Vibration Measurement and Analysis of knee-Ankle-Foot Orthosis (KAFO) Metal-Metal type

This paper deals with calculate stresses in Knee-Ankle-Foot-Orthosis as a result of the effect vibration during gait cycle for patient wearing KAFO .Experimental part included measurement interface pressure between KAFO and leg due to action muscles and body weigh on Orthosis. also measurement acceleration result from motion of defected leg by accelerometer .Results of Experimental part used input in theoretical part so as to calculate stresses result from applying pressure and acceleration on KAFO by engineering analysis program ANSYS 14.Resultes show stresses values in upper KAFO greater than lower KAFO that is back to muscles more effective in thigh part lead to recoding pressure higher than pressure in shank part.


INTRODUCTION
An orthosis is a device that is applied to a part of the body to correct deformity, improve function or relieve symptoms of a disease. The word is derived from ortho, meaning straight [Alaa'SaeedHadi].
Orthoses added to the body to stabilize or immobilize a body part, prevent deformity, protect against injury or to assist with function. They can be divided into different types based on their intended function [CIGNA HealthCare].
The term KAFO is an acronym that stands for Knee-Ankle-Foot Orthoses and describes the part of the body that the device encompasses. The device extends from the thigh to the foot and is generally used to control instabilities in the lower limb by maintaining alignment and controlling motion. Instabilities can be either due to skeletal problems: broken bones, arthritic joints, bowleg, knock-knee, knee hyperextension or muscular weakness and paralysis [Jumaa S. Chiad].
Typically, KAFOs are extremely mechanically simple and often have few moving parts. This simplicity is accompanied by ease of donning and durability but leaves functional abilities only partially improved. Historically, KAFOs have locked the knee joint, providing stance phase stability while preventing knee motion during swing. Alternatively, KAFOs with an eccentric knee joint allow knee motion during swing but provide limited stability during stance. Either design results in inefficient gait[Jumaa S. Chiad].
These devices use a knee joint that is mechanically stable during the stance phase but releases at swing phase. The resulting gait is much smoother than the gait with a traditional KAFO where the knee remains locked throughout the entire gait cycle. Continued engineering development and creativity will be required for evolution of these designs into viable components for use by patients with knee instability during stance[Jumaa S. Chiad].
The human being in the environments of modern technology has to endure stresses of many and varied kinds of vibrations. These vibrations have significant effects on the physical and mental health. It has been observed that the stresses imposed by vibration have produced changes in the normal functions of the human body. The Whole body vibration can cause severe motion sickness which depends on the mechanical properties of the human body [AkeelZeki Mahdi].

EXPERIMENTAL PROCEDURE
The measurement occurred on girl under going from Polio in her left leg as a case study. The pathological subject is of age, weight, length and the residual palsy limb of 30years, 59kg, 156 cm, and 76 cm respectively. so as to know the magnitude of stress that result from vibration in each position of knee Ankle Foot orthoses during dress up by patient must be measuring and calculate many necessary vibration data 1. Measure acceleration for KAFO by using portable acceleration sensor as shown in Fig.1 in different position the sensor was located in a. The center of ankle. b. The mid of knee. c. The mid of the thigh The sensor was recording data, while patient was walking in her normal speed on the ground in straight way.
2. Measuring pressure: The pressure between the leg and knee Ankle foot orthotic was measured by using piezoelectric sensor as shown in Fig.2 .The pole of sensor connected with multi-meter devise to obtain the magnitude of voltage that result from response of sensor through the stance phase explained in Fig.3. .The multi-meter and piezoelectric are interface with the computer and recording data as shown in Fig. 4. The pressure measured in shank and thigh region each position was divided into three parts longitudinal, in the middle and two parts on the terminal of the piece as shown in Fig. 5.The program of multi-meter giving maximum and minimum value of voltage with time Take maximum value of this to be the pressure in this point .The procedure will be recurred to another part so as to obtain on the pressure values in all position that contact with muscles of leg as shown in Fig. 6. To convert the measurements to pressure, the following calibration steps must be done: 1. Using different disc masses of 50,100,….500gm 2. Put the gradual steps the masses over the pressure sensor and read the voltage from the multi-meter as shown 3. Develop the mass (or force) with voltage relationship. 4. Convert the force-voltage relation to pressure-voltage relation by dividing each force by the circular cross sectional area of sensor. The chart of calibration in Fig. 7 is already now to using.

