Team+6

 **__Team J.A.M.A!__**


 * __Research Question:__

To what extent do forces and kinematics of prosthetic legs mimic those of real legs?**

__**Background Information:**__

Though prosthetics seem like a modern invention, they have been around since the early civilizations of Egypt, Greece, and Rome. Back in the day, prosthetics were simply replacements for missing body parts, but now they help people have normal and active lives. Wars allowed for prosthetic advancements but significant prosthetic developments did not occur until World War II because of the low amount of amputees in World War I. The United States government worked with military companies to improve prosthetics during the war and this allowed for other countries such as Russia to begin improving the prosthetics to be more efficient and comfortable. From wooden legs we find on pirates to the highly advanced robotic legs we find on paralympic runners, prosthetics have come a long way and the physics behind them allows for amputees to understand their new body part and how to enjoy them in their active lives.


 * __Time Line:__**

1529: Ambroise Pare introduces the concept of amputation to his community. He is considered the “Father of Prosthetics.” Later in his life, he began to create artificial limbs which became concepts for future prosthetics. 1696: A Dutch surgeon named Pieter Andriannszoon Verduyn developed the first non-locking prosthesis for below the knee. This prosthesis is the basis for current joint prosthesis. 1861-1865: The American Civil War marked the beginning of the prosthetics field in the United States. History recorded around 30,000 amputations for the Union side alone. Therefore, the need for prosthetics was in high demand. 1914-1918: With telephones and phone directories, the prosthetics field was enhanced because doctors would have more patients desiring prosthetics. Because there were more patients, the prosthetics were further developed to suit the patients’ needs. 1939-1945: The most significant prosthetic developments occurred after World War II. The World War II veterans found that their current prosthetics were insufficient for their lifestyle and desired for more advancements in the prosthetic field. Instead of improving weaponry, the US government made deals with military governments to improve prosthetics. Along with these deals, the government also provided prosthetics training and increased funding for engineering research in universities like UNC. 1960-1970: Before this time period, prosthetics functioned by man-power. After the Vietnam war, the new group of amputees stimulated more refinements in the prosthetic field. These refinements led to prosthetics that could be controlled electronically instead of manually. Present: Along with advancements for humans, the prosthetics field is now creating prosthetics for animals. We have come a long way.


 * __Log Sheet__**

||= Date ||= Time ||= Content || ||=  9/23  ||=  :45  ||=  Decided on the topic of submarine depth charges || ||=  10/3  ||=  1 hr  ||=  Researched topic and updated page || ||=  10/9  ||=  :15  ||=  Determined inviability of current topic and selected a new topic || Research and Writing ||= 11/16 ||=   2 hrs ||= Researched forces on prosthetics and began setting up board || Analysis and Writing ||= 11/20 ||=   1.5 hrs ||= Began to analyze the data we found and began writeup for board || Board Assembly ||= 11/28 ||=   2 hrs ||= Finished writeups and nearly finished board assembly || Final Board Assembly ||= 11/30  ||=  1 hr  ||= Board completed and project finished! || ||=    ||=    ||=    ||  ||=    ||=    ||= ||
 * = Name(s)
 * = Topic Selection
 * = Research
 * = Topic Modification

Include history of prosthetics along bottom of board. Use Load Transfer Mechanics for its diagram on the forces acting on a prosthetic leg. Include in center of board. Also discuss energy used in prosthetics and speed of gait. Conclude including its ethical/international implications
 * __Plan for Board__**:

Angela - History, background, research question Anayeli - Energy in a prosthetic leg compared to a natural leg Matt - Forces exerted during prosthetic gait Joanna - Momentum and velocity in prosthetics v. natural limbs
 * __Work Assignments__**

