Model and measurement studies on stages of prosthetic gait.



Introduction - In the current thesis, entitled ’Model and measurement studies on stages of prosthetic gait - Predictions on how not to walk symmetrically with a mechanical prosthetic limb’, we used several two dimensional inverse and forward dynamics mathematical models to investigate principles of transfemoral amputee prosthetic gait. For four specific stages of prosthetic gait, namely gait initiation, weight bearing, prosthetic limb swing and gait termination, mathematical models were designed which allowed us to conceptually analyze phenomena observed in the real world. The outcome of the models were used to make predictions about certain choices in strategies that can be made when using prosthetic limbs. Data of transfemoral amputees and able-bodied subjects using a kneewalker prosthetic device were used to validate the models, which were all checked for (internal) consistency, conservation of energy and unrealistic values. The four stages that were studied are described in separate chapters in this thesis.

Gait initiation - During prosthetic gait initiation transfemoral amputees control the spatial and temporal parameters which modulate the propulsive forces, the positions of the center of pressure and the center of mass. Whether their sound limb or prosthetic limb is leading, the transfemoral amputees reach the same end velocity. We wondered how the center of mass velocity build up is influenced by the differences in propulsive components in the limbs and how the trajectory of the center of pressure differs from the center of pressure trajectory in healthy subjects. Seven transfemoral subjects and eight able-bodied subjects were tested on a force plate and on an eight meter long walkway. On the force plate, they initiated gait two times with their sound limb leading and two times with their prosthetic limb leading. Force data were used to calculate the center of mass velocity curves in horizontal and vertical directions. Gait initiated on the walkway was used to determine the limb preference. We hypothesized that because of the differences in propulsive components, the motions of the center of pressure and the center of mass have to be different, as ankle muscles are used to help generate horizontal ground reaction force components. Also, due to the absence of active ankle function in the prosthetic limb, the vertical center of mass velocity during gait initiation may be different when leading with the prosthetic limb compared to when leading with the sound limb. The data showed that whether the transfemoral subjects initiated gait with their prosthetic limb or with their sound limb, their horizontal end velocity was equal. The subjects compensated the loss of propulsive force under the prosthesis with the sound limb, both when the prosthetic limb was leading and when the sound limb was leading. In the vertical center of mass velocity a tendency for differences between the two conditions was found. When initiating gait with the sound limb, the downward vertical center of mass velocity at the end of the gait initiation was higher compared to when leading with the prosthetic limb. Our subjects used a gait initiation strategy that depended mainly on the active ankle function of the sound limb; therefore they changed the relative durations of the gait initiation anticipatory postural adjustment phase and the step execution phase. Both limbs were controlled in one single system of gait propulsion.
The shape of the center of pressure trajectories, the applied forces and the center of mass velocity curves are described in this chapter.

Weight bearing - In this study, the occurrences of stabilizing and destabilizing external moments of force on a prosthetic knee during stance, in the first steps after gait initiation, in inexperienced users were investigated. Primary aim was to identify the differences in the external moments during gait initiation with the sound limb leading and the prosthetic limb leading. A prosthetic limb simulator device, with a flexible knee, was used to test able-bodied subjects, with no walking aid experience. Inverse dynamics calculations were performed to calculate the external moments. The subjects learned to control the prosthetic limb within 100 steps, without walking aids, evoking similar patterns of external moments of force during the steps after the gait initiation, either with their sound limb loading or prosthetic limb leading. Critical phases in which a sudden flexion of the knee can occur were found just after heelstrike and just before toe off, in which the external moment of force was close to the internal moment produced by a knee extension aiding spring in the opposite direction.

Prosthetic limb swing - In this study, conditions that enable a prosthetic knee flexion strategy in transfemoral amputee subjects during obstacle avoidance were investigated. This study explored the hip torque principle and the static ground principle as object avoidance strategies. A prosthetic limb simulator device was used to study the influence of applied hip torques and static ground friction on the prosthetic foot trajectory. Inverse dynamics was used to calculate the energy produced by the hip joint. A two-dimensional forward dynamics model was used to investigate the relation between the obstacle-foot distance and the necessary hip torques utilized during obstacle avoidance. The study showed that a prosthetic knee flexion strategy was facilitated by the use of ground friction and by larger active hip torques. This strategy required more energy produced by the hip compared to a knee extension strategy. We conclude that when amputees maintain sufficient distance between the distal tip of the foot and the obstacle during stance, they produce sufficiently high, yet feasible, hip torques and use static ground friction, the amputees satisfy the conditions to enable stepping over an obstacle using a knee flexion strategy.

