Effects of Bone Deformities on Muscle Moment Arms: Analytical Essay

1.1 Abstract

In this paper, we try to answer the question which is “How Bone Deformation Effect on Muscle Moment Arm” and showing how that is affect in the motion of human body. By knowing the reasons of these deformations in bones we have an ability to simulate that in the “Solid Work” program. The next step “Effect Bone Deformation on Muscle Moment Arm” is a topic that needs more time and as possible an accurate work to get well results. Here we list some subtopics that could be the next step in this topic:

Make the 3D model of bone that used in the study to be more accurate and with more details, to get more accurate results.

How can this topic have an effect in children growth and its result at the adulthood and motion of human body?

As we know the reasons that cause this defamation, we may know how to treat this issue with high percent of success of treatment.

Study more about the deformation by analyses different bones and joints in the human body.

1.2 Introduction

In our daily life, we do various activities walking, washing, using phone and many more. These movements which are done in a few seconds. But it is a very complex movement in the scientific aspect. These activities are done by cooperating relation between muscles and bones, disturbance of this relation may affect our normal life. That relation can be found in any part of a human body which results in angular motion, rectilinear movement and curve motion. A unique part of human body is having a muscle moment arm, this is usually found in lateral parts that have the major role of our movement activates that make these parts important. Although muscle moment arm is important, the movement is not done without a cooprationing relation with bone. In summary, to have a good movement we consider the state of bone and muscle to be at normal state.

1.3 Objects

In this paper we will talk about some aspects of “Effects of Bone Deformities on Muscle Moment Arms”, and it: Muscle Bone Relation – Muscle Moment Arm – Bone Deformation.

1.4 Previous Investigation

• “The preceding evidence suggests muscle loads the skeleton to induce bone adaptation. However, there is also evidence that muscle can also be protective of bone loading” [2].
• “The goal of this paper is to present a rigorous, clear and unambiguous definition of muscle moment-arm” [1].
• the goal of this paper is describing and understanding the bone characteristics, types of fractures, bone diseases and their treatment [3].

2. Muscle Bone Relation

“Muscle and bone are inextricably linked genetically, molecularly, and mechanically, the intertwining of the connections at the different organizational levels (subcellular, cellular, and sup acellular) makes it difficult to tease out the relative contributions of each connection” [2]

3. Muscle Moment Arm

3.1 Definition of Muscle Moment Arm

At the beginning let's define the Muscle Moment Arm, what is it?

“In Newton’s second law, the link between the force generated by a muscle and the motion of the system is the muscle moment-arm” [1]. The equation that used to calculate muscle moment arm is:

• F: Applied Force unit in Newton (N). d= Moment Arm (Lever Arm) which is the perpendicular distance from the force’s line of application the axis of rotation, and its unit is unit of length (m, cm, mm…). T: Moment (Torque) is the mathematical product of applied force and moment arm its unit is (N.m, N.cm, …). For a specific muscle, the moment on each body are computed by isolating each body and considering the forces applied by the muscle on the body, keeping in mind that forces are transmitted through the joints. The total moment is then defined as the sum of the moment created by each force at one of the joints associated with the body. [1]

3.2 Classes of Moment Arms

• First-Class Lever: The axis of rotation is between applied force and resistive force.
• Second-Class Lever: The resistive force is between the axis of rotation and applied force.
• Third-Class Lever: The applied force is between the axis of rotation and resistive force. These classes are shown in figure (1).

Figure (1)

this picture explains a different classis of moment arm.

These classes of moment arm are introducing us to the term Mechanical Advantage. Mechanical advantage (M.A) is describe how relative efficient of the class lever and it is calculated by this equation: Mm / MR. Mm: Moment arm of the muscle force. MR: Moment arm of the resistance force. When 1 > M.A it is a disadvantage mechanical system, 1 < M.A it is an advantage mechanical system.

4. Bone Tissue Structure and Its Physical Characteristics

Bones have two types of tissues (compact) and (spongy) they may also be called either cortical or trabecular, these two types of bones are categorizing that way because of their porosity level [3].

• location:

1. 1- cortical: in diaphysis of long bones [3]

Characteristics: 1-cortical: high density and low porosity level between 5% - 10%, it forms the external shield of trabecular bone, consist of 80% of bone mass [3]

1. 2- spongy bone: low density, very high porosity level (50% - 90%), its 1000 micro-meter and 0.2 micro-meter thick[3].It has no definite structure like cortical, trabeculae do not blood vessel in the central canal, it is task with absorption and transfer energy from joints, it is a total of 20% of bone mass because of its structure that has a larger surface than compact [3].The polymer and minerals are the reason for bone characteristics [3]. Location: at the epiphysis of long bone and in the vertebral bodies and flat bones [3]. Compact bone: the basic of it is osteon, osteon layers are concentric or the thickness of lamella between (3 micro-meter to 7 micro-meter) [3]. Osteocyte is a network that are connected to each other through cytoplasmic extension that occupy tiny canals (canaliculi) that’s used for communication on areas of deformation and are found in ellipsoid lacunae that are found between lamella [3]. Lamellae consist of type 1 collagen and minerals that been deposited in collagen fibres, the fibres have individual lamellae with an orientation and are in parallel position [3].

4.1 Bone tissue characteristics

1. 1- self-regeneration: (after being injured it heal all tissue in the organism) and adapt to it so that next time it well has a better resistance to mechanical load, we cannot treat it as rigid material but dynamic, that’s why it changes structure constantly [3]. A fully-grown bone (mature) has a certain range of deformation which it remains elastic after a force application [3].

