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Engineering analysis of shoulder dystocia in the human birth process by the finite element method A Meghdari, PhD, MemASME, R Davoodi, MSc and F Mesbah, MD* Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
This paper presents an engineering analysis ofshoulder dystocia (SO) in the human birth process which usually results in damaging the brachial plexus nerves and the humerus andlor clavicle bones of the baby. The goal is to study these injuries from the mechanical engineering point of view. T w o separatefinite element models of the neonatal neck and the clavicle bone have been simulated using eight-node three-dimensional elements and beam elements respectively. Simulated models haoe been analysed under suitable boundary conditions using the ‘SAP80’Jinite element package. Finally, results obtained have been verified by comparing them with published clinical and experimental observations. 1 INTRODUCTION
The birth process is defined as the passage of the foetus through the contours of the birth canal. There is no doubt that this process takes place in a proper manner only when the size of the foetus is proportional to the size of the birth canal. Otherwise, complications concerning the foetus and/or the mother may arise. One such complication is when the size of the foetus’s shoulders are large compared to the mother’s pelvic canal. In this case, after the foetal head is delivered, the large size of the shoulders prevents the continuation of the natural birth process. This may cause a delay in birth which can result in asphyxiation, followed by nerve damage, mental retardation, speech impediments and even neonatal death. In an effort to reduce the delay time, the clinicians usually try to force the baby out, typically in less than five minutes. This may cause various levels of damage to the brachial plexus nerves and fracture of the humerus and/or clavicle bones of the baby. However, this is thought to be less dangerous and more treatable than the possible consequences of a prolonged delay in the birth process. To study the mechanics of fracture in the clavicle bone and the level of damage to the brachial plexus, the clavicle bone and neonatal vertebral column can be simulated by a suitable computer model. By applying relevant forces, the stress field can then be computed using software packages containing finite element methods for further analysis. Utilizing the computed stresses, the level of possible damage due to these forces can be predicted. For example, the dependency of the clavicle’s fracture on the properties of its material can be studied. Furthermore, the relationship between the level of stretch in the brachial plexus on the neck and the forces applied to the foetal head by clinicians during the delivery can be analysed. Sorab (1) has developed experimental models of the foetus and the birth canal in order to analyse the applied forces in shoulder dystocia and to obtain the necessary forces for the fracture of the clavicle bone and stretching of the brachial plexus nerves. In this regard, The MS was received on I1 August 1992 and wus accepted for publication on 18 December 1992.
* Present address. Sussnn Hospitul, Tehran, Iran. H07392 0 IMechE 1992
Sharma (2) modelled the clavicle bone and the brachial plexus using two-dimensional elements and studied their behaviour under the application of clinician forces using the finite element method (FEM). This paper examines the connection between these forces and the level of damage to the foetus. Furthermore, the aim is to determine the maximum permissible forces in order to warn the clinician when the applied forces are too large. An analysis is presented of the types of forces applied to the foetus at the time of delivery during shoulder dystocia. Specifically, the effects of these forces on the clavicle bone and the brachial plexus nerves, two of the most common areas of damage to the foetus during SD, are discussed. First the necessary data about the dimensions and material properties of the neonatal’s clavicle bone and neck are collected from the literature (2--5).Using these data, suitable models of the clavicle and neck are simulated. These models under appropriate boundary conditions and forces have been analysed by the finite element method. Finally, results are compared with previously published clinical and experimental observations.
2 SHOULDER DYSTOCIA (SD)
Shoulder dystocia (SD) is a complication in obstetrics that requires emergency treatment and is frequently associated with birth injuries of the clavicle bone and the brachial plexus nerve. Shoulder dystocia occurs due to impaction of the anterior shoulder of the foetus against the mother’s pelvis. As a result the clinician is unable to free the shoulder and hence is unable to deliver the baby without additional manipulation. This incident is reported to occur in about 2 per cent of all deliveries, and so far there is no known method to predict such an incident. Figure 1 clearly shows a neonate in the birth canal when shoulder dystocia occurs. Excessive forces applied to the foetal head by the cIinician may result in various kinds of damage, the most serious being fracture of clavicle bones and stretching/tearing of the brachial plexus nerves. Figure 2 shows two areas of common damage when shoulder dystocia occurs (6-8).