Gait termination - In this study we investigated how leading limb angles combined with active ankle moments of a sound ankle or passive stiffness of a prosthetic ankle, influence the center of mass velocity during the single limb support phase in gait termination. Also, we studied how the trailing limb velocity influences the center of mass velocity during this phase. We analyzed force plate data from a group of experienced transfermoral amputee subjects using a prosthetic limb, and the outcome from a two dimensional mathematical forward dynamics model. We found that when leading with the sound limb, the subjects came almost to a full stop in the single limb support phase, without the use of the prosthetic limb. When leading with the prosthetic limb, the center of mass deceleration was less in a relatively short single limb support phase, with a fast forward swing of the trailing sound limb. Slowing down the heavier trailing sound limb, compared to the prosthetic limb, results in a relatively larger braking force at the end of the swing phase. The simulations showed that only narrow ranges of leading limb angle and ankle moments could be used to achieve the same center of mass velocities with the mathematical model as the average start and end velocities of the prosthetic limb user. We conclude that users of prosthetic limbs have a narrow range of options for the dynamics variables to achieve a target center of mass velocity. The lack of active control in the passive prosthetic ankle prevents the transfermoral amputee subjects from producing sufficient braking force when terminating gait with the prosthetic limb leading, forcing the subjects to use both limbs as a functional unit, in which the sound limb is mostly responsible for the gait termination.

Discussion and conclusion - In contrast to other researchers, who suggest that it would be of benefit to develop a uniform, robust modelling strategy for both research and clinical rehabilitation practice, it is my opinion that specialised, custom-developed mathematical models can be used to model phenomena that occur in the real world. Based on Occam’s razer principle, we used models that were relatively simple with only limited assumptions, to investigate the principles of transfemoral amputee prosthetic gait.
It should be taken into account that when we want to use these models to make predictions about the four phases of gait in for example the clinical setting, one more important step has to be made in the research process. The validity and usability of our models in both the conceptual and real world have to be verified further by (learning) experiments with transfemoral amputees or with able-bodied subjects using a prosthetic limb simulator device in various conditions, with various (microprocessor controlled) prosthetic components and properties in various environments.

The predictions, outcomes and insights gained from our model and measurement studies contributed to the development of our theory about asymmetry, functional ability and learning, and also formed our ideas about trunk motions and microprocessor controlled limb limbs prosthetics. Based on our findings, we concluded that it is impossible to walk symmetrically with a mechanical prosthetic limb, unless additional efforts are made to compensate for the shortcomings in the prosthetic limb. We expect that improving functional ability, instead of minimizing asymmetry, will contribute to the improvement of the patient satisfaction. According to the principles of Discovery Learning and learning as a function of attentional focus, improving the functional ability can best be achieved by training in environments which enable the transfemoral amputee to find individual optimal performance patterns for complex motor skills.

This thesis is part of a series of theses 1; 2; 3 resulting from the project ’Postural control after lower limb amputation; changes in body representation and the recovery in postural control’. The project is the result of a collaboration between the Center for Rehabilitation Medicine of the University Medical Center Groningen, the Netherlands and the Center for Human Movement Sciences of the University Medical Center Groningen, University of Groningen, the Netherlands.
This integrated approach unites two types of research: research from a clinical science approach and research from an fundamental sciences approach. The clinical research was performed by medical specialist for rehabilitation Aline H. Vrieling. Her thesis (2009) formed the base for the current thesis. Many of the findings that were reported in her thesis were studied from a biomechanics perspective in this second part of the project. Parts of the datasets that were reported in her thesis were also used in the current thesis.


  1. Aline H. Vrieling. Movement and balance control in lower limb amputees. PhD thesis, University of Groningen, 2009.
  2. Carolin Curtze. Neuromechanics of movement in lower limb amputees. PhD thesis, University of Groningen, 2012.
  3. Helco G. van Keeken. Model and measurement studies on stages of prosthetic gait. PhD thesis, University of Groningen, 2013.


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