Patellofemoral joint forces

In this review of patellofemoral joint forces as they might apply to implant design, methodologies for estimating forces on the patella and estimates of the forces, as reported in the literature, are summarized. Two methodologies exist for studying joint loads; one that measures kinematics in-vivo and uses analysis to estimate the joint loads and another that measures ground reaction forces and uses analysis to estimate the joint loads. In both these analyses many assumptions are required with varying degrees of uncertainty; here, those assumptions are examined with data from the published literature. The topics covered include: relationships between quadriceps forces and patellofemoral forces or patella ligament forces, relationships between knee joint moments and quadriceps forces, knee joint moments in various gaits, relationships between patellofemoral forces and lateral subluxation forces, and relationships between patella forces and inferior-superior forces. In many cases, there is little data on patella forces during normal activities, in other cases, there are some discrepancies in reported patella forces, i.e. during squat.     

Takeoff and landing forces of leaping strepsirhine primates.

Knowledge of the forces animals generate and are exposed to during locomotion is an important prerequisite for understanding the musculoskeletal correlates of locomotor modes. We recorded takeoff and landing forces for 14 animals representing seven species of strepsirhine primates with a compliant force pole. Our sample included both specialized vertical clingers and leapers and more generalized species. Takeoff forces are higher than landing forces. Peak forces during acceleration for takeoff ranged from 6 to 12 times body weight, and the peak impact forces at landing are between 5 and 9 times body weight. There is a size-related trend in peak force magnitudes. Both takeoff and landing forces decrease with increasing body size in our sample of animals from 1 kg to over 5 kg. Peak forces increase with distance leapt. The distance effect is less clear, probably due to the narrow range of distances represented in our sample. A comparison of subadult and adult animals of two species of sifakas reveals a tendency for the young animals to exert relatively higher peak forces in comparison to their adult conspecifics. Finally, Lemur catta and Eulemur rubriventer, the "generalists" in our sample, tend to generate higher forces for equal tasks than the specialized vertical clingers and leapers (i.e., the indriids and Hapalemur).A broad-scale comparison of peak leaping forces and peak forces for quadrupedal and bipedal walking and running shows that leaping at small body size is associated with exceptionally high forces. Whereas relative forces (i.e., forces divided by body weight) decrease with increasing body mass for leaping, forces for walking and running do not change much with size. Leaping forces in our sample scale to (mass)(-1/3), which is consistent with expectations derived from geometric similarity models. Forces associated with other locomotor activities do not appear to follow this pattern. The very high forces found in strepsirhine leapers do not seem to be matched by bone robusticity beyond that documented for quadrupedal species.     

A 3D lower limb musculoskeletal model for simultaneous estimation of musculo-tendon,joint contact,ligament and bone forces during gait

Musculo-tendon forces and joint reaction forces are typically estimated using a two-step method, computing first the musculo-tendon forces by a static optimization procedure and then deducing the joint reaction forces from the force equilibrium. However, this method does not allow studying the interactions between musculo-tendon forces and joint reaction forces in establishing this equilibrium and the joint reaction forces are usually overestimated. This study introduces a new 3D lower limb musculoskeletal model based on a one-step static optimization procedure allowing simultaneous musculo-tendon, joint contact, ligament and bone forces estimation during gait. It is postulated that this approach, by giving access to the forces transmitted by these musculoskeletal structures at hip, tibiofemoral, patellofemoral and ankle joints, modeled using anatomically consistent kinematic models, should ease the validation of the model using joint contact forces measured with instrumented prostheses. A blinded validation based on four datasets was made under two different minimization conditions (i.e., C1 – only musculo-tendon forces are minimized, and C2 – musculo-tendon, joint contact, ligament and bone forces are minimized while focusing more specifically on tibiofemoral joint contacts). The results show that the model is able to estimate in most cases the correct timing of musculo-tendon forces during normal gait (i.e., the mean coefficient of active/inactive state concordance between estimated musculo-tendon force and measured EMG envelopes was C1: 65.87% and C2: 60.46%). The results also showed that the model is potentially able to well estimate joint contact, ligament and bone forces and more specifically medial (i.e., the mean RMSE between estimated joint contact force and in vivo measurement was C1: 1.14BW and C2: 0.39BW) and lateral (i.e., C1: 0.65BW and C2: 0.28BW) tibiofemoral contact forces during normal gait. However, the results remain highly influenced by the optimization weights that can bring to somewhat aphysiological musculo-tendon forces.     