THE NUMEIRCAL ANLAYSIS
The finite element method (FEM) is now widely used in a variety of fields in engineering and science. Taking the advantage of the rapid development of digital computers with large memory capacity, as well as, fast computation. The method is recognized as one of the most powerful numerical methods because of its capabilities which include complex geometrical boundaries and non-linear material properties. In this work, FEM is with aid of ANSYS Workbench 14 software used as a numerical tool to determine the behavior of maximum stress [The Iron & Steel Society].
• Building the geometry as a model.
• Applying the boundary conditions load and obtaining the solution.
• Reviewing the results.

GRAPHING OF THE GEOMETRY
In this paper selection metal-metal knee ankle foot orthosis (KAFO) model was drawn by using CAD system (AUTOCAD) which processed according to an default pattern in three dimensions .The dimension was taken from the same KAFO that done on it measurement of experimental part. The aim of drawing models by AUTOCAD so as to use in ANSYS workbench program for modeling, meshing and defining boundary condition such as applied load. The models is illustrate in the Fig. 8.

MATERIAL SELECTION IN KAFO's
Various materials used in the manufacturing of KAFO depending on the type of KAFO such as (metal-metal, plastic-metal) and position of each section that building structure of KAFO like material used in the knee joint different from used in sole , the materials are: Stainless steel, Polypropylene and Aluminum

Stainless Steel
Stainless steel used for making the uprights side bars, knee joint system, ankle joint system and system shoe stirrup in of Metal -Metal KAFO as shown in Fig. 8. Stainless steel using in this sections because of the good characteristics like resistance to corrosion in many environments, their good mechanical properties over an extremely wide range of temperatures, and their superior resistance to oxidation and scaling at very high temperatures [The Iron & Steel Society], the mechanical properties of standard Stainless steel are listed in the Table 2.

Polypropylene
PP has low density and good flexibility and resistance to chemicals, abrasion and moisture, but decreased dimensional stability, mechanical strength, and resistance to UV (ultraviolet) light and heat [Maier C, & Calafut].Polypropylene used for making sole section of Metal -Metal KAFO, The mechanical properties of standard polypropylene are listed in the Table 3.

Aluminum:
Aluminum alloys 1200 were selected as the material for the calf band in the metal -metal KAFO in the thigh and shank section due to their light weight, high strength-to-weight ratio, corrosion resistance, and relatively low cost. , The mechanical properties of standard aluminum alloy 1200 are listed in the Table 4.

MESH OF THE MODEL
The meshing process has been done by choosing the volume, and then the shape of element was selected as tetrahedron (Automatic meshing), for metal-metal model as shown in Fig. 9 contain total number of elements was (95298 elements) with total a number of nodes of (182108 nodes).

DEFINING THE ANALYSIS TYPE AND APPLYING LOAD
The boundary condition applying in the ANSYS Workbench software will be fixed support at the sole and the tip of the calf for both of shank and thigh segments. While, the interface pressure was distributed on the calf for both of shank and thigh segments shown in Fig. 10, and enters the values of acceleration measured in thigh, knee and Ankle shown in Fig.11.