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have been considered: one assumes the clavicle to be curved only in one plane (that is the planar curvature model) while the other considers a more accurate model of clavicle with body curvatures appearing in all planes (the spatial curvature model). The total length of clavicle is assumed to be 40 mm, and is divided into 20 parts, where each part is modelled by 12 elements. On the whole, the spatial model consists of 504 nodes and 240 elements. Choosing three-dimensional elements facilitates the modelling of curvatures and variable thicknesses in the clavicle bone. Figure 4 shows the prepared model of the clavicle bone for finite element analysis. Figure 5 shows the assumed boundary conditions of the kind pin joint and roller joint for the acromial and sternal ends of the clavicle. Considering various boundary conditions, these are chosen to be the most suitable ones due to the specific orientation of the clavicle with other bones in the body during shoulder dystocia (9). However, it was assumed that when the acromial end of the clavicle bone is placed (locked) behind the mother's symphysis pubic bone (where only clavicle rotation about the axis normal to the body's plane is admissible at the acromial end), the clinician's applied forces to the neonatal head are transferred to the sternal end of the clavicle via the vertebral column, ribs and sternum.
Fig. 1 Shoulder dystocia in the birth canal Brachial plexus
3.2 Neonatal neck model --=--*
\
Fig. 2 Areas of damage during shoulder dystocia
3 MODELLING THE NEONATAL CLAVICLE BONE AND NECK
3.1 Clavicle bone model Figure 3 shows a typical clavicle bone of the neonate (3). The clavicle is a long bone characterized by a relatively long shaft, which is not straight but is usually curved in two directions. It is hollow, cylindrical, contracted and narrowed. Its walls consist of dense, compact bone tissue of greater thickness in the middle, but becoming thinner towards the extremities. To model the complex shape of the neonatal clavicle it is assumed to be shaped like a hollow cylindrical beam with circular cross-sections throughout its length. Furthermore, it is assumed that the compact and spongy bone tissues have linear, elastic and isotropic material properties under quasi-static loading. Taking account of these properties, a spatial model of this bone has been simulated using eight-node three-dimensional elements. To analyse the importance of body curvatures in the clavicle, in these simulations two different cases Compact hone ti\\ue
\
Spongy bone tisbue
/
Medullary cavity
Cartilage
Fig. 3 Schematic of a neonatal clavicle
The neonatal neck is a flexible structure formed by a series of bones called vertebrae connected by intervertebra1 discs and cartilage. It may be regarded as a chain of seven vertebrae joining the head to the rest of the body. In this analysis, beam elements are used to model the neonatal's neck. Modelling is done such that a set of vertebrae and an intervertebral disc is considered equivalent to a beam. Then its geometrical as well as material properties are chosen such that its stiffness in different directions is similar to the combination of vertebrae and disc in the neonatal neck. For the sake of analysis, the neonatal vertebral column is modelled by seven interconnected beams. Elastic elements are used to model the brachial plexus (BP) nerve. Since the brachial plexus nerve does not resist to any great extent against the neck movements, in order to study the level of stretch in BP nerves, the longest BP nerve which is connected to the fifth vertebra was chosen for sample analysis. The assumption was made that the level of stretch in the chosen BP nerve is greater than others and is more at risk of damage. Figure 6 shows the neonatal neck model considered in this study and analysis. 4 MECHANICAL PROPERTIES OF THE NEONATE'S BODY TISSUES
There is not much information available about the mechanical properties of the newborn's body tissues; most of the available data concern adults. Considering the fact that the mechanical properties of the human body are seriously affected by age, direct utilization of the data available for adults for this study does not seem correct. However, by referring to the existing references, some of the mechanical properties of newborns were extracted and some of the data were approximated by extrapolation of the data available for adults. Tables OIMechE 1992
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Top-most fibre
Sternal end
Fig. 4 The clavicle bone model for FEM analysis
1 and 2 provide the data obtained from published sources, which were utilized for the analysis of the neonatal’s clavicle and neck models.
5 RESULTS AND ANALYSIS
5.1 Clavicle bone analysis
The planar and spatial models of the clavicle have been analysed with suitable boundary conditions shown in Fig. 5 under lateral force (the force transmitted to the clavicle from the neonate’s head via the vertebral column, ribs and the sternum, assuming that the joints Sternal end
Acrornial end
L
Fig. 5 Assumed boundary conditions for the modelled clavicle
--:-a 12 mm
Beam elements
among them are rigid) using the ‘SAPSO’ finite element package. The results indicate that the maximum stresses are created at the bottom-most and the top-most fibres (fibres formed by connecting all nodes along the clavicle bone, located at the lowest and the highest points of the model respectively). Hence, by analysing the stress field distribution in these fibres, the maximum allowable force can be determined by studying the relationship between the applied forces and the created stresses. Figures 7 to 13 clearly show the results obtained. Figure 7 shows the created stresses in the top-most and bottom-most fibres throughout the clavicle in the planar curvature model. At the sternal end, created stresses in the top-most and bottom-most fibres are of the tensile and compressive kinds respectively. This observation is totally reversed at the acromial end. Based on detailed analyses in references (2) and (9), it is shown that boundary conditions, wall thickness, clavicle curvatures and its diameter are important factors for the created stresses. Changing each of these parameters directly affects the stress distribution. As observed, most of the stresses are created at the point where the sternal end is connected to the clavicle midTable 1 Mechanical properties of the modelled clavicle (2) 1.16 x 1.05 x lo4 55 80
Density of compact bone Elastic modulus of compact bone Ultimate tensile strength Ultimate compressive strength Poisson’s ratio
0.3
N/mm3 N/mmz N/mmz N/rnmz -
c3
Table 2 Total stiffness of the neck at various vertebral levels (2,4,5) ~
Elastic element
TI
Fig. 6 The neonatal neck model (every beam element models the combination of vertebrae plus an intervertebral disc)
Vertebrae levels
Tensile stiffness N/mm
Shear stiffness N/mm
Torsional stiffness N mm/rad
c7 C6 C5 c4 c3
38.613 17.498 10.885 7.616 5.176 5.524 5.333
3.7124 1.8296 1.1874 0.8728 0.6619 0.519
3358 1679 1119 839.5 671.6 559.6 479.7
c2 c1
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Top Bottom
Length
mm
Fig. 7 Principal stress at the top- and bottom-most fibres (two-dimensional clavicle model)
shaft. The maximum compressive stress in the bottommost fibre is computed as 70 N/mm2 whereas the maximum tensile stress at the top-most fibre is 40 N/mmz. Figures 8 and 9 show the effect of lateral force on the created stresses at the top-most and bottom-most fibre in the planar curvature model. By applying a 41 N lateral force in the direction of force application in Fig. 5, the compressive stress at the bottom-most fibre reaches the fracture limit of 80 N/mm2 whereas the maximum tensile stress at the top-most fibre reaches about 42 N/mm*, which is lower than the fracture limit. Hence, in this model using the 41 N lateral force, the first point to reach the fracture limit is at the lowest connection point of the sternal end and the clavicle mid-shaft. Figures 10 and 11 show the effects of an increase in lateral force on the principal stresses at the top-most
and bottom-most fibres in the three-dimensional model of the clavicle based on the maximum stress failure theory. In the three-dimensional model with an applied force of 39.5 N, the first point to reach the fracture limit is observed. It seems that the main reason for the difference in the required force of fracture in two- and threedimensional models is the existence of torsional moment in the three-dimensional model. Torsional moment results in torsional stress which adds up with bending and axial stresses, resulting in a reduction of the required force for clavicle fracture. Figure 12 shows the lateral displacement of the planar and spatial models of the clavicle under application of the same lateral force. The displacement in the three-dimensional model is about 17 per cent greater than in the two-dimensional model, which is solely due to the effect of torsion. Figure 13 shows the created stresses at the bottom-most fibres of the planar and
-
__t_
F=31N F=36N F=41N
Length mm
Fig. 8
Effect of increasing lateral force on principal stress at the top-most fibre (two-dimensionalclavicle model)
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__t_ _t_
__Ei._
V”
0
4
F=31N F=36N F=41N
12
8
241
16
20
24
28
32
36
40
Length __ mm
Fig. 9 Effect of increasing lateral force on principal stress at the bottommost fibre (two-dimensional clavicle model)
-
F=26N F=34N F = 39.5 N
__t_
Length mm
Fig. 10 Effect of increasing lateral force on principal stress at the top-most fibre (three-dimensional clavicle model)
-
__c_ F=26N
F=34N
--8- F = 39.5 N
Length mm
Fig. 11 Effect of increasing lateral force on principal stress at the bottommost fibre (three-dimensional clavicle model) 0 IMechE 1992
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_t_
Two-dimensional model Three-dimensional model
Length mm
Fig. 12 Lateral displacements in two- and three-dimensional clavicle models
spatial model of the clavicle. Due to the torsional moment, the created stress in the three-dimensional model is greater than in the two-dimensional model. As a result, the required force of fracture for the threedimensional model is lower than for the twodimensional model.
Table 3 Magnitudes of applied traction, shear and torsional forces for load steps in Figs 14 and 15 Load steps
Traction ~
5.2 The brachial plexus nerve analysis The neonatal's neck model is formed from equivalent beam elements and has been analysed under application of three possible loading conditions : namely pure longitudinal traction, pure shear and pure torsion, or their simultaneous combination. Figures 14 and 15 show the results of these analyses (9), where the load steps are considered in accordance with the values given in Table 3. Figure 14 shows the strain set-up in the brachial plexus nerve under application of traction, shear and torsional forces. It can be seen that the effect of shear force is the greatest, the effect of torsion being the least
Shear ~
N
N
10 20 30 40 50 60 70 80
2.5 5.0 7.5 10.0
12.5 15.0 17.5 20.0
Torsion
N mm 60 120 I80 240 300 360
420 480
and negligible. Clinical experiments indicate that an increase in length of about 20 per cent damages the brachial plexus nerve (2). As shown in Fig. 14, within the usual limits of the applied forces, traction and torsional forces are not able to create such a length change. On the other hand, a 17.5 N shear force is sufficient to
Three-dimensional model model 6 0 . - .. : . i ..i ..i .i. i.. i .. : .,.. : .... : .. . : . . i . .i . i. ... .... . ... . ... . .. . ... . .. _g_
- 3 ~ -Two-dimensional -
0
4
8
12
16
20 ~
24
28
32
36
40
Length mm
Fig. 13 Principal stresses at the bottom-most fibre (two- and threedimensional clavicle models) Part H : Journal of Engineering in Medicine
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249
Shear Traction Torsion
'
1
2
3
4
5
6
7
8
h d d Step
Fig. 14 Strain set-up in BP nerve under traction, shear and torsion
maximum permissible force that a clinician could apply to the neonatal head during the birth process is about 80 N. This is the required force for the first point in the clavicle to reach the fracture stress. Hence, it is expected that for a complete fracture a greater force is required. On the other hand, not all of the force applied to the neonatal's head transmits to the clavicles. Hence, a greater force than 80 N is normally required for fracture of the clavicles. This result compares very well with the clinical and experimental results reported in the literature, which indicates that a 100 N force applied to the neonate's head is sufficient for fracture of the clavicles
create such a length increase and damage the brachial plexus nerve. Figure 15 shows the effect of shear force, traction force and their simultaneous application on the brachial plexus nerve. It can be seen that the effect of simultaneous application of these forces adds up, and results in increased danger for the brachial plexus nerve. 6 CONCLUSIONS
In conclusion the results obtained from the study of shoulder dystocia will be summarized by the following statements. The analysed models indicate that the clavicle always fractures under application of compressive stresses at the lowest point of the sternal end connection to the clavicle mid-shaft. Applying lateral traction of 40 N causes the fracture process in the clavicle to begin. Assuming that the effect of applied force on the neonatal's head equally divides on both clavicles, it can be concluded that the
-
(1).
It has been reported that stretch of about 15 to 20 per cent can damage the brachial plexus nerves (2). Considering this fact and observing the results shown in Figs 14 and 15 indicate that in normal circumstances the traction and torsional forces are not able to create such an effect, whereas a 13 N shear force can provide such damage. Furthermore, by considering the limited motion of the neonatal neck and the forces that are
Shear Traction Shear and traction
Load level
Fig. 15 Strain set-up in BP nerve under traction, shear and simultaneous
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normally applied to its head, torsional force has the least effect whereas the shear force provides the greatest effect on stretching the brachial plexus nerves. Applying equal amounts of forces, the effect of shear force is about 14 times the effect of traction force and is much more than the effect of torsional force. Hence, it is recommended that application of shear forces be avoided as much as possible during shoulder dystocia. Finally, since simultaneous application of these three forces results in a summation of strains on the brachial plexus nerve, the possibility of damaging the nerve increases under such circumstances.
REFERENCES 1 Sorah, J. Design and development of engineering aids to evaluate
the birthing process. MSc thesis, University of Houston, August 1988.
2 Sharma, V. Applications of finite element and expert systems methods to a study of shoulder dystocia. MSc thesis, University of Houston, August 1988. 3 Crelin, E. S. Anatomy of’ the newborn-an atlas, 1969 (Lea and Faberger). 4 Mack, G., Gardner-Morse, J. P. L. and lan, A. F. S. Incorporation of spinal flexibility measurements into finite element analysis. J . Biomech. Engng, November 1990, 112,481-483. 5 Manohar, M. P., Richard, A. B. and Augustus, A. W. Threedimensional flexibility and stilhess properties of the human thoracic spine. J . Biomechanics, 1976, 9, 185-192. 6 Cristela, H. and George, D. W. Shoulder dystocia. Clin. Obstet. Gynecol., September 1990,33(3). 7 Eastman, N. J. and Hellman, L. M. Williams obstetrics, 1961 (Appleton Century Crofts Inc.). 8 James, A. 0. and Helene, B. L. Shoulder dystocia: prevention and treatment. Am. 1.Ubstet. Gynecol., January 1990, 162(1). 9 Davoodi, R. Engineering analysis of shoulder dystocia in the human birth process by finite element method. MSc thesis, Mechanical Engineering Department, Sharif University of Technology, Iran, May 1992. 10 Edward, W. and Ashraf, H. SAP80 structural analysis programs. University of California, Berkeley, 1986.
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Engineering analysis of shoulder dystocia in the human birth process by the finite element method A Meghdari, PhD, MemASME, R Davoodi, MSc and F Mesbah, MD* Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
This paper presents an engineering analysis ofshoulder dystocia (SO) in the human birth process which usually results in damaging the brachial plexus nerves and the humerus andlor clavicle bones of the baby. The goal is to study these injuries from the mechanical engineering point of view. T w o separatefinite element models of the neonatal neck and the clavicle bone have been simulated using eight-node three-dimensional elements and beam elements respectively. Simulated models haoe been analysed under suitable boundary conditions using the ‘SAP80’Jinite element package. Finally, results obtained have been verified by comparing them with published clinical and experimental observations. 1 INTRODUCTION
The birth process is defined as the passage of the foetus through the contours of the birth canal. There is no doubt that this process takes place in a proper manner only when the size of the foetus is proportional to the size of the birth canal. Otherwise, complications concerning the foetus and/or the mother may arise. One such complication is when the size of the foetus’s shoulders are large compared to the mother’s pelvic canal. In this case, after the foetal head is delivered, the large size of the shoulders prevents the continuation of the natural birth process. This may cause a delay in birth which can result in asphyxiation, followed by nerve damage, mental retardation, speech impediments and even neonatal death. In an effort to reduce the delay time, the clinicians usually try to force the baby out, typically in less than five minutes. This may cause various levels of damage to the brachial plexus nerves and fracture of the humerus and/or clavicle bones of the baby. However, this is thought to be less dangerous and more treatable than the possible consequences of a prolonged delay in the birth process. To study the mechanics of fracture in the clavicle bone and the level of damage to the brachial plexus, the clavicle bone and neonatal vertebral column can be simulated by a suitable computer model. By applying relevant forces, the stress field can then be computed using software packages containing finite element methods for further analysis. Utilizing the computed stresses, the level of possible damage due to these forces can be predicted. For example, the dependency of the clavicle’s fracture on the properties of its material can be studied. Furthermore, the relationship between the level of stretch in the brachial plexus on the neck and the forces applied to the foetal head by clinicians during the delivery can be analysed. Sorab (1) has developed experimental models of the foetus and the birth canal in order to analyse the applied forces in shoulder dystocia and to obtain the necessary forces for the fracture of the clavicle bone and stretching of the brachial plexus nerves. In this regard, The MS was received on I1 August 1992 and wus accepted for publication on 18 December 1992.
* Present address. Sussnn Hospitul, Tehran, Iran. H07392 0 IMechE 1992
Sharma (2) modelled the clavicle bone and the brachial plexus using two-dimensional elements and studied their behaviour under the application of clinician forces using the finite element method (FEM). This paper examines the connection between these forces and the level of damage to the foetus. Furthermore, the aim is to determine the maximum permissible forces in order to warn the clinician when the applied forces are too large. An analysis is presented of the types of forces applied to the foetus at the time of delivery during shoulder dystocia. Specifically, the effects of these forces on the clavicle bone and the brachial plexus nerves, two of the most common areas of damage to the foetus during SD, are discussed. First the necessary data about the dimensions and material properties of the neonatal’s clavicle bone and neck are collected from the literature (2--5).Using these data, suitable models of the clavicle and neck are simulated. These models under appropriate boundary conditions and forces have been analysed by the finite element method. Finally, results are compared with previously published clinical and experimental observations.
2 SHOULDER DYSTOCIA (SD)
Shoulder dystocia (SD) is a complication in obstetrics that requires emergency treatment and is frequently associated with birth injuries of the clavicle bone and the brachial plexus nerve. Shoulder dystocia occurs due to impaction of the anterior shoulder of the foetus against the mother’s pelvis. As a result the clinician is unable to free the shoulder and hence is unable to deliver the baby without additional manipulation. This incident is reported to occur in about 2 per cent of all deliveries, and so far there is no known method to predict such an incident. Figure 1 clearly shows a neonate in the birth canal when shoulder dystocia occurs. Excessive forces applied to the foetal head by the cIinician may result in various kinds of damage, the most serious being fracture of clavicle bones and stretching/tearing of the brachial plexus nerves. Figure 2 shows two areas of common damage when shoulder dystocia occurs (6-8).
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have been considered: one assumes the clavicle to be curved only in one plane (that is the planar curvature model) while the other considers a more accurate model of clavicle with body curvatures appearing in all planes (the spatial curvature model). The total length of clavicle is assumed to be 40 mm, and is divided into 20 parts, where each part is modelled by 12 elements. On the whole, the spatial model consists of 504 nodes and 240 elements. Choosing three-dimensional elements facilitates the modelling of curvatures and variable thicknesses in the clavicle bone. Figure 4 shows the prepared model of the clavicle bone for finite element analysis. Figure 5 shows the assumed boundary conditions of the kind pin joint and roller joint for the acromial and sternal ends of the clavicle. Considering various boundary conditions, these are chosen to be the most suitable ones due to the specific orientation of the clavicle with other bones in the body during shoulder dystocia (9). However, it was assumed that when the acromial end of the clavicle bone is placed (locked) behind the mother's symphysis pubic bone (where only clavicle rotation about the axis normal to the body's plane is admissible at the acromial end), the clinician's applied forces to the neonatal head are transferred to the sternal end of the clavicle via the vertebral column, ribs and sternum.
Fig. 1 Shoulder dystocia in the birth canal Brachial plexus
3.2 Neonatal neck model --=--*
\
Fig. 2 Areas of damage during shoulder dystocia
3 MODELLING THE NEONATAL CLAVICLE BONE AND NECK
3.1 Clavicle bone model Figure 3 shows a typical clavicle bone of the neonate (3). The clavicle is a long bone characterized by a relatively long shaft, which is not straight but is usually curved in two directions. It is hollow, cylindrical, contracted and narrowed. Its walls consist of dense, compact bone tissue of greater thickness in the middle, but becoming thinner towards the extremities. To model the complex shape of the neonatal clavicle it is assumed to be shaped like a hollow cylindrical beam with circular cross-sections throughout its length. Furthermore, it is assumed that the compact and spongy bone tissues have linear, elastic and isotropic material properties under quasi-static loading. Taking account of these properties, a spatial model of this bone has been simulated using eight-node three-dimensional elements. To analyse the importance of body curvatures in the clavicle, in these simulations two different cases Compact hone ti\\ue
\
Spongy bone tisbue
/
Medullary cavity
Cartilage
Fig. 3 Schematic of a neonatal clavicle
The neonatal neck is a flexible structure formed by a series of bones called vertebrae connected by intervertebra1 discs and cartilage. It may be regarded as a chain of seven vertebrae joining the head to the rest of the body. In this analysis, beam elements are used to model the neonatal's neck. Modelling is done such that a set of vertebrae and an intervertebral disc is considered equivalent to a beam. Then its geometrical as well as material properties are chosen such that its stiffness in different directions is similar to the combination of vertebrae and disc in the neonatal neck. For the sake of analysis, the neonatal vertebral column is modelled by seven interconnected beams. Elastic elements are used to model the brachial plexus (BP) nerve. Since the brachial plexus nerve does not resist to any great extent against the neck movements, in order to study the level of stretch in BP nerves, the longest BP nerve which is connected to the fifth vertebra was chosen for sample analysis. The assumption was made that the level of stretch in the chosen BP nerve is greater than others and is more at risk of damage. Figure 6 shows the neonatal neck model considered in this study and analysis. 4 MECHANICAL PROPERTIES OF THE NEONATE'S BODY TISSUES
There is not much information available about the mechanical properties of the newborn's body tissues; most of the available data concern adults. Considering the fact that the mechanical properties of the human body are seriously affected by age, direct utilization of the data available for adults for this study does not seem correct. However, by referring to the existing references, some of the mechanical properties of newborns were extracted and some of the data were approximated by extrapolation of the data available for adults. Tables OIMechE 1992
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ENGINEERING ANALYSIS OF SHOULDER DYSTOCIA BY THE FINITE ELEMENT METHOD
Top-most fibre
Sternal end
Fig. 4 The clavicle bone model for FEM analysis
1 and 2 provide the data obtained from published sources, which were utilized for the analysis of the neonatal’s clavicle and neck models.