Ideally, the velocity of the different aspects of a prosthetic and natural limb should be similar. Although forces must be applied somewhat differently due to how the prosthetic leg is joined to the stump, prosthetics attempt to identically mimic the velocity of the natural leg. Essentially, walking is cyclical motion, since force is put into the system to ensure a similar pattern for each step. The mechanics of how walking is accomplished is the same in both a prosthetic and a natural leg. The basic principle is that the knee is lifted forward by the quadriceps and, because of the momentum of the knee’s velocity, the lower leg swings forward until the knee locks. After the knee locks, momentum and the force of gravity pull the heel into the ground until it strikes. Then, gait is initiated by the quadriceps in the other leg, and the continuous momentum changes the center of gravity such that the back leg has force in its toe, not the heel. In spite of the similarities, the nature of prosthetics can change the velocity and momentum of normal gait. In particular, if a prosthetic is modified to increase stiffness, such as through the insertion of a spring, movement is not as damped in the prosthetic as it would be in a natural leg. [1] That is why the International Association of Athletics Federation questioned the eligibility of double-amputee Oscar Pistorius to compete in the Olympics: with their heightened stiffness, his prosthetics were able to conserve momentum and thus generate more velocity. Therefore, modifications to prosthetics change the velocity and momentum, thus affecting their similarity to natural limbs. The other factor to consider is that the model that expresses the similarity between prosthetic and natural mechanics ignores the idea of imperfect gait. Humans do not always walk as the model suggests. Instead, we often drag our feet or lock our knee for the duration of the gait when we are progressing more slowly. However, in order for the patterns of prosthetics to be effective, prosthetic users must use the swing-strike pattern, which is common in natural gait, but not exclusively how humans walk.
 * __Momentum and Velocity in Prosthetics Compared to Natural Limbs__** (a preliminary version)

[1] Synthesis of Human Walking: A Three-Dimensional Model for Single Support, 12.


 * __Forces in Prosthetics__**

Picture from: Load transfer mechanics between trans-tibial prosthetic socket and residual limb—dynamic effects by Ming Zhang


 * Comparison of Forces Exerted Upon Real and Prosthetic Legs**


 * Intro**

Thanks to centuries of technological development, we now can nearly replicate a human leg in the form of a prosthesis. Prosthetic legs especially have made great strides towards allowing amputees to regain a normal life. However, the leg is still just a prosthetic and requires years of practice on the part of the amputee before he or she returns to anywhere near to their normal gait. One of the factors that make learning how to use a prosthesis such a challenge is the difference in the forces that are exerted upon a normal leg and a prosthesis while walking and even just standing still. The two main forces to consider that act upon both real and prosthetic legs are the Ground Reaction Force (GRF) and the forces around the knee joint. Both of these forces are divided into three directions: vertical, mediolateral, and anteroposterior. However, because these forces vary based on the design of the the prosthesis, especially those around the knee, this portion of the board will only focus on the GRF and just refer to them as a whole. The other physics-related components to take into account when comparing a prosthetic leg with a real, are the four pressure regions around the knee: the patella tendon (PT), the poplitial depression (PD), the lateral tibia (LT), and the medial tibia (MT). During different stages of walking and standing on a prosthetic leg, different amounts of pressure are exerted upon these four regions.


 * Ground Reaction Forces**

Below are two graphs (Graph 1) comparing the GRF during a normal walking gait of an able bodied child to a child with an above-knee amputation and prosthesis. The graphs show the amount of force that the ground is exerting back on the child throughout one stride. However, in order to understand the significance of these graphs, its important to be able to know where each percentage of the stride correlates within an actual step, and what the significance of that is. The graph begins at the terminal position where the body is directly over the legs, spans one stride, and ends in the same place. On both of the graphs above there are two clear peaks where the GRFs are the highest, however, there is much less variance in the amplitude of the GRF in the cild with a prosthesis. The difference in the amplitudes signifies that either the child cannot lift the leg as high (which would limit how hard it comes down) or that the knee joint simply absorbs more of the shock. In either case the GRF between an able-bodied child and a child with an above-knee prosthesis is pretty similar.


 * Pressure and Stress**

Very similar graphs appeared in “Load Transfer Mechanics Between Trans-Tibial Prosthetic Socket and Residual Limb — Dynamic Effects” performed by Xiaohong Jia, Ming Zhang, and Winson C. C. Lee from the Jockey Club Rehabilitation Engineering Center in The Hong Kong Polytechnic University of Hong Kong, China and the Department of Precision Instruments in Tsinghua University of Beijing. These graphs, Graphs A - C of Figure 1 and Figure 2, clearly demonstrate the double peak pattern as well, however, they are representing the pressures and stresses exerted upon the four pressure regions around the knee, as opposed to the GRF, that were mentioned before. On these graphs, the authors of this article determined that the first peak is the moment (a force) to extend the limb, and the second is the moment to flex it. In between the two peaks is when the lower leg is in the swing phase meaning that more force is being exerted by the muscles to extend the limb, but GRF is temporarily nonexistent. During the first peak the pressure increases on the anterior proximal and posterior distal sides of the knee joint but decreases on the anterior distal and posterior proximal causing the patella tendon to be the only pressure region with increased pressure. During the second peak on the curves the pressure is the opposite and the other three pressure regions are receiving a majority of the force. The significance here is that despite the similarities of the curves between the load transfer mechanics between the Trans-Tibial Prosthetic Socket and the residual limb and the GRFs, the pressures themselves are completely different. Because of the sensitivity of the stump that is left below the knee after an amputation, the majority of the force from walking needs to be absorbed by the outside of the leg as opposed to transfered right up the middle as it would be with the tibia. So on a real leg the stresses on the four regions are similar, but for slightly different reasons. The patella tendon increases in stress as it extends the lower leg, whether real or not, during the swing phase. How close that amount of stress is most likely depends on the weight of the prosthetic leg. The medial and lateral regions of the tibia would most likely be slightly greater when attached to a prosthetic leg, however, because of how the weight must be distributed in the prosthetic leg liner. A similar situation applies for the poplitial depression region. Since the pressure exerted upon these different regions of the knee is dependent upon the GRF, the GRF of an able-bodied person and one with a below-knee amputation must be pretty similar as well.

Graph 1

**__Energy Expenditure__** By measuring the energy expenditure for a prosthetic, a general conclusion about how efficient prosthetic-users are in walking can be reached. Simply put, prosthetic gait in lower-limb amputees requires a much higher energy input than that of normal people. Amputees expend more metabolic energy in walking a given distance as compared to a normal person. However, metabolic energy consumption in amputee gait is affected by the variation of the mass of the prosthetic limb. Although it may seem counterintuitive to many amputees, a prosthetic limb is generally lighter than the natural limb, but it feels much heavier since it is an addition to the body and not a natural part, which means that muscles must actively carry the prosthetic. In lighter prosthetics, less energy is required to carry mass of the prosthetic. Unfortunately, if the mass of the prosthetic is significantly reduced, it may have the opposite of the desired effect, and increase the energy required for the amputee to walk because of a loss of symmetry. In measurement, the amount of energy expended is either a total energy cost or a rate of expenditure. The energy cost of walking is the rate at which metabolic energy is consumed by the muscles while walking. The energy expenditure rate is equal to the energy cost multiplied by the steady-state walking speed. In order to measure energy expenditure, scientists generally use a face mask to capture respirations to monitor O2 consumption and CO2 production while the subjects walk around, since this indirect measure indicates how fast the body is metabolizing and thus how much energy is being consumed. The best way to estimate how much energy is consumed while walking is to think of the body as a whole system and see how much energy is necessary to move through a walking motion. Prosthetic users prefer a walking speed that is 21% slower and at the same time have aerobic demands 49% higher than subjects with natural legs. When a speed is specified in the experiment, aerobic demands were 55% to 83% higher for the prosthetic users (Peasgood 2004). In conclusion, a person with a prosthetic lower-limb requires higher energy consumption than a healthy person. The mass of the prosthetic may lower the energy consumption but may affect the function of the prosthetic to mimic the limb.

http://www.unc.edu/~mbritt/Prosthetics%20History%20Webpage%20-%20Phys24.html Biomechanics of Normal and Prosthetic Gait. Edited by J.L. Stein Postural control in male patients with hip osteoarthritis A musculoskeletal model of the human lower extremity: The effect of muscle, tendon, and moment arm on the moment-angle relationship of musculotendon actuators at the hip, knee, and ankle Load transfer mechanics between trans-tibial prosthetic socket and residual limb—dynamic effects Prosthetic gait of unilateral transfemoral amputees: A kinematic study by S.Jaegers, J.Arendzen, H.de Jongh http://www.oandp.org/jpo/library/1997_04_168.asp Forces on normal gait versus prosthetic gait http://www.uwspace.uwaterloo.ca/handle/10012/880 Determinats of Increased Energy Cost in Prosthetic Gait. Synthesis of Human Walking: A Three-Dimensional Model for Single Support. Part 2. By MG Pandy and N Berme. From Biomechanics of Normal and Prosthetic Gait, edite by J.L. Stein. American Society of Mechanical Engineers, New York, 1987. Pg. 9
 * __References__**: