Linking Myometrial Physiology to Intrauterine Pressure; How Tissue-Level Contractions Create Uterine Contractions of Labor
[['Over the past several decades , a large body of literature has addressed intracellular [1] and intercellular [2] signaling in pregnant myometrium , but comparatively little effort has been spent seeking to describe the mechanisms that coordinate contractions at the level of the whole uterus .', 'It is clear that at the cellular level , electrical excitability properties control both the signal to contract and the mechanism to directly raise intracellular calcium .', 'Tissue recruitment by action potential propagation is dominant at the tissue-level [2] , [3] ( in the order of centimeters ) , and it is generally believed to play a key role at the organ-level in human labor [4] , [5] ( in the order of several 10 s of centimeters ) .', 'However , it remains unclear how the pregnant uterus coordinates a kilogram of myometrium into repetitive , synchronous contractions of normal human labor .', 'Several mathematical simulations of organ-level functioning have been published , including action potential propagation mechanisms alone [6] , [7] , calcium waves [8] , and a previous cellular automaton approach [9] .', 'Each has significant limitations , including failure to predict uterine behavior across the spectrum of clinical function , or direct disagreement with subsequently published data [10] .', 'These limitations seem to reveal a poor understanding of how the uterus communicates at the organ-level .', 'In the canonical action potential propagation model , an action potential originates at a pacemaker site , travels through the wall of the entire uterus , exciting and recruiting tissue as it propagates [4] , [5] .', 'Despite being widely accepted , there is no direct evidence to suggest that organ-level recruitment utilizes a stable pacemaker site or a single propagating action potential .', 'Indeed , there is good evidence to the contrary .', 'The highest resolution electrical mapping of the pregnant uterus was reported by Lammers et al . in the guinea pig [11] .', 'They found that the first spike of the action potential rarely activated the entire field .', 'A given action potential burst seemed limited to about 10 cm2 , and burst propagation speeds were much slower than action potential propagation speeds .', 'Additionally , a stable pacemaker was not identified , and the pathways of propagation were described as “tortuous” .', 'The only high resolution mapping of the entire front of the human uterus are by Ramon [12] and Eswaran [13] , using an array of superconducting quantum interference devices ( SQUID ) .', 'Synchronization analysis suggested that the human uterus is similar to the guinea pig uterus , as there appears to be a maximum distance of propagation for an action potential .', 'Specifically , wave fronts of electrical activity that propagated long distances were not observed .', 'Although recurrent electrical activities tended to occur in the same physical locations , they also failed to observe a stable pacemaker .', 'These observations raise the possibility that despite its irrefutable importance at the tissue-level , a mechanism using only action potential propagation for tissue recruitment is insufficient , and a second mechanism may be functioning at the organ-level .', 'In 1970 the action potential propagation model was the leading candidate for organ-level signaling , but Csapo [14] proposed an alternate mechanism - mechanotransduction by pressure-tension sensing .', 'In brief , he proposed that increases of intrauterine pressure cause increases of wall tension ( per the Law of Laplace; T\u200a=\u200aP*r/w ) , which then initiate contractions throughout the uterus .', 'Unfortunately , the way mechanotransduction was initially presented suggested that contractions were controlled by stretch , and that electrical activity , if present at all , played a minimal role in initiating contractions or recruiting tissue .', 'This seemed to present a choice between two mutually exclusive mechanisms .', 'Over the next several years it was established without question that electrical activity causes contractions [3] , and expression of an action potential is necessary and sufficient for tissue-level contractions [15] .', 'Thus , the action potential propagation hypothesis was viewed as the winner , and over time , mechanotransduction was largely forgotten .', "However , given the difficulty action potential propagation alone has explaining organ-level function , we revisited Csapo's mechanotransduction mechanism .", 'It is has long been known that quickly stretching smooth muscle can initiate a contraction , and myometrium is no exception .', 'In the 1970s , however , Csapo was perhaps unaware that acutely stretching , or increasing tension on myometrium , initiates an action potential burst which contributes to at least part of the underlying mechanism of stretch-initiated contractions [16] .', 'Hence , mechanotransduction and action potential propagation are complementary and not mutually exclusive .', 'In this work we will use the term “mechanotransduction” primarily to refer to the mechanism , and “stretch-initiated” to refer to the phenomenon .', 'In the discussion we will explain what we mean by the phrase “myometrial myogenic response” , which , we suggest , emphasizes the importance of stretch-initiated contractions to normal function .', 'This term is also intended to highlight the similarity of myometrial and vascular smooth muscle functioning , and imply that the cellular mechanisms may overlap .', 'The arterial myogenic response is understood in fair detail [17] , but the physiological processes following acute stretch of myometrium are only superficially understood .', 'To build the model that incorporates both action potential propagation and mechanotransduction , we make one key assumption .', 'That is , there is an upper limit on the distance each tissue-level action potential can travel .', 'If