Integrins and extracellular matrix in mechanotransduction

Integrins bind extracellular matrix fibrils and associate with intracellular actin filaments through a variety of cytoskeletal linker proteins to mechanically connect intracellular and extracellular structures. Each component of the linkage from the cytoskeleton through the integrin-mediated adhesions to the extracellular matrix therefore transmits forces that may derive from both intracellular, myosin-generated contractile forces and forces from outside the cell. These forces activate a wide range of signaling pathways and genetic programs to control cell survival, fate, and behavior. Additionally, cells sense the physical properties of their surrounding environment through forces exerted on integrin-mediated adhesions. This article first summarizes current knowledge about regulation of cell function by mechanical forces acting through integrin-mediated adhesions and then discusses models for mechanotransduction and sensing of environmental forces.     

External forces on the limbs of jumping lemurs at takeoff and landing

Ground reaction forces were recorded for jumps of three individuals each of Lemur catta and Eulemur fulvus. Animals jumped back and forth between a ground-mounted force plate and a 0.5-m elevated platform, covering horizontal distances of 0.5-2 m. In total, 190 takeoffs and 263 landings were collected. Animals typically jumped from a run up and into a run out, during which they gained or into which they carried horizontal impulse. Correspondingly, vertical impulses dominated takeoffs and landings. Peak forces were moderate in magnitude and not much higher than forces reported for quadrupedal gaits. This is in contrast to the forces for standing jumps of specialized leapers that considerably exceed forces associated with quadrupedal gaits. Force magnitudes for the lemur jumps are more comparable to peak forces reported for other quadrupeds performing running jumps. Takeoffs are characterized by higher hindlimb than forelimb peak forces and impulses. L. catta typically landed with the hindlimbs making first contact, and the hindlimb forces and impulses were higher than the forelimb forces and impulses at landing. E. fulvus typically landed with the forelimbs striking first and also bearing the higher forces. This pattern does not fully conform to the paradigm of primate limb force distribution, with higher hindlimb than forelimb forces. However, the absolute highest forces in E. fulvus also occur at the hindlimbs, during acceleration for takeoff.     

Traction forces generated by locomoting keratocytes

Traction forces produced by moving fibroblasts have been observed as distortions in flexible substrata including wrinkling of thin, silicone rubber films. Traction forces generated by fibroblast lamellae were thought to represent the forces required to move the cell forwards. However, traction forces could not be detected with faster moving cell types such as leukocytes and growth cones (Harris, A. K., D. Stopak, and P. Wild. 1981. Nature (Lond.). 290:249-251). We have developed a new assay in which traction forces produced by rapidly locomoting fish keratocytes can be detected by the two-dimensional displacements of small beads embedded in the plane of an elastic substratum. Traction forces were not detected at the rapidly extending front edge of the cell. Instead the largest traction forces were exerted perpendicular to the left and right cell margins. The maximum traction forces exerted by keratocytes were estimated to be approximately 2 x 10(-8) N. The pattern of traction forces can be related to the locomotion of a single keratocyte in terms of lamellar contractility and area of close cell- substratum contact.     

The effect of vastus medialis forces on patello-femoral contact: a model-based study

A mathematical model of the patello-femoral joint was introduced to investigate the impact of the vastus medialis (longus, obliquus) forces on the lateral contact force levels. In the model, the quadriceps were represented as five separate forces: vastus lateralis, vastus intermedius, rectus femoris, vastus medialis longus (VML), and obliquus (VMO). By varying the relative force generation ratios of the quadriceps heads, the patello-femoral contact forces were estimated. We sought to analytically determine the range of forces in the VMO and VML that cause a reduction or an increase of lateral contact forces, often the cause of patello-femoral pain. Our results indicated that increased contact forces are more dependent on combinations of muscle forces than solely VMO weakness. Moreover, our simulation data showed that the contact force levels are also highly dependent on the knee flexion angle. These findings suggest that training targeted to reduce contact forces through certain joint angles could actually result in a significant increase of the contact forces through other joint angles.     

