Human Biomechanics I Course Project
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Dateof submission:
Biomechanicsand particularly biostatics analysis can be used in designingrehabilitation parameters for a patient with torn distal bicepstendon. The diagram below depicts the forearm of a human being interms of force and an angle between the forearm on a horizontal basisand F_{m}. The purpose of this project is to conduct biostatics analysis aimedat developing a rehabilitation programmme for an employee with a torndistal biceps tendon. The employee has been advised by a specialistnot to subject the tendon to a force exceeding 500N duringrehabilitation.
Fig1: Pictorial diagram of the extended fore arm handling a variablemass.
Diagramof the forearm system.
Inthis system, Force is given in Newtons as the unit of measure. Weshall also assume that a 1kg mass gives a force of 10N due togravitational pull. F_{m}is the effort in the system or tension that is experienced at thebiceps attached to radius. Mcis the load at the palm which is supinated. The weight of theforearm, m_{b}at 21.0cm from O, is also included in the system since it will exertsome tension on the tendon. Point O is a fixed pivotal point at theelbow and a = 5.7 is the distance between the point O and the pointat which the tendon attaches to the radius.
Anexpression for the magnitude F_{m}can be derived from the following equilibrium equation:
F_{m}x 5.7 = (21 x 16.6) + (40.6 x m_{c})
F_{m}= {(21 x 16.6) + (40.6 x m_{c})/ 5.7}
Sincethe force will also depend on the angle betweenF_{m}and the forearm with respect to the horizontal, then the finalexpression for F_{m}in this system is
F_{m}= {(21 x 16.6) + (40.6 x m_{c})/ 5.7}/ Cosθ
Cosθis a factor that checks the motion of the effort since in thissystem, the forearm is held horizontally and a change in the angle iseffected by adjusting the upper arm and maintaining the foreman in ahorizontal position.
Usingthe expression above, the effort and tension exerted by a given forceat the palm of a supinated hand was calculated. The force was thenvaried from 20N to 30N, 40N, 50N and 60N. Correspondingly, the anglebetween the long axis of the upper arm was varied from 30^{0}to 40^{0},50^{0},60^{0}and 70^{0}. Results obtained from the calculations summarized in the table belowwere used to plot graphs on which the limit of 500N was indicated.
Dataand results
Table1 below shows values of F_{m}obtained using the expression above with varying values of θ and m_{c}.
Table1: values of F_{m}for the arm
  
Θ 

  
30^{0} 
40^{0} 
50^{0} 
60^{0} 
70^{0} 

m_{c} (N) 
20 
235 
266 
317 
407 
595 
30 
317 
359 
428 
550 
804 

40 
400 
452 
538 
692 
1013 

50 
481 
545 
649 
834 
1221 

60 
563 
638 
760 
977 
1430 
Thefirst column gives values of m_{c}in N while the first row gives the angle between the forearm and F_{m}. The values highlighted have exceeded the value advised by the injuryspecialist.
Thegraphs below show the relationship obtained when Fm is plottedagainst values of mc and θ respectively. The red line in the graphsindicates the limit as advised by the specialist.
Graphof F_{m}against θ when m_{c}= 20N
Graphof F_{m}against θ when m_{c}= 30N
Graphof F_{m}against θ when m_{c}= 40N
Graphof F_{m}against θ when m_{c}= 50N
Graphof F_{m}against θ when m_{c}= 60N
GraphsofF_{m}plotted against m_{c}aregiven below
Graphof F_{m}against m_{c}when θ = 30^{0}
Graphof F_{m}against m_{c}when θ = 40^{0}
Graphof F_{m}against m_{c}when θ = 50^{0}
Graphof F_{m}against m_{c}when θ = 60^{0}
Graphof F_{m}against m_{c}when θ = 70^{0}
Discussion
Itis evident from the table and the graphs that the force exerted onthe tendon increases as with an increase in angle θ and an increasein Fm. To keep the force within the recommended limits, it is clear fromthe table and the graphs that the mass should never get to 60N andthe angle should never go beyond 70^{0}. When θ approaches zero, the tension on the tendon will approach amaximum. However, this analysis is limited in that it is not easy tomake calculations when the effort compliments the mass in direction.It is also not possible for the forearm to overlap the upper arm andcalculations for a case where the forearm is parallel to the upperarm are also limited.
Conclusionand recommendations
Basedon these calculations, the injured employee should undergo onthejobrehabilitation strictly following the parameters given and keepingwithin the limits of tendon force or effort as recommended by thespecialist. The most favorable parameters for rehabilitation basedon these computations would be alternating between a force 50N at30^{0},40N at 40^{0},30N at 50^{0}and 20N at 60^{0}or other combinations below these values.