term results of combining a megaprosthesis with a pedicled fibula flap for extensor reinsertion, revealed a high level of independent function. The patients performed well, without the need for aids, and gait study evidence of minimal gait deviations.
Article
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3D free-hand ultrasound (3DFUS) is becoming increasingly popular to assist clinical gait analysis because it is cost- and time-efficient and does not expose participants to radiation. The aim of this study was to evaluate its reliability in localizing the anterior superior iliac spine (ASIS) at the pelvis and the hip joint centers (HJC). Additionally, we evaluated its accuracy to get a rough estimation of the potential to use of 3DFUS to segment bony surface. This could offer potential to register medical images to motion capture data in future. To evaluate reliability, a test–retest study was conducted in 16 lean and 19 obese individuals. The locations of the ASIS were determined by manual marker placement (MMP), an instrumented pointer technique (IPT), and with 3DFUS. The HJC location was also determined with 3DFUS. To quantify reliability, intraclass correlation coefficients (ICCs), the standard error of measurement (SEm), among other statistical parameters, were calculated for the identified locations between the test and retest. To assess accuracy, the surface of a human plastic pelvic phantom was segmented with 3DFUS in a distilled water bath in 27 trials and compared to a 3D laser scan of the pelvis. Regarding reliability, the MMP, but especially the IPT showed high reliability in lean (SEm: 2–3 mm) and reduced reliability in obese individuals (SEm: 6–15 mm). Compared to MMP and IPT, 3DFUS presented lower reliability in the lean group (SEm: 2–4 mm vs. 2–8 mm, respectively) but slightly better values in the obese group (SEm: 7–11 mm vs. 6–16 mm, respectively). Correlations between test–retest reliability and torso body fat mass (% of body mass) indicated a moderate to strong relationship for MMP and IPT but only a weak correlation for the 3DFUS approach. The water-bath experiments indicated an acceptable level of 3.5 (1.7) mm of accuracy for 3DFUS in segmenting bone surface. Despite some difficulties with single trials, our data give further rise to the idea that 3DFUS could serve as a promising tool in future to inform marker placement and hip joint center location, especially in groups with higher amount of body fat.
Chapter
Ultrasound imaging provides a means to look inside the body and examine how tissues respond to mechanical stress or muscle contraction. As such, it can provide a valuable tool for understanding how muscle, tendon, and ligament mechanics influence the way we move, or vice versa, in health and disease, or to understand how and why these tissues might get injured due to chronic or acute loading. This chapter explores the basic concepts of ultrasound and how it can be used to examine muscle, tendon, and ligament structure and mechanical function. It introduces different techniques, like conventional B-mode imaging, three-dimensional ultrasound, and various forms of elastography that can be used to quantify geometrical and mechanical properties of the muscle, tendon, and ligament. Furthermore, methods to quantify muscle and tendon mechanical function during dynamic human movement are explored, and recommendations provided on which techniques are most suitable for different biomechanical investigations. Finally, some predictions about how new ultrasound imaging technologies might continue to advance our understanding of human motion are proposed and explored.
Article
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This study aimed to calculate the flexion-extension axis (FEA) of the knee through in-vivo knee kinematics data, and then compare it with two major anatomical axes of the femoral condyles: the transepicondylar axis (TEA) defined by connecting the medial sulcus and lateral prominence, and the cylinder axis (CA) defined by connecting the centers of posterior condyles. The knee kinematics data of 20 healthy subjects were acquired under weight-bearing condition using bi-planar x-ray imaging and 3D-2D registration techniques. By tracking the vertical coordinate change of all points on the surface of femur during knee flexion, the FEA was determined as the line connecting the points with the least vertical shift in the medial and lateral condyles respectively. Angular deviation and distance among the TEA, CA and FEA were measured. The TEA-FEA angular deviation was significantly larger than that of the CA-FEA in 3D and transverse plane (3.45° vs. 1.98°, p < 0.001; 2.72° vs. 1.19°, p = 0.002), but not in the coronal plane (1.61° vs. 0.83°, p = 0.076). The TEA-FEA distance was significantly greater than that of the CA-FEA in the medial side (6.7 mm vs. 1.9 mm, p < 0.001), but not in the lateral side (3.2 mm vs. 2.0 mm, p = 0.16). The CA is closer to the FEA compared with the TEA; it can better serve as an anatomical surrogate for the functional knee axis.