5 RESULTS AND ANALYSIS
5.1 Clavicle bone analysis
The planar and spatial models of the clavicle have been analysed with suitable boundary conditions shown in Fig. 5 under lateral force (the force transmitted to the clavicle from the neonate’s head via the vertebral column, ribs and the sternum, assuming that the joints Sternal end
Acrornial end
L
Fig. 5 Assumed boundary conditions for the modelled clavicle
--:-a 12 mm
Beam elements
among them are rigid) using the ‘SAPSO’ finite element package. The results indicate that the maximum stresses are created at the bottom-most and the top-most fibres (fibres formed by connecting all nodes along the clavicle bone, located at the lowest and the highest points of the model respectively). Hence, by analysing the stress field distribution in these fibres, the maximum allowable force can be determined by studying the relationship between the applied forces and the created stresses. Figures 7 to 13 clearly show the results obtained. Figure 7 shows the created stresses in the top-most and bottom-most fibres throughout the clavicle in the planar curvature model. At the sternal end, created stresses in the top-most and bottom-most fibres are of the tensile and compressive kinds respectively. This observation is totally reversed at the acromial end. Based on detailed analyses in references (2) and (9), it is shown that boundary conditions, wall thickness, clavicle curvatures and its diameter are important factors for the created stresses. Changing each of these parameters directly affects the stress distribution. As observed, most of the stresses are created at the point where the sternal end is connected to the clavicle midTable 1 Mechanical properties of the modelled clavicle (2) 1.16 x 1.05 x lo4 55 80
Density of compact bone Elastic modulus of compact bone Ultimate tensile strength Ultimate compressive strength Poisson’s ratio
0.3
N/mm3 N/mmz N/mmz N/rnmz -
c3
Table 2 Total stiffness of the neck at various vertebral levels (2,4,5) ~
Elastic element
TI
Fig. 6 The neonatal neck model (every beam element models the combination of vertebrae plus an intervertebral disc)
Vertebrae levels
Tensile stiffness N/mm
Shear stiffness N/mm
Torsional stiffness N mm/rad
c7 C6 C5 c4 c3
38.613 17.498 10.885 7.616 5.176 5.524 5.333
3.7124 1.8296 1.1874 0.8728 0.6619 0.519
3358 1679 1119 839.5 671.6 559.6 479.7
c2 c1
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A MEGHDARI, R DAVOODI AND F MESBAH __t_
Top Bottom
Length
mm
Fig. 7 Principal stress at the top- and bottom-most fibres (two-dimensional clavicle model)
shaft. The maximum compressive stress in the bottommost fibre is computed as 70 N/mm2 whereas the maximum tensile stress at the top-most fibre is 40 N/mmz. Figures 8 and 9 show the effect of lateral force on the created stresses at the top-most and bottom-most fibre in the planar curvature model. By applying a 41 N lateral force in the direction of force application in Fig. 5, the compressive stress at the bottom-most fibre reaches the fracture limit of 80 N/mm2 whereas the maximum tensile stress at the top-most fibre reaches about 42 N/mm*, which is lower than the fracture limit. Hence, in this model using the 41 N lateral force, the first point to reach the fracture limit is at the lowest connection point of the sternal end and the clavicle mid-shaft. Figures 10 and 11 show the effects of an increase in lateral force on the principal stresses at the top-most
and bottom-most fibres in the three-dimensional model of the clavicle based on the maximum stress failure theory. In the three-dimensional model with an applied force of 39.5 N, the first point to reach the fracture limit is observed. It seems that the main reason for the difference in the required force of fracture in two- and threedimensional models is the existence of torsional moment in the three-dimensional model. Torsional moment results in torsional stress which adds up with bending and axial stresses, resulting in a reduction of the required force for clavicle fracture. Figure 12 shows the lateral displacement of the planar and spatial models of the clavicle under application of the same lateral force. The displacement in the three-dimensional model is about 17 per cent greater than in the two-dimensional model, which is solely due to the effect of torsion. Figure 13 shows the created stresses at the bottom-most fibres of the planar and
-
__t_
F=31N F=36N F=41N
Length mm
Fig. 8
Effect of increasing lateral force on principal stress at the top-most fibre (two-dimensionalclavicle model)
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__t_ _t_
__Ei._
V”
0
4
F=31N F=36N F=41N
12
8
241
16
20
24
28
32
36
40
Length __ mm
Fig. 9 Effect of increasing lateral force on principal stress at the bottommost fibre (two-dimensional clavicle model)
-
F=26N F=34N F = 39.5 N
__t_
Length mm
Fig. 10 Effect of increasing lateral force on principal stress at the top-most fibre (three-dimensional clavicle model)
-
__c_ F=26N
F=34N
--8- F = 39.5 N
Length mm
Fig. 11 Effect of increasing lateral force on principal stress at the bottommost fibre (three-dimensional clavicle model) 0 IMechE 1992
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_t_
Two-dimensional model Three-dimensional model
Length mm
Fig. 12 Lateral displacements in two- and three-dimensional clavicle models
spatial model of the clavicle. Due to the torsional moment, the created stress in the three-dimensional model is greater than in the two-dimensional model. As a result, the required force of fracture for the threedimensional model is lower than for the twodimensional model.
Table 3 Magnitudes of applied traction, shear and torsional forces for load steps in Figs 14 and 15 Load steps
Traction ~
5.2 The brachial plexus nerve analysis The neonatal's neck model is formed from equivalent beam elements and has been analysed under application of three possible loading conditions : namely pure longitudinal traction, pure shear and pure torsion, or their simultaneous combination. Figures 14 and 15 show the results of these analyses (9), where the load steps are considered in accordance with the values given in Table 3. Figure 14 shows the strain set-up in the brachial plexus nerve under application of traction, shear and torsional forces. It can be seen that the effect of shear force is the greatest, the effect of torsion being the least
Shear ~
N
N
10 20 30 40 50 60 70 80
2.5 5.0 7.5 10.0
12.5 15.0 17.5 20.0
Torsion
N mm 60 120 I80 240 300 360
420 480
and negligible. Clinical experiments indicate that an increase in length of about 20 per cent damages the brachial plexus nerve (2). As shown in Fig. 14, within the usual limits of the applied forces, traction and torsional forces are not able to create such a length change. On the other hand, a 17.5 N shear force is sufficient to
Three-dimensional model model 6 0 . - .. : . i ..i ..i .i. i.. i .. : .,.. : .... : .. . : . . i . .i . i. ... .... . ... . ... . .. . ... . .. _g_
- 3 ~ -Two-dimensional -
0
4
8
12
16
20 ~
24
28
32
36
40
Length mm
Fig. 13 Principal stresses at the bottom-most fibre (two- and threedimensional clavicle models) Part H : Journal of Engineering in Medicine
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ENGINEERING ANALYSIS OF SHOULDER DYSTOCIA BY THE FINITE ELEMENT METHOD
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Shear Traction Torsion
'
1
2
3
4
5
6
7
8
h d d Step
Fig. 14 Strain set-up in BP nerve under traction, shear and torsion
maximum permissible force that a clinician could apply to the neonatal head during the birth process is about 80 N. This is the required force for the first point in the clavicle to reach the fracture stress. Hence, it is expected that for a complete fracture a greater force is required. On the other hand, not all of the force applied to the neonatal's head transmits to the clavicles. Hence, a greater force than 80 N is normally required for fracture of the clavicles. This result compares very well with the clinical and experimental results reported in the literature, which indicates that a 100 N force applied to the neonate's head is sufficient for fracture of the clavicles
create such a length increase and damage the brachial plexus nerve. Figure 15 shows the effect of shear force, traction force and their simultaneous application on the brachial plexus nerve. It can be seen that the effect of simultaneous application of these forces adds up, and results in increased danger for the brachial plexus nerve. 6 CONCLUSIONS
In conclusion the results obtained from the study of shoulder dystocia will be summarized by the following statements. The analysed models indicate that the clavicle always fractures under application of compressive stresses at the lowest point of the sternal end connection to the clavicle mid-shaft. Applying lateral traction of 40 N causes the fracture process in the clavicle to begin. Assuming that the effect of applied force on the neonatal's head equally divides on both clavicles, it can be concluded that the
-
(1).
It has been reported that stretch of about 15 to 20 per cent can damage the brachial plexus nerves (2). Considering this fact and observing the results shown in Figs 14 and 15 indicate that in normal circumstances the traction and torsional forces are not able to create such an effect, whereas a 13 N shear force can provide such damage. Furthermore, by considering the limited motion of the neonatal neck and the forces that are
Shear Traction Shear and traction
Load level
Fig. 15 Strain set-up in BP nerve under traction, shear and simultaneous
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normally applied to its head, torsional force has the least effect whereas the shear force provides the greatest effect on stretching the brachial plexus nerves. Applying equal amounts of forces, the effect of shear force is about 14 times the effect of traction force and is much more than the effect of torsional force. Hence, it is recommended that application of shear forces be avoided as much as possible during shoulder dystocia. Finally, since simultaneous application of these three forces results in a summation of strains on the brachial plexus nerve, the possibility of damaging the nerve increases under such circumstances.
REFERENCES 1 Sorah, J. Design and development of engineering aids to evaluate
the birthing process. MSc thesis, University of Houston, August 1988.
2 Sharma, V. Applications of finite element and expert systems methods to a study of shoulder dystocia. MSc thesis, University of Houston, August 1988. 3 Crelin, E. S. Anatomy of’ the newborn-an atlas, 1969 (Lea and Faberger). 4 Mack, G., Gardner-Morse, J. P. L. and lan, A. F. S. Incorporation of spinal flexibility measurements into finite element analysis. J . Biomech. Engng, November 1990, 112,481-483. 5 Manohar, M. P., Richard, A. B. and Augustus, A. W. Threedimensional flexibility and stilhess properties of the human thoracic spine. J . Biomechanics, 1976, 9, 185-192. 6 Cristela, H. and George, D. W. Shoulder dystocia. Clin. Obstet. Gynecol., September 1990,33(3). 7 Eastman, N. J. and Hellman, L. M. Williams obstetrics, 1961 (Appleton Century Crofts Inc.). 8 James, A. 0. and Helene, B. L. Shoulder dystocia: prevention and treatment. Am. 1.Ubstet. Gynecol., January 1990, 162(1). 9 Davoodi, R. Engineering analysis of shoulder dystocia in the human birth process by finite element method. MSc thesis, Mechanical Engineering Department, Sharif University of Technology, Iran, May 1992. 10 Edward, W. and Ashraf, H. SAP80 structural analysis programs. University of California, Berkeley, 1986.
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