Decoupling Substrate Stiffness, Spread Area, and Micropost Density: A Close Spatial Relationship between Traction Forces and Focal Adhesions

Mechanical cues can influence the manner in which cells generate traction forces and form focal adhesions. The stiffness of a cell's substrate and the available area on which it can spread can influence its generation of traction forces, but to what extent these factors are intertwined is unclear. In this study, we used microcontact printing and micropost arrays to control cell spreading, substrate stiffness, and post density to assess their effect on traction forces and focal adhesions. We find that both the spread area and the substrate stiffness influence traction forces in an independent manner, but these factors have opposite effects: cells on stiffer substrates produce higher average forces, whereas cells with larger spread areas generate lower average forces. We show that post density influences the generation of traction forces in a manner that is more dominant than the effect of spread area. Additionally, we observe that focal adhesions respond to spread area, substrate stiffness, and post density in a manner that closely matches the trends seen for traction forces. This work supports the notion that traction forces and focal adhesions have a close relationship in their response to mechanical cues.     

A method of calculating physiologically relevant joint reaction forces during forward dynamic simulations of movement from an existing knee model

In the commonly used SIMM software, which includes a complete musculoskeletal model of the lower limbs, the reaction forces at the knee are computed. These reaction forces represent the bone-on-bone contact forces and the soft tissue forces (e.g. ligaments) other than muscles acting at the joint. In the knee model integrated into this software, a patellotibial joint rather than a patellofemoral joint is defined, and a force acting along the direction of the patellar ligament is not included. Although this knee model results in valid kinematics and muscle moment arms, the reaction forces at the knee calculated do not represent physiologic knee joint reaction forces. Hence our objectives were to develop a method of calculating physiologic knee joint reaction forces using the knee model incorporated into the SIMM software and to demonstrate the differences in the forces returned by SIMM and the physiologic forces in an example. Our method converts the anatomically fictional patellotibial joint into a patellofemoral joint and computes the force in an inextensible patellar ligament. In our example, the rectus femoris was fully excited isometrically, with the knee and hip flexed to 90 degrees . The resulting SIMM tibiofemoral joint reaction force was primarily shear, because the quadriceps force was applied to the tibia via the fictional patellotibial joint. In contrast the physiologic tibiofemoral joint reaction force was primarily compression, because the quadriceps force was applied through the patellar ligament. This result illustrates that the physiologic knee joint reaction forces are profoundly different than the forces returned by SIMM. However physiologic knee joint reaction forces can be computed with postprocessing of SIMM results.     

A biomechanical model for the analysis of the cervical spine in static postures.

To gain a better understanding of the forces working on the cervical spine, a spatial biomechanical computer model was developed. The first part of our research was concerned with the development of a kinematic model to establish the axes of rotation and the mutual position of the head and vertebrae with regard to flexion, extension, lateroflexion and torsion. The next step was the introduction of lines of action of muscle forces and an external load, created by gravity and accelerations in different directions, working on the centre of gravity of the head and possibly a helmet. Although the results of our calculations should be interpreted cautiously in the present stage of our research, some conclusions can be drawn with respect to different head positions. During flexion muscle forces and joint reaction forces increase, except the force between the odontoid and the ligamentum transversum atlantis. This force shows a minimum during moderate flexion. The joint reaction forces on the levels C0-C1, C1-C2, and C7-T1 reach minimum values during extension, each in different stages of extension. Axial rotation less than 35 degrees does not need great muscle forces, axial rotation further than 35 degrees causes muscle forces and joint reaction forces to increase fast. While performing, lateral flexion muscle forces and joint reaction forces must increase rapidly to balance the head. We obtained some indications that the order of magnitude of the calculated forces is correct.     

