Gait Spatio-Temporal Parameters
Spatio-temporal parameters, as its name indicates, can be divided into two categories: the step parameters, related to spatial configuration, and the time related parameters. Spatial parameters The spatial parameters are used to describe distances travelled by the feet during the gait cycle. These are:
• stride length – total distance covered by the left (or right) foot during a gait cycle. It includes two step lengths: left and right.
• (left) step length – distance measured from the anterior right foot to the posterior left foot in the displacement direction, see figure 2.2. The definition of the right step length follows the same logic.
• (left) step height – maximum height reached by the left foot during its displacement.
The maximum toe height is considered. The definition for the right side is likewise.
• step width – sidewards distance between the two feet.
• foot progression angle – foot angle measured with respect to the displacement direction.
Analysis and treatment of CP locomotion disorders
Nowadays, in order to help therapeutic analysis and decision, two main type of exams are performed:
• a physical examination, which allows the establishment of an analytical evaluation of the orthopaedic state of the different anatomical regions considered.
• a Clinical Gait Analysis (CGA), which takes advantage of biomechanical parameters (kinematics, kinetics and electromyography (EMG)) to answer medical needs.
Its purpose is to identify, quantify and understand the gait abnormalities found in a specific patient, in order to help choosing the most appropriate treatment. As it helps to identify the underlying causes of the gait disorders, the CGA helps improving the therapeutic recommendations [DeLuca et al., 1997, Kay et al., 2000a, Kay et al., 2000b]. In France, this exam is part of the medical acts recognized by the health insurance (act NKQP003), and increasingly more centres of CGA are in activity or in project.
In a standard CGA exam, reflective markers are placed on the patient according to a chosen representation model. A set of electrodes to capture muscle activity during gait is also placed. The patient is then asked to walk on a corridor, where force plates may be in place. The trajectory of the markers in space, which allows the computation of kinematics of section 2.1.2, activity of muscles and ground reaction forces and moments may be recorded, see figure 2.7. A video can also be captured at the same time. The recorded data is then processed, by the recording software or by a personal developed software, and a report is made. Gait abnormalities and potential causes can then be found by analysing the data.
Most common surgeries among CP
Even though the therapeutic decision is not straight forward and depends on the patient data, some surgeries are common among Cerebral Palsy children. They can be divide in two groups: muscle/tendon and bone surgery.
Examples of common surgeries performed on the muscle/tendon complex, are: Psoas lengthening, Hamstrings lengthening, Rectus Femoris Transfer, . . . Examples of common surgeries performed on the bones are: Femoral Derotation Osteotomy, Femoral Extension Osteotomy, . . . In what follows, a brief and schematic description of the therapeutic indications and expected outcomes for these procedures is made.
Psoas lengthening Psoas is a muscle that relies the lumbar spine and the pelvis to the femur, passing in front of the hip.
The surgical procedure of psoas lengthening is recommended when there is.
• a deficit in the hip extension at physical examination.
• an excess of anteversion of the pelvis during walking (in certain cases).
• a deficit in the hip extension at the end of the single support phase.
Statistical prediction of surgical outcomes
Given the different thresholds for the recommendations and the difficulty to predict the result of surgeries association, researchers concentrate on how to improve these recommendations.
A common approach found in the literature for this improvement is statistics. This is the approach used in the other part of the project in which this thesis take part, as explained in the introduction. With the use of statistical tools, researchers are able to predict, within a certain range of accuracy and parameters, the expected outcome of a surgery. Two main categories of results can be established: qualitative and quantitative studies.
In the work of Hicks et al. [Hicks et al., 2011], the prediction study is narrowed down to one condition, the crouch gait. As the surgical outcomes for these patients may be variable, they develop a regression model able to predict if kinematics is improved or not with over 70% accuracy, given biomechanical variables and other subject measures taken during CGA and physical examination.
