Finite element modelling of an energy–storing prosthetic foot during the stance phase of transtibial amputee gait

Energy-storing prosthetic feet are designed to store energy during mid-stance motion and to recover it during latestance motion. Gait analysis is the most commonly used method to characterize prosthetic foot behaviour during walking. In using this method, however, the foot is generally modelled as a rigid body. Therefore, it does not take into account the ability of the foot to deform. However, the way this deformation occurs is a key parameter of various foot properties under gait conditions. The purpose of this study is to combine finite element modelling and gait analysis in order to calculate the strain, stress and energy stored in the foot along the stance phase for self-selected and fast walking speeds. A finite element model, validated using mechanical testing, is used with boundary conditions collected experimentally from the gait analysis of a single transtibial amputee. The stress, strain and energy stored in the foot are assessed throughout the stance phase for two walking speed conditions: a self-selected walking speed (SSWS), and a fast walking speed (FWS). The first maximum in the strain energy occurs during heel loading and reaches 3 J for SSWS and 7 J for FWS at the end of the first double support phase. The second maximum appears at the end of the single support phase, reaching 15 J for SSWS and 18 J for FWS. Finite element modelling combined with gait analysis allows the calculation of parameters that are not obtainable using gait analysis alone. This modelling can be used in the process of prosthetic feet design to assess the behaviour of a prosthetic foot under specific gait conditions

Mechanical work performed by individual limbs of transfemoral amputees during step-to-step transitions: Effect of walking velocity

The greater metabolic demand during the gait of people with a transfemoral amputation limits their autonomy and walking velocity. Major modifications of the kinematic and kinetic patterns of transfemoral amputee gait quantified using gait analysis may explain their greater energy cost. Donelan et al. proposed a method called the individual limb method to explore the relationships between the gait biomechanics and metabolic cost. In the present study, we applied this method to quantify mechanical work performed by the affected and intact limbs of transfemoral amputees. We compared a cohort of six active unilateral transfemoral amputees to a control group of six asymptomatic subjects. Compared to the control group, we found that there was significantly less mechanical work produced by the affected leg and significantly more work performed by the unaffected leg during the step-to-step transition. We also found that this mechanical work increased with walking velocity; the increase was less pronounced for the affected leg and substantial for the unaffected leg. Finally, we observed that the lesser work produced by the affected leg was linked to the increase in the hip flexion moment during the late stance phase, which is necessary for initiating knee flexion in the affected leg. It is possible to quantify the mechanical work performed during gait by people with a transfemoral amputation, using the individual limb method and conventional gait laboratory equipment. The method provides information that is useful for prosthetic fitting and rehabilitation

Teoría del control óptimo: ¡Una guía para principiantes!

El objetivo de este artículo es doble: en una primera parte, se dan las principales intuiciones de la teoría de control óptimo. En la segunda parte se expondrán las grandes familias de problemas de control óptimo, así como las teorías correspondientes. Las aplicaciones a problemas económicos de esos teoremas serán ilustrados a lo largo de todo el documento.

Carath\'eodory Theory and A Priori Estimates for Continuity Inclusions in the Space of Probability Measures

In this article, we extend the foundations of the theory of differential inclusions in the space of probability measures with compact support, laid down recently in one of our previous work, to the setting of general Wasserstein spaces. Anchoring our analysis on novel estimates for solutions of continuity equations, we propose a new existence result ``\`a la Peano'' for this class of dynamics, under mere Carath\'eodory regularity assumptions. The latter is based on a set-valued generalisation of the semi-discrete Euler scheme proposed by Filippov to study ordinary differential equations with measurable right-hand sides. We also bring substantial improvements to the earlier versions of the Filippov theorem, compactness and relaxation properties of the solution sets of continuity inclusions which are derived in the more restrictive Cauchy-Lipschitz setting

Vaulting quantification during level walking of transfemoral amputees

Background: Vaulting is a gait compensatory mechanism used by transfemoral amputees to assist toe clearance during the prosthetic swing phase. It is defined by a plantar flexion of the contralateral ankle during the single-limb support phase. The aim of the study is to propose a method to quantify vaulting of transfemoral amputees. Methods: 17 transfemoral amputees and 28 asymptomatic subjects participated in the data collection. Kinematics and kinetics of thewhole bodywere recordedwhile subjectswerewalking on a level surface. Biomechanical gait analysis was focused on a reduced set of parameters linked to the contralateral ankle, the contralateral knee and the trajectory of the center of pressure. The patients were classified in two groups: with orwithout vaulting using video recordings. Differences between both groups and the control group were analyzed. Findings: A higher generated ankle powerwas found during the single support phase of the contralateral limb of transfemoralamputees presenting vaulting. These subjects presented also a higher dissipated knee flexion power before the peak in ankle flexion power. The trajectory of the center of pressurewas also modified by the vaulting. Interpretation: Vaulting for transfemoral amputees is characterized by a propulsive plantar flexion at the contralateral ankle. Quantifying the ankle flexion power during the contralateral single support phase will help in understanding vaulting.This study was supported by the French National Research Agency, under reference ANR-2010-TECS-020. The authors are deeply grateful to F. Lavaste, N. Martinet, J. Paysant, and N. Rapin for their contribution to the study