Article
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This report describes algorithms for fitting certain curves and surfaces to points in three dimensions. All fits are based on orthogonal distance regression. The algorithms were developed as reference software for the National Institute of Standards and Technology's Algorithm Testing System, which has been used for 5 years by NIST and by members of the American Society of Mechanical Engineers' B89.4.10 standards committee. The Algorithm Testing System itself is described only briefly; the main part of this paper covers the general linear algebra, numerical analysis, and optimization methods it employs. Most of the fitting routines rely on the Levenberg-Marquardt optimization routine.
Article
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Accurate localization of the hip joint centre is required to obtain accurate kinematics, kinetics and musculoskeletal modelling results. Literature data showed that conclusions drawn from synthetic data, adult normal subjects and cerebral palsy children may vary markedly. This study investigated the localization accuracy of the hip joint centre against EOS. The EOS system allowed us to register the hip joint centres with respect to the skin markers on standing subjects. A comprehensive set of predictive and functional calibration techniques were tested. For the functional calibration techniques, our results showed that algorithm, range of motion and self-performance of the movement were factors significantly affecting the results. Best results were obtained for comfortable range and self-performance of the movement. The best method in this scenario was the functional geometrical sphere fitting method which localized the hips 1.1 cm from the EOS reference in average and 100% of the time within 3 cm. Worst results for functional calibration methods occurred when the movement was assisted with a reduced range of movement. The best method in this scenario was the Harrington et al. regression equations since it does not rely on a functional calibration movement. Harrington et al. equations put the hips 1.7 cm from the EOS reference in average and 97% of the time within 3 cm. We conclude that accurate localization of the hip joint centre is possible in gait analysis providing that method to localize the hip joint centres are adapted to the population studied: functional geometrical sphere fitting when hip calibration movements are not a problem and Harrington et al. predictive equations otherwise
Article
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Background: The transepicondylar axis (TEA) is often used as a surrogate for the flexion-extension axis, ie, the axis around which the tibia moves in space, because of a belief that both axes lie perpendicular to the mechanical axis. However, studies suggest the cylindrical axis (CA), defined as a line equidistant from contact points on the medial and lateral condylar surfaces from 10(o) to 120(o) flexion, more closely approximates the axis around which the tibia moves in space. Questions/purposes: We examined the TEA and CA angles relative to mechanical axes to determine whether one more consistently and closely approximates the surgical goal of orthogonality to the mechanical axis. Methods: Three-dimensional (3-D) models were reconstructed from CT scans of five cadaver limbs. Three observers repeated three measurement sets to locate the TEA, CA, and femoral mechanical and tibial mechanical axes. Angles of the TEA and CA relative to the mechanical axes were calculated in two-dimensions (2-D) and as 3-D projections and compared for differences in magnitude and variance. Results: Angles between CA and the mechanical axes were closer to 90° than the TEA in 2-D (92° versus 94° for the femur, 93° versus 94° for the tibia) and 3-D (88° versus 87° for the femur, 88° versus 86° for the tibia). Variance of the TEA was higher than the CA in 2-D. Conclusions: The CA forms angles more orthogonal to the mechanical axes of the thigh and leg than the TEA. Clinical relevance: Although we found a consistently greater deviation of the TEA from the mechanical axis than the CA with small differences, future studies will need to determine whether these differences are biomechanically or clinically important.
Article
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Functional calibration techniques have been proposed as an alternative to regression equations for estimating the position of the hip within the pelvic co-ordinate system for clinical gait analysis. So far validation of such techniques has focussed on healthy adults. This study evaluated a range of techniques based on regression equations or functional calibration procedures techniques in 46 children representative of those attending a major clinical gait analysis service against previously validated 3-D ultrasound techniques for determining the hip joint centre. Best agreement with ultrasound for the position of the hip within the pelvic coordinate system was found for the Harrington equations (mean 14 mm, sd 8 mm). Sphere fitting (mean≈22 mm, sd 11 mm) performed better than transformational techniques applied locally (mean≈33 mm, sd 12 mm) or globally (mean=30 mm, sd 14 mm). The participants with cerebral palsy showed reduced range of movement compared with healthy adults. Differences between these results and studies modelling the effects of simulated noise on functional techniques can probably be attributed to differences between that noise and the soft tissue displacements that are actually occurring.