In this same category, studies concerning a unique surgical gesture can be found [Reinbolt et al., 2009, Schwartz et al., 2013, Sebsadji et al., 2012]. In [Reinbolt et al., 2009], only the rectus femoris transfer is considered. This surgery is a common treatment for stiff knee gait in children with cerebral palsy, but the improvement in knee motion afterwards is not always the same. Using a predictive model based on some preoperative CGA measurements, the authors reach a 88% accuracy in predicting if the outcome of rectus femoris transfer is good (improvement of knee motion), or bad, providing therefore a tool able to help indications for rectus femoris transfer. Another surgery that interests Schwartz et al. [Schwartz et al., 2013] is psoas lengthening. Based upon preoperative data extracted from a database, the authors develop a criteria able to predict the outcome of a limb for this surgery. The authors estimate that the application of the criteria may increase the rate of good pelvis-hip outcome in psoas lengthening from 58% to 72% among children with diplegia who undergo SEMLS with a psoas lengthening.
Table of contents :
1.1.1 Cerebral Palsy
1.1.2 Orthopaedic Surgery
1.3 Manuscript contents
2 Walking: definition, analysis, disorders, treatment and simulation
2.1 The walking activity
2.1.1 Gait Spatio-Temporal Parameters
2.1.2 Kinematical Parameters
2.1.3 Dynamical Parameters
2.1.4 Balance Parameters
2.2 Analysis and treatment of CP locomotion disorders
2.2.1 Most common surgeries among CP
2.3 Statistical prediction of surgical outcomes
2.4 Tools for the simulation of human walking
2.5 Proposed Approach
3 Framework for the simulation of a walking motion for a virtual human
3.1 XDE Physics Engine
3.1.1 Kinematic structure and Inertial Parameters
3.2 Linear Quadratic Programming Controller
3.2.1 Actuation Constraints
188.8.131.52 Torque limits
184.108.40.206 Acceleration limits
220.127.116.11 Velocity limits
18.104.22.168 Joint limits
3.2.2 Contact Constraints
3.2.3 Tasks for the Walking motion
22.214.171.124 Full Joint Task
126.96.36.199 Left/Right Foot Task
188.8.131.52 CoM Task
184.108.40.206 Pelvis Height & Pelvis Orientation Tasks
220.127.116.11 Pelvis-Torso Joint & Torso-Head Joint Tasks
3.2.4 Contacts Manager
3.3 Simulation example
3.3.2 Results & Discussion
18.104.22.168 Spatio-temporal Parameters
22.214.171.124 Kinematical parameters
126.96.36.199 Dynamical parameters
188.8.131.52 Balance parameters
4 Developing a more human-like walking
4.1 Foot Modelling
4.1.1 Foot Models in the literature
4.1.2 Articulated Foot
4.2 Contacts Management
4.2.1 Toe Walking
4.2.2 Non Pathological Walking
4.2.3 New Flat Feet Walking
4.3 References for the Foot Related Tasks
4.3.1 The CoM Task
4.3.2 The Foot Tasks
4.4 Gait Initialization
4.4.1 Gait Initialization in the literature
4.4.2 Gait Initialization in the Walking Procedure
5 Simulation Experiments
5.1 Non Pathological Walking
5.1.2 Results & Discussion
184.108.40.206 Spatio-temporal Parameters
220.127.116.11 Kinematical parameters
18.104.22.168 Dynamical parameters
22.214.171.124 Balance parameters
5.2 Toe Walking
5.2.2 Results & Discussion
126.96.36.199 Spatio-temporal Parameters
188.8.131.52 Kinematical Parameters
184.108.40.206 Dynamical Parameters
220.127.116.11 Balance parameters
5.3 Flat Feet Walking
5.3.2 Results & Discussion
18.104.22.168 Spatio-temporal Parameters
22.214.171.124 Kinematical Parameters
126.96.36.199 Dynamical Parameters
188.8.131.52 Balance Parameters
6 Simulation and Analysis of Pathological Walking Patterns
6.1 Pathological Walking Patterns among Cerebral Palsy Children
6.1.1 Knee extension limitation
6.1.2 Ankle dorsiflexion limitation
6.2 Simulation of gait abnormalities
6.2.2 Results & Discussion
184.108.40.206 Knee extension restriction effect on the non pathological contact
220.127.116.11 Knee extension restriction effect on toe walking .
18.104.22.168 Ankle dorsiflexion restriction effect on toe walking .
6.3 Concluding remarks
A Markers used in CGA exams