RESULTS AND DISCUSSION
Observed by comparing the results of acceleration and frequency in the case of metal -metal knee ankle foot orthosis in Table 1 to a person suffering from poliomyelitis disease find increase in the value of acceleration and frequency in knee joint this is due to more movement at knee joint comparing with ankle and thigh joints during gait walk cycle also it is very important to know that the knee joint is a bone region this is mean that there is no muscles working as a damper to reduce acceleration and frequency at this region according to this analysis acceleration and frequency increased in knee joint with about (62.3% and 46%) respectively comparing with ankle joint and with (30.19 %and 18.46% )respectively comparing with thigh joint.
All the readings of the interface pressure measurement are shown in Fig. 5.The difference between all these reading is related to value of pressure which is related to the activity of the muscles during which the pressure sensor is connected to measure the value of the interface pressure. The max value of IP in KAFO lower bands was recorded at gastrocnemius muscles with values of 28 Kpa While the max value of IP in KAFO upper band is recorded at biceps femoris and semitendinosus muscles with values of 58 Kpa.  (28) shows that the values of stresses at the upper KAFO bands (thigh) are greater than the lower KAFO bands (shank).This is certainly because of the values of pressure in the upper leg (thigh muscles )are higher than the pressure in shank muscles.

CONICLUSIONS
1-The max value of interface pressure in KAFO upper calf was recorded at semitendinosus muscles with values of 58 Kpa while the max value of interface pressure in KAFO lower calf was recorded at gastrocnemius muscles with values of 28Kpa.
2-The level of stresses in the upper KAFO thigh calf is greater than the lower KAFO shank thigh due to the high activities of the thigh muscles in comparison to shank muscles.
3-The maximum stress in the KAFO which was calculated numerically recorded at the bar contact with Gracilis muscle for Knee Ankle Foot Orthosis Aluminum.
4-Maximum value of frequency was recorded in knee joint with the value 6.5 Hz and maximum value of acceleration at knee joint about 5.578

FINITE ELEMENT EQUATION
The displacements are represented by the following equations: Considering the nodal displacements, the following equations must be satisfied: Similarly, requirements must be satisfied: Also: Substitution of respective nodal values into Eq. (1), results in 12 equations and 12 unknowns: Also, And Solving for the unknown C-coefficients, substituting the results back into Eq.(1), and regrouping the parameters, obtained: The shape functions are: Where V, the volume of the tetrahedral element, is computed from: The a I , b I , c I, d I … d L -terms are: The only six independent stress components are needed to characterize the general state of stress at a point. These components are: Where σxx, σ yy , and σ zz are the normal stresses and τ xy, τ yz , and τ xz are the shear-stress components. For the displacement vectors that measure the changes occurring in the position of a point within a body when the body is subjected to a load, it may be recall that the displacement vector → δ can be written in terms of its Cartesian component as: The general state of strain is characterized by six independent components as given by: Where ε xx , ε yy ,and ε zz are the normal strains and γ xy , γ yz , and γ xz are the shear-strain components. The relationship between the strain and the displacement is represented by: Equations (10) can be represented in matrix form as: Where: L is commonly referred to as the linear-differential operator. Over the elastic region of material, there is also exists a relationship between the state of stressed and strains, according to the generalized Hook's law. This relationship is given by the following equations: The relationship between the stress and strain can be expressed in a compact-matrix form as:   (14) can be written as: By using the four-node tetrahedral element to formulate the stiffness matrix. Recall that this element has four nodes, with each node having three translational degrees of freedom in the nodal x-, y-, and z-directions. The displacements u, v, and w in terms of the nodal values and are represented by: Beginning by relating the strains to the displacement field and, in turn, to the nodal displacements through the shape functions. It is needed to take the derivatives of the components of the displacement field with respect to the x-, y-, and z-coordinates according to the strain-displacement relation, Eq.(11). The operation results in: Substituting for the shape function using the relation of equation (4)  and, subsequently, the expression for the stiffness matrix, which is: Where V is the volume of the element. Note that the resulting stiffness matrix will have the dimensions of 12x12. The load matrix for a tetrahedral element is a 12x1 matrix. For a concentrated -loading situation, the load matrix is formed by placing the components of the load at appropriate nodes in a appropriate directions. For a distributed load, the load matrix is computed from the equation: