Mathematic modeling of forces associated with shoulder dystocia: A comparison of endogenous and exogenous sources Bernard Conik, biD, Alberta Walker, and Michele Grimm, Phi) Detroit, Michigan OBJECTIVE: A mathematic model was developed to estimate the compressive pressure on the fetal neck overlying the roots of the brechial plexus by the symphysis pubis during a shoulder dystocia event. The induced pressure was calculated for both exogenous (clinician applied) and endogenous (maternal and uterine) forces during the second stage of labor. STUDY DESIGN: Intrauterine pressure and clinician-applied force data were taken from the existing literature. A free-body diagram was generated and equilibrium equations were used to calculate the contact pressure between the bass of the fetal neck and the symphysis pubis during a shoulder dystocia event. RESULTS: Clinician-applied traction to the fetal head (exogenous force) led to an estimated contact pressure of 22.9 kPa between the fetal neck and the symphysis pubis. In contrast, uterine and maternal expulsive efforts (endogenous forces) resulted in contact pressures that ranged from 91.1 to 202.5 kPa. The estimated pressures resulting from endogenous forces are 4 to 9 times greater than the value calculated for clinicianapplied forces. CONCLUSION: Neonatal brachial plexus injury is not a priori explained by iatrogenically induced excessive traction. Spontaneous endogenous forces may contribute substantially to this type of neonatal trauma. (Am J Obstet Gyneco12000;182:689-91 .)
Key words: Brachial plexopathy, engineering, force, shoulder
S h o u l d e r dystocia is a commonly r e p o r t e d obstetric complication, associated with both maternal and fetal risks for injury) When neonatal brachial plexus palsy is found after a shoulder dystocia event, its occurrence is frequently presumed to be related to iatrogenic trauma during the birth process, despite a paucity o f objective clinical evidence. Brachial plexus injury has been shown to occur as a result of both compressive and tensile forces on the associated nerves. 2 Although tension to the nerve bundle during childbirth has been empirically argued to be induced through clinician-applied traction, compression of the bmchial plexus during a shoulder dystocia event may be caused by any force acting to deliver the infant. Recent reports have documented cases of brachial plexus injury in the neonate unrelated to recognized birth trauma, s, 4 As Jennett and Tarby4 pointed out, =To maintain a posteriori that brachial plexus impairment in itself is evidence that such (extreme lateral traction) pressure must have been used is untenable."
From the Departments of Obstetrics and Gynecology and Mechanical Engineering, WayneState University. Receivedfor publication August 12, 1999; acceptedNovember 2, 1999. Retmnt requests: Bernard Gonik, MD, Department of Obstetrics and Gynecology, Wayne State University School of Medicine, 6071 W Outer Dr, Detroit, M148235. Copyright © 2000 by Mosby, Inc. 0002-9378/2000 $12.00 + 0 6/1/104214 doi:10, l O67/mob.2000.104 214
dystoda T h e forces associated with the birth process have b e e n studied only in a limited fashion. Average measurements o f intrauterine pressure d u r i n g the second stage of labor have r a n g e d from 54.4 m m H g (7.25 kPa) to 120.9 m m H g (16.15 kPa),5, 6 with m u c h of the variation d e p e n d i n g on gravidity a n d whether the patient was bearing down. The m a t e r n a l expulsive efforts included in some of these measurements occur spontaneously and reflexively during the second stage of laborY T h e only data on clinician-applied traction forces after delivery o f the fetal head were obtained by Allen et al.s This study n o t e d a m e a n p e a k traction force of 47 N for routine deliveries and 100 N in cases of shoulder dyst~ cia. T h e study used a tactile sensing glove on the hands o f the clinician to r e c o r d the applied traction force. In a laboratory m o d e l o f shoulder dystocia the average peak traction force required to free the anterior shoulder was f o u n d to range between 47 N and 106 N, depending on pelvic positioning and the bidavicular diameter o f the infant's shoulders. 9 To d a t e n o pressure m e a s u r e m e n t s o r calculations have b e e n m a d e at the site o f impact between the base of the fetal neck and the symphysis pubis in either normal o r shoulder dystocia deliveries. Compression at this site s h o u l d be o f i n t e r e s t for individuals c o n c e r n e d with brachial plexopathy because of the anatomic proximity of t h e brachial plexus nerve roots to the region of impaction. Because o f the complexity o f measuring this pressure in vivo, we developed a simplified mathematic 689
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calculationof endogenousforces Fig 1. Free-body diagram used to estimate contact pressure between base of fetal neck and symphysis pubis (.SIP)from endogenous (maternal and uterine) or exogenous (clinician-applied traction) delivery forces.
m o d e l with which to p r e d i c t the c o n t a c t stress between the symphysis pubis a n d the base o f the fetal neck.
Material and methods To develop a simplified m a t h e m a t i c m o d e l o f the compressive stress (pressure) b e t w e e n the base of the fetal n e c k and the symphysis pubis, a free-body d i a g r a m was constructed (Fig 1). O n the basis o f an e q u i l i b r i u m balance o f force (F), the following e q u a t i o n s were generated to calculate the target pressure (Pcontact) : ~,F = 0
[1]
Fdelivery - Fcontact = 0 Pcontact = Fcontact/Asymphysis pubis
[2] [3]
T h e c o n t a c t a r e a b e t w e e n the symphysis pubis (Asymphysis pubis) and t h e base o f the fetal n e c k was estim a t e d as a trapezoid a n d calculated a c c o r d i n g to the following equation: Asymphysispubis = ½[bl + b9]h
[4]
where h is the h e i g h t o f the trapezoid a n d b 1 and b9 are the lengths o f the u p p e r and lower edges o f the structure. T h e s e g e o m e t r i c p a r a m e t e r s w e r e m e a s u r e d directly with a m o d e l o f a r e p r e s e n t a t i v e f e m a l e pelvic skeleton. T h e delivery force (Fdelivery) was divided into two categories, e x o g e n o u s (clinician applied) and e n d o g e n o u s ( u t e r i n e c o n t r a c t i o n a n d m a t e r n a l expulsive forces). T h e s e forces were estimated on the basis o f data p r o v i d e d in the literature. 5, 6, 8 T h e e x o g e n o u s delivery force was d e f i n e d as the traction r e q u i r e d to deliver the a n t e r i o r s h o u l d e r d u r i n g a s h o u l d e r dystocia e v e n t a n d was assigned the representative value o f 100 N. T h e e n d o g e nous force was estimated a c c o r d i n g to the m o d e l o f a piston (infant) within a thin-walled pressure vessel (uterus). T h e expulsive force o n the piston (Fpiston) was t h e n def i n e d as follows: Fpiston = Pchamber " Apiston
[5]
where Pchamber is the pressure developed within the vessel and Apiston is the cross-sectional area of the m o v i n g structure. F o r the case o f childbirth Pchamber can be assumed to be the intrauterine pressure g e n e r a t e d by uterine contraction and m a t e r n a l b e a r i n g down and Apiston represents the cross-sectional area of the infant's body within the uterus. Because o f the difficulty of d e t e r m i n i n g this area as a result o f the u n k n o w n a r r a n g e m e n t of the torso and limbs within the uterus and the variable and complex geometry, the piston area was estimated as the midtransverse cross-sectional area o f a term intrauterine cavity. T h e uterus was a p p r o x i m a t e d as an ellipsoid and the cross-sectional area in the mid-transverse plane was calculated f r o m the following equation: Auterus = x n . d / 4 [6] where D and d are the lengths o f the m a j o r and m i n o r axes o f the elliptic cross-section, respectively. To obtain a representative value for the uterine cross-sectional area, m e a s u r e m e n t s were m a d e of the external dimensions of a t e r m uterus. T h e e n d o g e n o u s delivery force was calculated for a r a n g e o f i n t r a u t e r i n e pressures (Table I) a c c o r d i n g to the following equation: Fendogenous = Pintrauterine" Auterus
[7]
T h e resisting c o n t a c t force a n d p r e s s u r e at the impaction p o i n t between the base of the fetal n e c k and the symphysis pubis were calculated f r o m equations 2 and 3. T h e e n d o g e n o u s and e x o g e n o u s forces were assumed to occur independently.
Results T h e calculated areas for the transverse cross-section o f the uterus and the contact area of the symphysis pubis were 0.0549 m 2 a n d 0.00437 m 2, respectively. T h e end o g e n o u s delivery forces were calculated on the basis o f the r a n g e o f i n t r a u t e r i n e pressures d e s c r i b e d by L i n d r e n 6 and are given in Table I. W h e n the m o d e l was applied to d e t e r m i n e the contact pressure between the base o f the fetal n e c k and the symphysis pubis, the values r a n g e d between 91.1 and 202.5 kPa as a result o f endogenous delivery forces. In contrast, the estimate o f exogenously g e n e r a t e d traction force exerted by the clinician i n d u c e d a contact pressure of 22.9 kPa at this same site o f fetal impaction (Table I). T h e contact stress caused by exo g e n o u s forces was a f o u r t h to a ninth that resulting f r o m the e n d o g e n o u s pressure g e n e r a t e d d u r i n g the second stage of labor in u n c o m p l i c a t e d deliveries.
Comment Obviously, the m a t h e m a t i c exercise p r e s e n t e d h e r e can only crudely e x a m i n e this c o m p l e x issue o f forces and pressures related to the shoulder dystocia event. F o r example, the m o d e l does n o t account for soft tissue resistances, the dissipation o f force t h r o u g h o u t the uterus, o r
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Table I. Calculated delivery forces and contact pressures at i m p a c t i o n site lntrautmine pmsure e Condition Primigravid, not bearing down Multigravid, not bearing down Multigravid, bearing down Primigravid, bearing down With dinidan-applied traction 8
ram Hg
kPa
54.4 68.6 113.8 120.9 NA
7.25 9.14 15.13 16.15 NA
Delivery force (N) 398.1 501.9 832.7 884.7 100.0
Contact pressure at impaction site (kPa) 91.1 114.9 190.6 202.5 22.9
Endogenous forces were estimated from literature values of intrauterine pressure during the second stage of labor in uncomplicated deliveries. The exogenous force was taken as a representative value for peak traction applied by a clinician to deliver the anterior shoulder during a shoulder dystocia event. NA, Not applicable.
t h e additive n a t u r e o f traction and c o m p r e s s i o n forces t h a t m a y b e a p p l i e d concomitantly. Additionally, t h e r e are n o data to quantify the threshold pressures n e e d e d to i n d u c e traction versus compression related n e r v e injury. O f i n t e r e s t , however, a similar m o d e l o f e n d o g e n o u s force was previously used by Pearse l° to estimate natural forces associated with expulsion of the fetal h e a d in comp a r i s o n to forceps deliveries. T h e s e results do h i g h l i g h t the fact t h a t t h e e n t i r e process o f the second stage o f labor is dynamic, involving b o t h e n d o g e n o u s and e x o g e n o u s forces. Intimately involved in the passage o f the passenger t h r o u g h the passageway are considerable e n d o g e n o u s u t e r i n e a n d maternal forces, m a n y o f which are reflexive in nature. It should be n o t e d that the assumptions in this study used to calculate t h e m a t e r n a l expulsive efforts were actually g e n e r a t e d u n d e r n o r m a l conditions rather than d u r i n g an obstructive process (with the anterior fetal s h o u l d e r i m p a c t e d ben e a t h the symphysis pubis). This suggests that these data m a y have u n d e r e s t i m a t e d those maternally derived forces a n d t h a t d u r i n g a shoulder dystocia event there may be an even g r e a t e r divergence of attributable forces between end o g e n o u s and e x o g e n o u s sources. W h e n a clinician reports that routine external traction was u s e d o n a n e o n a t e s u b s e q u e n t l y f o u n d to h a v e a b r a c h i a l plexus injury, alternative (noniatrogenic) pathophysiologic m e c h a n i s m s should be considered. I n d e e d , A c k e r e t all1 r e p o r t e d that in their e x p e r i e n c e Erb palsy was associated with rapid deliveries a n d unusually forceful expulsive efforts in a third o f cases. Even w h e n should e r dystocia has occurred, necessitating additional man e u v e r s to deliver the i m p a c t e d a n t e r i o r shoulder, t h e
e n d o g e n o u s c o n t r i b u t i o n o f potentially harmful forces should be k e p t in mind. Counterintuitive approaches, including attempts at cessation o f p u s h i n g until the anterior s h o u l d e r is freed, may have m e r i t in limiting injury. Finally, m o r e scientific studies are n e e d e d to e x a m i n e detailed aspects o f the m e c h a n i c s o f brachial plexus t r a u m a in this specific setting to b e t t e r define the factors l e a d i n g to injury.
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