Article
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Locating the position of the hip joint centre (HJC) is an important part of lower limb modeling for gait analysis. Regression equations have been used in the past but a range of functional calibration methods are now available. This study compared the accuracy of HJC localization from two sets of regression equations and five different functional calibration methods against three dimensional ultrasound (3-DUS) on a population of 19 able bodied subjects. Results show that the geometric sphere fitting technique was the best performer with mean absolute distance error of 15mm and 85% of measurements being within 20mm. The results also show that widely used regression equations perform particularly badly whereas the most recent equations performed very closely to the best functional method with a mean absolute error of 16mm and 88% of measurements being within 20mm. In vivo results are more than an order of magnitude worse than predictions using synthetic data suggesting that additional work is required before soft tissue artifact can be effectively modelled.
Article
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In 13 unloaded living knees we confirmed the findings previously obtained in the unloaded cadaver knee during flexion and external rotation/internal rotation using MRI. In seven loaded living knees with the subjects squatting, the relative tibiofemoral movements were similar to those in the unloaded knee except that the medial femoral condyle tended to move about 4 mm forwards with flexion. Four of the seven loaded knees were studied during flexion in external and internal rotation. As predicted, flexion (squatting) with the tibia in external rotation suppressed the internal rotation of the tibia which had been observed during unloaded flexion.
Article
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The aim of this study was to image tibio-femoral movement during flexion in the living knee. Ten loaded male Caucasian knees were initially studied using MRI, and the relative tibio-femoral motions, through the full flexion arc in neutral tibial rotation, were measured. On knee flexion from hyperextension to 120 degrees , the lateral femoral condyle moved posteriorly 22 mm. From 120 degrees to full squatting there was another 10 mm of posterior translation, with the lateral femoral condyle appearing almost to sublux posteriorly. The medial femoral condyle demonstrated minimal posterior translation until 120 degrees . Thereafter, it moved 9 mm posteriorly to lie on the superior surface of the medial meniscal posterior horn. Thus, during flexion of the knee to 120 degrees , the femur rotated externally through an angle of 20 degrees . However, on flexion beyond 120 degrees , both femoral condyles moved posteriorly to a similar degree. The second part of this study investigated the effect of gender, side, load and longitudinal rotation. The pattern of relative tibio-femoral movement during knee flexion appears to be independent of gender and side. Femoral external rotation (or tibial internal rotation) occurs with knee flexion under loaded and unloaded conditions, but the magnitude of rotation is greater and occurs earlier on weight bearing. With flexion plus tibial internal rotation, the pattern of movement follows that in neutral. With flexion in tibial external rotation, the lateral femoral condyle adopts a more anterior position relative to the tibia and, particularly in the non-weight bearing knee, much of the femoral external rotation that occurs with flexion is reversed.
Article
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Axes of rotation e.g. at the knee, are often generated from clinical gait analysis data to be used in the assessment of kinematic abnormalities, the diagnosis of disease, or the ongoing monitoring of a patient's condition. They are additionally used in musculoskeletal models to aid in the description of joint and segment kinematics for patient specific analyses. Currently available methods to describe joint axes from segment marker positions share the problem that when one segment is transformed into the coordinate system of another, artefacts associated with motion of the markers relative to the bone can become magnified. In an attempt to address this problem, a symmetrical axis of rotation approach (SARA) is presented here to determine a unique axis of rotation that can consider the movement of two dynamic body segments simultaneously, and then compared its performance in a survey against a number of previously proposed techniques. Using a generated virtual joint, with superimposed marker error conditions to represent skin movement artefacts, fitting methods (geometric axis fit, cylinder axis fit, algebraic axis fit) and transformation techniques (axis transformation technique, mean helical axis, Schwartz approach) were classified and compared with the SARA. Nearly all approaches were able to estimate the axis of rotation to within an RMS error of 0.1cm at large ranges of motion (90 degrees ). Although the geometric axis fit produced the least RMS error of approximately 1.2 cm at lower ranges of motion (5 degrees ) with a stationary axis, the SARA and Axis Transformation Technique outperformed all other approaches under the most demanding marker artefact conditions for all ranges of motion. The cylinder and algebraic axis fit approaches were unable to compute competitive AoR estimates. Whilst these initial results using the SARA are promising and are fast enough to be determined "on-line", the technique must now be proven in a clinical environment.
Article
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Locating the true flexion-extension axis of the knee can play an important role in component placement in a total knee arthroplasty, especially using contemporary computer-assisted surgical navigation. We determined if the commonly used transepicondylar axis is an accurate and reproducible substitute for the flexion-extension axis. Twenty-three fresh-frozen cadaveric distal femurs with intact soft tissue were imaged with computed tomography and reconstructed in three-dimensional virtual space. The transepicondylar axis was compared with a line equidistant from the articular surface of each femoral condyle. Measures were performed by three observers three times for each specimen. Interobserver and intraobserver variations were small, but the differences between axes were approximately 5 degrees. The difference between axes decreased when projected from three-dimensional space to traditional two-dimensional planes (coronal and transverse), explaining why this discrepancy has not been previously documented. The greater difference in three-dimensional space may account for midrange instability reported in total knee arthroplasty. The increased accuracy afforded by computer-assisted surgical navigation in total knee arthroplasty may be lost and increased malposition of components may occur if this discrepancy between reference axes is not appreciated and addressed.
Article
Excessive femoral anteversion is common among children with cerebral palsy, and is, frequently treated by a femoral derotational osteotomy (FDO). It is important to understand surgical, indications for FDO, and the impact of these indications on the treatment outcomes. The Random Forest algorithm was used to objectively identify historical surgical indications in a large retrospective, cohort of 1088 limbs that had previously undergone single-event multi-level surgery. Treatment, outcome was based on transverse plane kinematics obtained from three-dimensional gait analysis. The, classifier effectively identified the historic indications (accuracy=.85, sensitivity=.93, specificity=.69, positive predictive value=.86, negative predictive value=.82), and naturally divided limbs into four, clusters: two homogeneous +FDO clusters (with/without significant internal hip rotation during gait), one homogeneous -FDO cluster, and a mixed cluster. Concomitant surgeries were similar among the, clusters. Limbs with excessive anteversion and internal hip rotation during gait had excellent outcomes, in the transverse plane. Limbs with excessive anteversion but only mild internal hip rotation had good, outcomes at the hip level; but a significant number of these limbs ended up with an excessive external, foot progression angle. The Random Forest algorithm was highly effective for identifying and, organizing historic surgical indications. The derived criteria can be used to give surgical decision making, guidance in a majority of limbs. The results suggest that limbs with anteversion and significant, internal hip rotation during gait benefit from an FDO, but limbs with excessive anteversion and only, mild internal hip rotation are at risk of developing an excessive external foot progression angle.
Article
Using a set of landmarks to represent a rigid body, a rotation of the body can be determined in least-squares sense as the solution of an orthogonal Procrustes problem. We discuss some geometrical properties of the condition number for the problem of determining the orthogonal matrix representing the rotation. It is shown that the condition number critically depends on the configuration of the landmarks. The problem is also reformulated as an unconstrained nonlinear least-squares problem and the condition number is related to the geometry of such problems. In the common 3-D case, the movement can be represented by using a screw axis. Also the condition numbers for the problem of determining the screw axis representation are shown to closely depend on the configuration of the landmarks. The condition numbers are finally used to show that the used algorithms are stable.
Article
Conventional models for determining joint rotation angles from marker positions as part of three-dimensional clinical gait analysis are susceptible to errors arising from mis-placement of the thigh markers. An analysis of idealised data reveals how the measured variables are affected by different angular offsets of the thigh marker from its true position. An artefact on the varus–valgus signal arising from the projection of true knee flexion onto a mal-aligned thigh segment axis is the most characteristic feature of this problem. If this is observed then the hip rotation profiles are also erroneous.A technique is proposed to determine a correction factor which can be applied to gait data to correct for this mal-alignment. Its use is demonstrated on a single case study and a subjective assessment of its use on a cohort of 40 patients is reported. A detailed discussion of the assumptions on which the method is founded is included as well as guidelines as to when the technique is likely to be successful.It is recommended that the technique is used as an aid to training staff in marker placement rather than as a routine retrospective correction of data for erroneously placed markers.
Article
The clinical objective of the gait analysis laboratory, developed by United Technologies Corporation (Hartford, CT, USA) in 1980, at the Newington Children's Hospital is to provide quantified assessments of human locomotion which assist in the orthopaedic management of various pediatric gait pathologies. The motion measurement system utilizes a video-based data collection strategy similar to commercially available systems for motion data collection. Anatomically aligned, passive, retroreflective markers placed on the subject are illuminated, detected, and stored in dedicated camera hardware while data are acquired from force platforms and EMG transducers. Three-dimensional marker position information is used to determine: (i) the orientation of segmentally-embedded coordinate systems, (ii) instantaneous joint center locations, and (iii) joint angles. Joint kinetics, i.e., moments and powers, may also be computed if valid force plate data are collected.
Article
This paper describes the calibration process for 3-D free hand ultrasound (3-DUS). The Cambridge calibration technique was determined to produce the most repeatable and accurate results when determining the location of a reference object within a water bath. This note additionally validates 3-DUS as a potential measurement tool for the determination of the hip joint centre. It shows that 3-DUS can accurately determine the inter-HJC distance to within 4+/-2mm. This indicates potential for 3-DUS to be used as a gold standard measurement tool in the identification of the hip joint centre.
Article
This systematic review critically evaluates the quantification of soft tissue artifact (STA) in lower limb human motion analysis. It has a specific focus on assessing the quality of previous studies and comparing quantitative results. A specific search strategy identified 20 published articles or abstracts that fulfilled the selection criteria. The quality of the articles was evaluated using a customised critical appraisal tool. Data extraction tools were used to identify key aspects reported in the articles. Most studies had small sample sizes of mostly young, slim participants. Eleven of the reviewed articles used physically invasive techniques to assess STA. STA was found to reach magnitudes of greater than 30 mm on the thigh segment, and up to 15 mm on the tibia. The range of soft tissue artifact reached greater than 25 mm in some cases when comparing the results of reviewed studies.
Article
Three-dimensional kinematic measures of gait are routinely used in clinical gait analysis and provide a key outcome measure for gait research and clinical practice. This systematic review identifies and evaluates current evidence for the inter-session and inter-assessor reliability of three-dimensional kinematic gait analysis (3DGA) data. A targeted search strategy identified reports that fulfilled the search criteria. The quality of full-text reports were tabulated and evaluated for quality using a customised critical appraisal tool. Fifteen full manuscripts and eight abstracts were included. Studies addressed both within-assessor and between-assessor reliability, with most examining healthy adults. Four full-text reports evaluated reliability in people with gait pathologies. The highest reliability indices occurred in the hip and knee in the sagittal plane, with lowest errors in pelvic rotation and obliquity and hip abduction. Lowest reliability and highest error frequently occurred in the hip and knee transverse plane. Methodological quality varied, with key limitations in sample descriptions and strategies for statistical analysis. Reported reliability indices and error magnitudes varied across gait variables and studies. Most studies providing estimates of data error reported values (S.D. or S.E.) of less than 5 degrees , with the exception of hip and knee rotation. This review provides evidence that clinically acceptable errors are possible in gait analysis. Variability between studies, however, suggests that they are not always achieved.
Article
Biplane roentgenography, axial roentgenography, and fluoroscopy are the usual roentgenographic methods of measuring femoral anteversion. These methods use a strict geometrical definition of anteversion. The computerized tomography method of measuring anteversion that was developed recently, and is now widely used, does not adhere to the accepted definition of anteversion and has not been tested for accuracy in a large series. In the present study, the widely used computerized-tomography method of measuring anteversion was tested on thirty-two femoral specimens. With that method, anteversion was consistently underestimated by an average of 10 degrees compared with direct measurements and was reproducible only to within +/- 3.6 degrees. Therefore, a new method of measuring anteversion using computerized tomography was developed. It was shown to be accurate to +/- 1 degree, as tested on the same specimens. This study demonstrated geometrically why the currently practiced computerized-tomography method of selecting the points that are used to define the axis of the femoral neck is not consistent with geometrical definitions of anteversion. A more accurate method for both defining the axis of the femoral neck and measuring femoral anteversion is described and recommended for clinical use.
Article
The problem of determining skeletal movements in three dimensions by using a number of landmarks is treated. We present a method that determines the motion of a rigid body by using the positions of the landmarks in least-squares sense. The method uses the singular value decomposition of a matrix derived from the positions of the landmarks. We show how one can use this method to express movement of skeleton segments relative to each other. As many others have pointed out, the movement can be very ill determined if the landmarks are badly configured. We present a condition number for the problem with good geometrical properties. The condition number depends on the configuration of the landmarks and indicates how to distribute the landmarks in a suitable way.
Article
In six unloaded cadaver knees we used MRI to determine the shapes of the articular surfaces and their relative movements. These were confirmed by dissection. Medially, the femoral condyle in sagittal section is composed of the arcs of two circles and that of the tibia of two angled flats. The anterior facets articulate in extension. At about 20 degrees the femur 'rocks' to articulate through the posterior facets. The medial femoral condyle does not move anteroposteriorly with flexion to 110 degrees. Laterally, the femoral condyle is composed entirely, or almost entirely, of a single circular facet similar in radius and arc to the posterior medial facet. The tibia is roughly flat. The femur tends to roll backwards with flexion. The combination during flexion of no anteroposterior movement medially (i.e., sliding) and backward rolling (combined with sliding) laterally equates to internal rotation of the tibia around a medial axis with flexion. About 5 degrees of this rotation may be obligatory from 0 degrees to 10 degrees flexion; thereafter little rotation occurs to at least 45 degrees. Total rotation at 110 degrees is about 20 degrees, most if not all of which can be suppressed by applying external rotation to the tibia at 90 degrees.
Article
Repeatability of traditional kinematic and kinetic models is affected by the ability to accurately locate anatomical landmarks (ALs) to define joint centres and anatomical coordinate systems. Numerical methods that define joint centres and axes of rotation independent of ALs may also improve the repeatability of kinematic and kinetic data. The purpose of this paper was to compare the repeatability of gait data obtained from two models, one based on ALs (AL model), and the other incorporating a functional method to define hip joint centres and a mean helical axis to define knee joint flexion/extension axes (FUN model). A foot calibration rig was also developed to define the foot segment independent of ALs. The FUN model produced slightly more repeatable hip and knee joint kinematic and kinetic data than the AL model, with the advantage of not having to accurately locate ALs. Repeatability of the models was similar comparing within-tester sessions to between-tester sessions. The FUN model may also produce more repeatable data than the AL model in subject populations where location of ALs is difficult. The foot calibration rig employed in both the AL and FUN model provided an easy alternative to define the foot segment and obtain repeatable data, without accurately locating ALs on the foot.
Article
The Cardanic or Eulerian description is the most commonly used method for the description of in vivo knee rotation. It is based on the determination of external anatomical landmarks used for the decomposition of the position of the tibia relative to the femur by three rotations about three pre-defined axes. However, the in vivo localisation of external anatomical landmarks is known to be difficult and subjective. Even a small mislocalisation may lead to dramatic consequences: the Cardanic description may become irreproducible and angle values may be overestimated. This error is well documented in the literature and known as the "cross-talk effect". Therefore this study proposes an additional calibration step of the classic Cardanic description by a reorientation procedure of rotation axes. The procedure is based on biomechanical constraints of knee kinematics as they appear during a knee squat exercise using the finite helical axis (FHA) method and is independent of anatomical landmark. The method was validated with the help of a special set-up modelling a perfect knee. Furthermore, an inter-session reliability study was performed involving tests on two healthy subjects during knee squat exercises. We found that the reorientation procedure was more reproducible than the classic Cardanic description. We observed a maximum inter-session difference of 37.1 degrees for the adduction angle obtained with the classic Cardanic description. In contrast, the maximum angle difference obtained with the reorientation procedure was less than 10 degrees.
Article
Gait analysis is a valuable tool in the evaluation of children and adults with movement disorders. The data produced from gait analysis, however, is not necessarily free of errors. The purpose of this study was two-fold: (i) to estimate the errors associated with quantitative gait data; and (ii) to propose a method for incorporating the knowledge of these errors into the clinical interpretation process. An experimental protocol was designed that allowed within-subject, within-observer and between-observer errors to be computed at each point in the gait cycle. The estimates were then used in a practical scheme for detecting significant deviations in joint angles. The results of this study provide a means for managing error, while simultaneously improving the rigor and objectivity of clinical interpretations.
Article
Joint centers and axes of rotation (joint parameters) are central to all branches of movement analysis. In gait analysis, the standard protocol used to determine hip and knee joint parameters is prone to errors arising from palpation, anthropometric regression equations, and misplaced alignment devices. Several alternative methods have been proposed, but to date none have been shown to be accurate and reliable enough for use in the clinical setting. This article describes a new method for joint parameter estimation. The new method can be summarized as follows: (i) the motions of two adjacent segments spanning a single joint are tracked, (ii) the axis of rotation between every pair of observed segment configurations is computed, (iii) the most likely intersection of all axes (effective joint center) and most likely orientation of the axes (effective joint axis) is found. Initial validation of the method was conducted on a hinged mechanical analog and a single healthy adult subject. For the analog, the center was found to be within 3.8 mm of the geometric center and 2.0 degrees of the geometric axis (standard deviation). For the adult subject, hip centers varied on the order of 1-3 mm, knee centers by 3-9 mm, and knee axes by 2.0 degrees. The results suggest that the new method is an objective, precise, and practical alternative to the standard clinical approach.
Article
The purpose of this study was to compare 3 methods of imaging knee position. Three fresh cadaver knees were imaged at 6 flexion angles between 0 degrees and 120 degrees by MRI, a combination of RSA and CT and 3D digitisation (in two knees). Virtual models of all 42 positions were created using suitable computer software. Each virtual model was aligned to a newly defined anatomically based Cartesian coordinate system. The angular rotations around the 3 coordinate system axes were calculated directly from the aligned virtual models using rigid body kinematics and found to be equally accurate for the 3 methods. The 3 rotations in each knee could be depicted using anatomy-based diagrams for all 3 methods. We conclude that the 3 methods of data acquisition are equally and adequately accurate in vitro. MRI may be the most useful in vivo.
Article
This review describes the anatomy of the articular surfaces and their movement in the normal tibio-femoral joint, together with methods of measurement in volunteers. Forces and soft tissues are excluded. To measure movement, the articular surfaces and natural or inserted movement markers must be imaged by some combination of MRI, CT, RSA or fluoroscopy. With the aid of computer-imaging, the movements can then be related to an anatomy-based co-ordinate system to avoid kinematic cross-talk. Methods of depicting these movements which are understandable to engineers and clinicians are discussed. The shapes of the articular surfaces are reported. They are relevant to landmarks and co-ordinate systems and form a basis for inferring the nature of the movements which take place in the knee. The movements of the condyles are described from hyperextension to full passive flexion. Medially the condyle hardly moves antero-posteriorly from 0 degrees to 120 degrees but the contact area transfers from an anterior pair of tibio-femoral surfaces at 10 degrees to a posterior pair at about 30 degrees . Thus because of the shapes of the bones, the medial contact area moves backwards with flexion to 30 degrees but the condyle does not. Laterally the femoral condyle and the contact area move posteriorly but to a variable extent in the mid-range causing tibial internal rotation to occur with flexion around a medial axis. From 120 degrees to full flexion both condyles roll back onto the posterior horn so that the tibio-femoral joint subluxes.
Article
This paper describes techniques for the visualization and processing of three-dimensional (3D) ultrasound data. The nature of such data demands specialized algorithms, which differ from those employed for other medical imaging modalities. In this paper, the emphasis is placed on generic processing techniques, which are relevant across a wide range of 3D ultrasound application domains.
Article
This paper derives a simple mathematical model relating changes in the orientations of the two Cartesian coordinate systems involved in recording knee movement and the varus-valgus and the internal-external rotation angles for describing the knee's motion. Rotation matrices are given for changing the orientations of the two Cartesian coordinate systems in such a way that the quadratic variations in the varus-valgus and in the external-internal angles are minimal. These estimated rotation matrices are used to correct for axis misalignment. The correction is calibrated by considering the impact of the new orientation of the thigh Cartesian coordinate system on the hip joint angles. The procedure is applied to kinematic data collected on normal subjects. The uncertainty about the specification of the thigh Cartesian coordinate system is shown to explain some of the between subject variability in the varus-valgus and in the internal-external rotation angles curves.