Chromosomal control of pig populations in France: 2002-2006 survey

The chromosomal control of pig populations has been widely developed in France over the last ten years. By December 31st, 2006, 13 765 individuals had been karyotyped in our laboratory, 62% of these since 2002. Ninety percent were young purebred boars controlled before service in artificial insemination centres, and 3% were hypoprolific boars. So far, 102 constitutional structural chromosomal rearrangements (67 since 2002) have been described. Fifty-six were reciprocal translocations and 8 peri- or paracentric inversions. For the first time since the beginning of the programme and after more than 11 000 pigs had been karyotyped, one Robertsonian translocation was identified in 2005 and two others in 2006. The estimated prevalence of balanced structural chromosomal rearrangements in a sample of more than 7700 young boars controlled before service was 0.47%. Twenty-one of the 67 rearrangements described since 2002 were identified in hypoprolific boars. All were reciprocal translocations. Twelve mosaics (XX/XY in 11 individuals, XY/XXY in one individual) were also diagnosed. Two corresponded to hypoprolific boars, and three to intersexed animals. The results presented in this communication would justify an intensification of the chromosomal control of French and, on a broader scale, European and North-American pig populations

Influence of physical capacities of males with transtibial amputation on gait adjustments on sloped surfaces

The aim of the study was to investigate how kinematic and kinetic adjustments between level and slope locomotion of persons with transtibial amputation are related to their individual muscular and functional capacities. A quantified gait analysis was conducted on flat and slope surfaces for seven patients with transtibial amputation and a control group of eight subjects to obtain biomechanical parameters. In addition, maximal isometric muscular strength (knee and hip extensors) and functional scores were measured. The results of this study showed that most of the persons with transtibial amputation could adapt to ramp ascent either by increasing ankle, knee, and hip flexion angles of the residual limb and/or by recruiting their hip extensors to guarantee enough hip extension power during early stance. Besides, 6-minute walk test score was shown to be a good predictor of adaptation capacities to slope ascent. In ramp descent, the increase of knee flexion moment was correlated with knee extensor strength and residual-limb length. However, no correlation was observed with functional parameters. Results show that the walking strategy adopted by persons with transtibial amputation to negotiate ramp locomotion mainly depends on their muscular capacities. Therefore, muscular strengthening should be a priority during rehabilitation.This material was based on work supported by the French National Research Agency (grant ANR-2010-TECS-020)

Pre- and postnatal adipose tissue development in farm animals: from stem cells to adipocyte physiology

To view supplementary material for this article, please visit http://dx.doi.org/10.1017/S1751731116000872Both white and brown adipose tissues are recognized to be differently involved in energy metabolism and are also able to secrete a variety of factors called adipokines that are involved in a wide range of physiological and metabolic functions. Brown adipose tissue is predominant around birth, except in pigs. Irrespective of species, white adipose tissue has a large capacity to expand postnatally and is able to adapt to a variety of factors. The aim of this review is to update the cellular and molecular mechanisms associated with pre- and postnatal adipose tissue development with a special focus on pigs and ruminants. In contrast to othertissues, the embryonic origin of adipose cells remains the subject of debate. Adipose cells arise from the recruitment of specific multipotent stem cells/progenitors named adipose tissue-derived stromal cells. Recent studies have highlighted the existence of a variety of those cells being able to differentiate into white, brown or brown-like/beige adipocytes. After commitment to the adipocyte lineage, progenitors undergo large changes in the expression of many genes involved in cell cycle arrest, lipid accumulation and secretory functions. Early nutrition can affect these processes during fetal and perinatal periods and can also influence or pre-determinate later growth of adipose tissue. How these changes may be related to adipose tissue functionalmaturity around birth and can influence newborn survival is discussed. Altogether, a better knowledge of fetal and postnatal adipose tissue development is important for various aspects of animal production, including neonatal survival, postnatal growth efficiency and health

Foot-flat Period Estimation During Daily Living Situations of Asymptomatic and Lower Limb Amputee Subjects

Walking in various situations is a challenging task for people with a lower limb amputation. Walking upslope and downslope requires a larger ankle range of motion than waking on a level ground. Most of prosthetic feet do not include an ankle joint. The ankle mobility is obtained via the deformation of a composite structure or via rub- bers. The range of motion of the “ankle-foot” component is directly linked to the stiffness of the structure and to the load applied on the prosthesis. In ramps, prosthetic “ankle-feet” present a lack of dorsiflexion when going up and a lack of plantar flexion when going down (Williams et al. 2009). A decreased “ankle-foot” range of motion results in a reduced foot-flat period (FFP) which can induce insta- bility. New systems were proposed to allow ankle-foot prostheses to adapt to slopes (Sup et al. 2009; Williams et al. 2009; Fradet et al. 2010). Foot flat evaluation during different situations within the asymptomatic population could help to define a tar- get for prosthetic design. This parameter could also be a very interesting tool for orthoprosthesist to give a feed- back of the fitting of the prosthesis to the patient (Agrawal et al. 2009). A good adaptation of the prosthetic foot to the ground should result in a longer FFP and traduce the security of the subject on its prosthesis during stance phase. In the same way, a correct toe clearance during the swing phase will correspond to a contralateral side FFP close to normal. Actually, amputee people often demon- strate vaulting during swing phase showing their fear to stumble and fall. The evaluation of this parameter is all the more interesting for comparison purpose as it is not well taken into account during nowadays prosthesis design (Williams et al. 2009). Besides, FFP can be determined from on board measurements (Mariani et al. 2013) in real life conditions. However, for the moment, there are no reference data of FFP available in the literature.his work was supported by the French National Research Agency [grant number ANR-292 2010-TECS-020]