Resistant: compressive > shear

Bone Trauma-Clinical Association

Bone healing is a difficulty process, a lot of factors involved to heal the bone function, different factors determine the healing process ( the mechanics of the organism and Biological factors) . [3]

4.2 Fractures and Their Categorisation

A normal and healthy bone (the cause of fracture): a strong force. A diseased causes change in shape (the cause of fracture): a strong and weak force.

Directed force: a fracture occurs at the spot of force application.

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Indirect force: the bone breaks in the weakest spot (lowest resistance) due to a shift [3]. Wolff’s law: shape, and size of bones is determined by direction and magnitude of the acting force.

4.3 Osteoporotic Fractures of the Femur

These types of fractures are the most common in elderly people. The average age of injured people is 75 years [3]. In younger patients, they result from high-energy injuries. 70% of these fractures occur in women. Factors, affecting this ration, are larger tendency to osteoporosis and longer life expectancy than in men. However, it is implied that the main cause for injuries is muscular weakness, paresis, instability due neurological diseases and osteoporosis is only a factor contributing to the injury [3]. At times the bone breaks due to severe osteoporosis when taking an awkward step and the fall results in a fracture. Due to osteoporotic changes in the bone tissue, comminuted fractures often occur [3].

4.4 Bone Tissue Characteristics

Healing bone can be by considering the bone as dynamic tissue because the bone tissue has a special advantage which is the regeneration of the bone structure. that will give us an ability to use Wolf's law [3]. Mature bone has a range of deformation, but that deformation makes bone still elastic even after applying a force. Bone behaviour is different with different types of loads, bone has the least resistance for shear load and more in compression [3]. The solidity of an individual bone depends on its shape, density, place of force application and speed of force [3]. If a force is applied for a short period of time, the bone will respond to it by increasing its solidity. The final goal of this adjustment is that the bone becomes more resistant to tension and as a result, will be able to absorb more energy before it will give in [3]. Therefore, fractures become comminuted after a sudden increase in force because the force will accumulate within the bone before the bone will give in, besides the bones’ ability to self-regenerate, the bone may also give in, and fractures may result if the material wears out and the frequency of the load exceeds the time frame necessary for bone regeneration and its adjustment to forces, as human body has a variety geometric shapes of bone, have a different solidity in each bone, solidity has some factors that affect the bone solidity like place of force application and speed of force, the relation between bone solidity and force speed, when applying force in short period of time, the bone’s solidity will increase as a result of that [3]. If a force is applied for a short period of time, the bone will respond to it by increasing its solidity [3].

5. Current study

Methodology:

Use Solid Work 2012 to simulate the effect of bone deformation on muscle moment arm.

We download a 3D model of left human femoral bone from Solid Work website figure (2).

Figure (2)

3D model of femur bone

Costume material has been made to satisfy bone mechanical properties, which is provided by Eng. Mohammad Alwahiby.

Apply bending flexion on the object, figure (3).with variation of the angles of deformations as shown in the table below, table(1)

Figure (3)

Bone after apply bending flexion.

In this experiment, we neglect the total body weight, by considering our mechanical system is the femur bone, for resistance force it is considered as the foot and leg weights, as shown in figure of free body diagram.

the foot and leg weight are provided from the references book of 228 and we also neglect femur weight

As an assumption and approximation, we take the value of muscle force is 37N then we measure the moment arm at every change, figure (4).

Figure (4)

Use measure tool to for measure moment arm

we calculate the torque as: 431.458 mm x 37 N = 15963.95 N.mm

Then we calculate the force required at every change in the muscle moment arm due to deformation of the bone. The Psoas major muscle acts as the muscle moment arm in the femur. Force = torque/ Muscle moment arm

• ∑▒〖M=(Fm×Mm)-(FR×MR)=0〗

Degree of flexion Resistance Moment Arm (mm) Resistance Force (N) Muscle moment arm (mm) Muscle force

(N)

1. 0 431.458 37 98.287 162.42
2. 2 431.027 37 98.287 162.25
3. 4 430.615 37 98.287 162.1
4. 6 429.968 37 98.287 161.86

Table (1)

5.2 Conclusion

The motion in human body has a several factors that affect their motion, in this paper, we had study about the bone deformation and how it is affect the main factor in every motion is the muscle moment arm. We did a simple and approximation experiment of these two factors in solid work and we found that

We found in the experiment that the muscle force decreases as the resistance moment arm decreases, in other words, the force needed to lift the femoral bone decreases as the angle of curvature increases in the femoral bone.

References

1. David, I. & Christoph, E. Alain, F. & Alexandre, T. & Philippe, M. (2013). Muscle moment-arms: a key element in muscle-force estimation. Computer Methods in Biomechanics and Biomedical Engineering. 18, 506-513. DOI: https://doi.org/10.1080/10255842.2013.818666
2. Avin, K.G., Bloomfield, S.A., Gross, T.S. et al. Curr Osteoporos Rep (2015) 13: 1. D.O.E: 4/4/2019. Retrived from: https://link.springer.com/article/10.1007/s11914-014-0244-x
3. Velnar, T., Bunc, G. and Gradisnik, L. (2015) Fractures and Biomechanical Characteristics of the Bone. Surgical Science, 6, 255-263. http://dx.doi.org/10.4236/ss.2015.66039