Dudley S. Childress, PhD and Steven A. Gard, PhD, Principal Investigators
George A. Bertos, MS, Project Director
Co-Investigators: Andrew H. Hansen, PhD; Margrit R. Meier, PhD; Edward C. Grahn; Rebecca L. Stine, MS; and Dilip Thaker
Funded by: National Institute on Disability and Rehabilitation Research (NIDRR)
During walking, persons with lower-limb amputation experience high forces that are transmitted through their prostheses to their trunk. These shock forces are not only uncomfortable and unhealthy for the amputee but may also contribute negatively to the quality of gait. We believe shock absorption is a fundamental aspect of normal and pathological walking which if not set properly can result in poor and injurious gait. We believe that the current prostheses and orthoses of the market may not supply the right shock absorption to the persons who walk with them. One of the reasons for this inadequate shock absorption supply is that there is no clear understanding of how shock absorption is really achieved during normal walking nor how it can be achieved for those who are lacking it.
The purpose of the project is therefore to investigate shock absorption during normal and amputee walking using engineering analysis, models and experiments. The acquired theoretical knowledge of these investigations may lead to the ultimate project goal of designing and prototype testing of new prosthetic devices that are based on this gained knowledge. New shock-absorbing devices could improve the users' comfort and gait, thus would be beneficial to the user community. The gained theoretical understanding will contribute to the science of prosthetics and thus advances our understanding of an important aspect of gait.
We hypothesize that walking may be improved during prosthetic gait (higher force attenuation, higher walking velocities) if proper mechanical impedance characteristics of the prosthesis/residual limb complex are achieved. By "proper mechanical impedance characteristics" we mean characteristics similar to the mechanical impedance characteristics of the able-bodied leg complex (locomotor system) during normal walking. We assume that the impedance characteristics of normal walking are the optimal for the task of human walking in general, normal or prosthetic. Thus we need to systematically characterize the mechanical impedance during able-bodied walking.
Current prostheses cannot automatically change their impedance characteristics. We believe the prostheses' impedance characteristics should change with walking speed (cadence) similar to that of the natural leg during normal walking. Thus, the mechanical impedance of a trans-femoral prosthetic leg (prosthesis plus residual limb) should be designed that it can vary with walking speed. The aim is that the total mechanical impedance of a trans-femoral prosthetic leg is approximately equal to the mechanical impedance of an able-bodied leg during walking.
Gait analysis of able-bodied subjects will be performed to properly characterize the mechanical impedance of non-pathological gait. The characterization of the mechanical impedance of amputee gait will be gained through gait analysis of persons with unilateral transfemoral amputation as well as through persons with bilateral transfemoral amputation. All three groups will walk at their normal selected walking speed, their slowest walking speed and their fastest walking speed.
In order to characterize the vertical mechanical impedance of the locomotor system of each of the subjects we assume a second order model  (see figure 1), for the unknown shock absorption mechanism. Based on the kinematic data we create the vertical path of a rocker-based inverted pendulum model without shock absorption present (terrain yb) and use this as the input to our identification method. The output of the identification method is the vertical BCOM trajectory, ym, (which contains all shock absorption mechanisms). The identification method estimates the values of the second order system matching the estimated output to the given output as close as possible.
Validation of the Model
After having characterized the able-bodied mechanical impedance and the mechanical impedance of the person with bilateral amputation the compensatory prosthesis will be calculated. If the compensatory prosthesis is connected in series with the bilateral amputee's locomotor system, then her or his total system will approximate the able-bodied system. We will validate the identification method used with simulations and a mechanical model, the "walking wheel" (see figure 2).
For one able bodied subject , the fitting of the model to the data was satisfactory. The Variance Accounted For (VAF), an indicator of the fit of a model, ranged from 75-80% for low speeds to 90-95% for normal and fast speeds. Our results support the theory that the damping ratio z = [B/2(Mek)1/2] is fairly constant (z = 0.4 - 0.7) across different walking speeds. Stiffness k appears to increase linearly with walking speed (r2=0.95), being around 6 kN/m at 1.2 m/sec. Damping B appears to increase with the square root of walking speed, (r2=0.75). During able-bodied walking the system appears to be underdamped (0<z<1) having a high performance from a control theory standpoint (fastest response with minimum ripple) with damping ratio z between 0.4 and 0.7. The results also show that the locomotor system of able-bodied walkers acts like a mechanical low-pass filter with cutoff frequency to be very close to the stepping frequency.
We were not able to identify with our previously described identification method  the mechanical impedance of the unilateral transfemoral amputees because of asymmetries between the sound and the affected side of the subject. We tried concatenation but the introduced discontinuities (or any filtering to smooth them) drastically changed the characteristics of the estimated system.
For our bilateral amputee (similar weight and height with our selected able-bodied subject and similar walking speed) we estimated the mechanical impedance via our method since there were no asymmetries between the two sides. The results show that the system is still underdamped but the location of the poles is different than the location of the poles of the able-bodied walker.
We calculated the proposed compensatory prosthesis approximating the able-bodied walker's locomotor system for that speed. The calculated compensatory prosthesis turned out to be a fourth order system which we approximated further to a first order system (simple spring and damper system).
The "walking wheel" model validated our identification method based on input and output data. It predicted correctly the values of the stiffness and damping which were known but not used in the estimation of these values. We are still working on this valuable model in order to develop a theory of shock absorption during walking.
The next step will be to construct two prostheses with the prescribed mechanical impedance values, fit the same bilateral transfemoral amputee with them and compare the resulted gait with the gait without any shock absorption mechanism.
 Bertos, G.A., Childress, D.S., Gard, S.A. (2005) "The vertical mechanical impedance of the locomotor system during human walking with applications in Rehabilitation", IEEE International Conference of Rehabilitation Robotics, Chicago, IL.
Bertos G. (2006) "Identification of the Mechanical Impedance of the Human Locomotor System and Quantification of Shock Absorption Characteristics with Applications in Prosthetics" [PhD Dissertation]. Evanston, IL: Biomedical Engineering, Northwestern University.
Bertos, G.A., Childress, D.S., Gard, S.A. (2005) "The vertical mechanical impedance of the locomotor system during human walking with applications in Rehabilitation", IEEE International Conference of Rehabilitation Robotics, Chicago, IL.
Bertos, G.A., Childress, D.S., Gard, S.A. (2003) "Mechanical impedance identification of the human locomotor system during able-bodied walking", American Society of Biomechanics Conference, Toledo, OH, September 25-27.
Bertos, G.A., Childress, D.S., Gard, S.A. (2003) "A steady state sinusoidal analysis method to identify the mechanical impedance of the human locomotor system during able-bodied walking", 26th International Conference of Rehabilitation Engineering & Assistive Technology of North America (RESNA), Atlanta, GA, June 19-23.