Cooperative retraction of bundled type IV pili enables nanonewton force generation

The causative agent of gonorrhea, Neisseria gonorrhoeae, bears retractable filamentous appendages called type IV pili (Tfp). Tfp are used by many pathogenic and nonpathogenic bacteria to carry out a number of vital functions, including DNA uptake, twitching motility (crawling over surfaces), and attachment to host cells. In N. gonorrhoeae, Tfp binding to epithelial cells and the mechanical forces associated with this binding stimulate signaling cascades and gene expression that enhance infection. Retraction of a single Tfp filament generates forces of 50–100 piconewtons, but nothing is known, thus far, on the retraction force ability of multiple Tfp filaments, even though each bacterium expresses multiple Tfp and multiple bacteria interact during infection. We designed a micropillar assay system to measure Tfp retraction forces. This system consists of an array of force sensors made of elastic pillars that allow quantification of retraction forces from adherent N. gonorrhoeae bacteria. Electron microscopy and fluorescence microscopy were used in combination with this novel assay to assess the structures of Tfp. We show that Tfp can form bundles, which contain up to 8–10 Tfp filaments, that act as coordinated retractable units with forces up to 10 times greater than single filament retraction forces. Furthermore, single filament retraction forces are transient, whereas bundled filaments produce retraction forces that can be sustained. Alterations of noncovalent protein–protein interactions between Tfp can inhibit both bundle formation and high-amplitude retraction forces. Retraction forces build over time through the recruitment and bundling of multiple Tfp that pull cooperatively to generate forces in the nanonewton range. We propose that Tfp retraction can be synchronized through bundling, that Tfp bundle retraction can generate forces in the nanonewton range in vivo, and that such high forces could affect infection.     

Effects of slope, substrate, and temperature on forces associated with locomotion of the ornate box turtle, Terrapene ornata

In spite of several studies of the locomotor performances of reptiles, we know as yet relatively little about the mechanical forces involved. The present investigation examined the effects of substrate, slope and temperature on the pulling forces exerted by ornate box turtles tethered to a force transducer. These forces increased with body mass in a nearly isometric manner. The forces exerted during the initial effort were greatest on a styrofoam substrate, whereas maximum forces generated were greatest on pea gravel. Both forces progressively increased as slope decreased from +30 degrees to -30 degrees. The rate of force generation (N/s) was greatest at intermediate slopes. Contact force tended to increase as normal force increased, and was strongly influenced by slope, increasing from -30 degrees to +30 degrees. Surprisingly, we found no significant effects of temperature on tether forces, contraction times, or rates. This evaluation of pulling forces associated with box turtle locomotion revealed some interesting, and at times unexpected, relationships.     

High-resolution micromechanical measurement in real time of forces exerted by living cells

The aim of this study was to compare uniaxial traction forces exerted by different cell types using a novel sensor design and to test the dependence of measured forces on cytoskeletal integrity. The sensor design detects forces generated between 2 contact points by cells spanning a gap. The magnitude of these forces varied according to cell type and were dependent on cytoskeletal integrity. The response time for drug-induced cytoskeletal disruption also varied between cell types: dermal fibroblasts exerted the greatest forces and had the slowest drug response times; EBV-transformed epithelial cells also had slow cytoskeletal depolymerisation times but exerted the lowest forces overall. Conversely, lung epithelial tumor cells exerted low forces but had the fastest depolymerisation drug response. These results provide proof of principle for a new design of force-measurement sensor based on optical interferometry, an approach that can be used to study cytoskeletal dynamics in real time.     

Force and torque production in static multifinger prehension: biomechanics and control. II. Control

 The coordination of digits during combined force/torque production tasks was further studied using the data presented in the companion paper [Zatsiorsky et al. Biol Cybern this issue, Part I]. Optimization was performed using as criteria the cubic norms of (a) finger forces, (b) finger forces normalized with respect to the maximal forces measured in single-finger tasks, (c) finger forces normalized with respect to the maximal forces measured in a four-finger task, and (d) finger forces normalized with respect to the maximal moments that can be generated by the fingers. All four criteria failed to predict antagonist finger moments when these moments were not imposed by the task mechanics. Reconstruction of neural commands: The vector of neural commands c was reconstructed from the equation c=W ⁻¹ F, where W is the finger interconnection weight matrix and F is the vector of finger forces. The neural commands ranged from zero (no voluntary force production) to one (maximal voluntary contraction). For fingers producing moments counteracting the external torque (`agonist' fingers), the intensity of the neural commands was well correlated with the relative finger forces normalized to the maximal forces in a four-finger task. When fingers produced moments in the direction of the external torque (`antagonist' fingers), the relative finger forces were always larger than those expected from the intensity of the corresponding neural commands. The individual finger forces were decomposed into forces due to `direct' commands and forces induced by enslaving effects. Optimization of the neural commands resulted in the best correspondence between actual and predicted finger forces. The antagonist moments are, at least in part, due to enslaving effects: strong commands to agonist fingers also activated antagonist fingers. Received: 8 August 2001 / Accepted in revised form: 7 February 2002     

Individual muscle contributions to the axial knee joint contact force during normal walking

Muscles are significant contributors to the high joint forces developed in the knee during human walking. Not only do muscles contribute to the knee joint forces by acting to compress the joint, but they also develop joint forces indirectly through their contributions to the ground reaction forces via dynamic coupling. Thus, muscles can have significant contributions to forces at joints they do not span. However, few studies have investigated how the major lower-limb muscles contribute to the knee joint contact forces during walking. The goal of this study was to use a muscle-actuated forward dynamics simulation of walking to identify how individual muscles contribute to the axial tibio-femoral joint force. The simulation results showed that the vastii muscles are the primary contributors to the axial joint force in early stance while the gastrocnemius is the primary contributor in late stance. The tibio-femoral joint force generated by these muscles was at times greater than the muscle forces themselves. Muscles that do not cross the knee joint (e.g., the gluteus maximus and soleus) also have significant contributions to the tibio-femoral joint force through their contributions to the ground reaction forces. Further, small changes in walking kinematics (e.g., knee flexion angle) can have a significant effect on the magnitude of the knee joint forces. Thus, altering walking mechanics and muscle coordination patterns to utilize muscle groups that perform the same biomechanical function, yet contribute less to the knee joint forces may be an effective way to reduce knee joint loading during walking.     

Computational biodynamics of human knee joint in gait: from muscle forces to cartilage stresses

Using a validated finite element model of the intact knee joint we aim to compute muscle forces and joint response in the stance phase of gait. The model is driven by reported in vivo kinematics-kinetics data and ground reaction forces in asymptomatic subjects. Cartilage layers and menisci are simulated as depth-dependent tissues with collagen fibril networks. A simplified model with less refined mesh and isotropic depth-independent cartilage is also considered to investigate the effect of model accuracy on results. Muscle forces and joint detailed response are computed following an iterative procedure yielding results that satisfy kinematics/kinetics constraints while accounting at deformed configurations for muscle forces and passive properties. Predictions confirm that muscle forces and joint response alter substantially during the stance phase and that a simplified joint model may accurately be used to estimate muscle forces but not necessarily contact forces/areas, tissue stresses/strains, and ligament forces. Predictions are in general agreement with results of earlier studies. Performing the analyses at 6 periods from beginning to the end (0%, 5%, 25%, 50%, 75% and 100%), hamstrings forces peaked at 5%, quadriceps forces at 25% whereas gastrocnemius forces at 75%. ACL Force reached its maximum of 343 N at 25% and decreased thereafter. Contact forces reached maximum at 5%, 25% and 75% periods with the medial compartment carrying a major portion of load and experiencing larger relative movements and cartilage strains. Much smaller contact stresses were computed at the patellofemoral joint. This novel iterative kinematics-driven model is promising for the joint analysis in altered conditions.     

Flow mechanotransduction regulates traction forces, intercellular forces, and adherens junctions

Endothelial cells respond to fluid shear stress through mechanotransduction responses that affect their cytoskeleton and cell-cell contacts. Here, endothelial cells were grown as monolayers on arrays of microposts and exposed to laminar or disturbed flow to examine the relationship among traction forces, intercellular forces, and cell-cell junctions. Cells under laminar flow had traction forces that were higher than those under static conditions, whereas cells under disturbed flow had lower traction forces. The response in adhesion junction assembly matched closely with changes in traction forces since adherens junctions were larger in size for laminar flow and smaller for disturbed flow. Treating the cells with calyculin-A to increase myosin phosphorylation and traction forces caused an increase in adherens junction size, whereas Y-27362 cause a decrease in their size. Since tugging forces across cell-cell junctions can promote junctional assembly, we developed a novel approach to measure intercellular forces and found that these forces were higher for laminar flow than for static or disturbed flow. The size of adherens junctions and tight junctions matched closely with intercellular forces for these flow conditions. These results indicate that laminar flow can increase cytoskeletal tension while disturbed flow decreases cytoskeletal tension. Consequently, we found that changes in cytoskeletal tension in response to shear flow conditions can affect intercellular tension, which in turn regulates the assembly of cell-cell junctions.     

Mechanotransduction in blood cells

Blood cells are subjected to various mechanical forces; including pressure, flow, shear force, gravity, and forces acting against them with varying stiffness (eg. blood vessel wall). Scientists have discovered that these forces have profound effects on cellular growth, differentiation, secretion of cytokines, cell death, and migration. These processes are called mechanotransduction, a conversion of mechanical forces to biochemical signals. In this article the author reviews biophysical forces that affect biological functions of blood cells and their responses in normal physiology and pathophysiology. Although input (forces) and output (cellular responses) have been well studied by utilizing recently developed various force-generating devices, the molecular mechanism of mechanotransudction is still a mystery. This is because reconstructing molecular interaction in the presence of mechanical forces in vitro is highly challenging and until now the molecular dynamics involved in structural changes caused by these forces are largely unknown. Nevertheless, the author has reviewed a few examples of potential structural effects on the molecular mechanism of mechanotransduction.     

How do low horizontal forces produce disproportionately high torques in human locomotion?

Although horizontal ground forces are only approximately 15% of vertical forces, they account for 47% and 33% of the metabolic cost in walking and running. To explain these disproportionately high metabolic costs, we hypothesized that low horizontal ground forces generate relatively high torques on body segments during locomotion and this is mediated by long moment arms. We compared external force moment arms and discreet torques applied to the body segments by horizontal and vertical forces during walking and running. Sixteen subjects (21.9+/-1.9 years) walked at 1.5m/s and ten subjects (23.2+/-2.0 years) ran at 3.83 m/s. Segmental torques in the sagittal plane were partitioned into components due to horizontal and vertical forces and quantified by their angular impulses. The mean (+/-S.E.) ratios of horizontal to vertical ground forces (GF ratio) and angular impulses (AI ratio) in walking were 0.131 (+/-0.003, 95% confidence interval (CI) 0.124-0.137) and 0.530 (+/-0.018, CI 0.497-0.569). Results were similar in running. In both gaits the AI ratios were significantly greater than the GF ratios because the respective CI's did not overlap. The horizontal forces produced 53% and 41% as much angular impulse on the body segments, as did the vertical forces in walking and running despite being only 13% as large. In the two movements the moment arms for the horizontal forces averaged across foot, leg, thigh, and trunk body segments were 3.8 fold larger than those for the vertical forces. The data supported the hypothesis and suggest that the relatively low horizontal vs. vertical forces accounted for a disproportionately higher percentage of the angular impulses placed on the body segments and this effect was due to relatively long moment arms for horizontal forces. These results partially explain the relatively large metabolic cost of generating relatively low horizontal forces.     

The effects of mechanical forces on intestinal physiology and pathology

The epithelial and non-epithelial cells of the intestinal wall experience a myriad of physical forces including strain, shear, and villous motility during normal gut function. Pathologic conditions alter these forces, leading to changes in the biology of these cells. The responses of intestinal epithelial cells to forces vary with both the applied force and the extracellular matrix proteins with which the cells interact, with differing effects on proliferation, differentiation, and motility, and the regulation of these effects involves similar but distinctly different signal transduction mechanisms. Although normal epithelial cells respond to mechanical forces, malignant gastrointestinal epithelial cells also respond to forces, most notably by increased cell adhesion, a critical step in tumor metastasis. This review will focus on the phenomenon of mechanical forces influencing cell biology and the mechanisms by which the gut responds these forces in both the normal as well as pathophysiologic states when forces are altered. Although more is known about epithelial responses to force, information regarding mechanosensitivity of vascular, neural, and endocrine cells within the gut wall will also be discussed, as will, the mechanism by which forces can regulate epithelial tumor cell adhesion.