Article
Minimising measurement variability associated with hip axial rotation and avoiding knee joint angle cross-talk are two fundamental objectives of any method used to define the knee joint flexion-extension axis for purposes of quantitative gait analysis. The aim of this experiment was to compare three different methods of defining this axis: the knee alignment device (KAD) method, a method based on the transepicondylar axis (TEA) and an alternative numerical method (Dynamic). The former two methods are common approaches that have been applied clinically in many quantitative gait analysis laboratories; the latter is an optimisation procedure. A cohort of 20 subjects performed three different functional tasks (normal gait; squat; non-weight bearing knee flexion) on repeated occasions. Three-dimensional hip and knee angles were computed using the three alternative methods of defining the knee joint flexion-extension axis. The repeatability of hip axial rotation measurements during normal gait was found to be significantly better for the Dynamic method (p<0.01). Furthermore, both the variance in the knee varus-valgus kinematic profile and the degree of knee joint angle cross-talk were smallest for the Dynamic method across all functional tasks. The Dynamic method therefore provided superior results in comparison to the KAD and TEA-based methods and thus represents an attractive solution for orientating the knee joint flexion-extension axis for purposes of quantitative gait analysis.
Article
We investigated the concept that the knee has a fixed flexion-extension axis in the posterior femoral condyles and that this functional axis corresponds to the surgical epicondylar axis in vivo. We used a biplanar image-matching technique to perform the in vivo analysis of 9 normal knees to determine the location of the functional flexion-extension axis of the knee using an optimization technique. The functional flexion-extension axis passed through the sulcus of the medial epicondyle and the prominence of the lateral epicondyle. Flexion and extension of the knee could be represented as a rotation around a fixed axis, and this functional axis corresponded to the surgical epicondylar axis during a 0 degrees to 90 degrees flexion. This study assists more understanding of knee kinematics and provides useful information for the design and positioning of the prostheses used in total knee arthroplasty.
Article
A simple method is developed for robustly estimating a fixed dominant axis of rotation (AoR) of anatomical joints from surface marker data. Previous approaches which assume a model of circular marker trajectories use plane fitting to estimate the direction of the AoR. However, when there is limited joint range of motion and rotation due to a second degree of freedom, minimizing only the planar error can give poor estimates of the AoR direction. Optimizing a cost function which includes the error component within a plane, instead of only the component orthogonal to a plane, leads to improved estimates of the AoR direction for joints which exhibit additional rotational motion from a second degree of freedom. Results from synthetic data validation show the ranges of motion where the new method has lower estimation error compared to plane-fitting techniques. Estimates of the flexion-extension AoR from empirical motion capture data of the knee and index finger joints were also more anatomically plausible.
Article
Several functional methods to determine joint centers of rotation (CoR) and axes of rotation (AoR) have been reported in the literature. These have previously been compared using noise introduced to marker positions. The current study compares four of these methods under both rigid body and deformable body conditions using a mechanical analog of the lower extremity. In the latter condition, significant inter-marker distance changes were present in patterns directly related to the joint motion. Both hip CoR location and knee AoR location and direction are determined. Results indicate that while all methods produced accurate measures under rigid body conditions (<5mm location and <2 degrees direction), there were many differences between methods in deformable conditions. Under these conditions, the method described by Gamage and Lasenby performed better than the other methods examined. Maximum mean errors for this technique were approximately 1cm for CoR and AoR locations and 1 degrees for AoR direction.
Clinical gait analysis: current methods and future directions
  • R Davis
  • P Deluca
Davis R, DeLuca P. Clinical gait analysis: current methods and future directions. In: Harris G, Smith P, editors. Hum. Motion Anal. Curr. Appl. Futur. Dir.. New York: The Institute of Electrical and Electronic Engineers Press, Inc.; 1996. p. 17-42.
Determining the movements of the skeleton using well-configured markers
  • I Soderkkvist
  • P A Wedin
Soderkkvist I, Wedin PA. Determining the movements of the skeleton using well-configured markers. J Biomech 1993;26:1473-7.