true , this limitation defines functional regions of the uterine wall .', 'The SQUID array synchronization analysis provides some evidence for the existence of these regions , and an approximate size of 8 cm×8 cm ( reference 12 , figure 8 ) .', 'Within regions , we assume , tissue recruitment is entirely by action potential propagation .', 'To coordinate regional contractions into organ-level contractions , we use mechanotransduction as follows: If one region contracts , the intrauterine pressure rises slightly .', 'This pressure rise would increase tension on the other areas of the uterine wall according to the Law of Laplace ( T\u200a=\u200aP*r/w ) .', 'Increasing tension could trigger a stretch-initiated contraction of another region .', 'With two regions contracting , pressure would increase further , and the cycle would repeat until all regions capable of expressing a stretch-initiated contraction were recruited .', 'A key feature of this mechanism is that it is a pressurized hydraulic system , similar to what is used for automobile braking .', 'Hydraulic systems rapidly transmit signals over long distances , and are not limited by physical proximity to the event that initiates the signal .', 'Therefore , because pressure is the signal used to recruit regions , coordinating a uterine contraction at the organ-level is not constrained by the speed of action potential propagation , even though tissue within regions may be wholly recruited by action potentials .', 'Here we report a mathematical simulation of our model for creating uterine contractions of human labor .', 'We use a variation of the cellular automaton ( CA ) technique .', 'A CA is a system of “cells” , each of which has a state that is defined by the state of the other cells through one or more “rules” .', 'As detailed above , our model divides the uterus into regions , where a cell represents each region ( e . g . “cell” does not refer to an individual myocyte ) .', 'With each iteration , or time step , the status of all the cells are simultaneously updated .', "Classical , or elemental CAs apply one rule and consider only the state of each cell's near neighbors .", 'Complex biological CAs use multiple rules to describe complex physiology , and the status of a cell may be influenced by cells that extend beyond the neighbors .'], ['For human labor , the contractile state of the uterus and the intrauterine pressure are of primary concern .', 'Since the intrauterine pressure is shared by all regions of the uterine wall regardless of relative location , we weight the nearest neighbors no more or less than the other regions .', 'The CA rules approach to simulation is computationally efficient but , more importantly , emphasizes the physiological properties of the tissues that make up the organ .', 'With this in mind , we define three specific rules ( see flowchart figure 1 ) :', '1 ) Intrauterine pressure at each time step is calculated as a function of the regional contractile activities .', '2 ) At the next time step , the intrauterine pressure sets the passive tension on each region according to the Law of Laplace .', '3 ) Within regions , electrical activity creates contractile activity ( defined as the tension of a contraction ) .', 'The tension on each region will initiate and maintain an action potential burst if it exceeds a defined threshold ( action potential threshold ) .', 'By definition , if any part of a region experiences an action potential , the action potential travels throughout the entire region , but no farther , and the region contracts as a unit .', 'When a region is experiencing an action potential burst , the contractile activity is calculated by multiplying the passive tension by the action potential multiplier ( a factor >1 ) .', 'Each region can remain electrically active no more than a defined number of time steps ( burst duration ) .', 'If a region has been electrically active for the maximum allowable number of time steps , it enters a refractory period .', 'When a region is in the refractory period , the tension is decreased by multiplying the passive tension by a factor <1 ( refractory multiplier ) .', 'The refractory period lasts a defined number of time steps ( refractory duration – not shown in figure 1 ) , then the region reverts back to expressing the passive tension .', 'In figure 2A we represent a hypothetical isometric contractility experiment , except that instead of a single tissue strip , tissues A through E are mechanically linked end-to-end .', 'The total tension on the system is T , which is the same for each tissue .', 'If any tissue contracts , T will increase and the new T will be expressed equally across each tissue .', 'In figure 2B we present the corresponding hydrodynamic experiment .', 'Here there are 5 hydraulically connected identical chambers , each containing one tissue strip that is fixed at the bottom and attached to a moveable piston at the top .', 'The entire volume is filled with an incompressible medium , because under these conditions , the volume of the system is constant .', 'For the human uterus , this is an excellent assumption since air is never seen within the uterine cavity , even after rupture of membranes .', 'In this hypothetical apparatus , contraction and shortening of one tissue would pull the piston downward and increase pressure throughout the system .', 'In the chambers with the 4 non-contracting tissues , the pistons would move outward , and the stretching would increase tension on each tissue .', 'While somewhat counterintuitive , the two arrangements in figure 2A and B are mechanically identical .', 'Translating these models to the physical structure of the gravid uterus , figure 2C represents the “tension” descriptor that is a wrap-around of figure 2A , and figure 2D represents a Law of Laplace interpretation that corresponds to both figures 2B and C . Consider the hydraulic system in figure 2B in detail .', 'Because of the viscoelastic properties of myometrium , the system is in hydraulic equilibrium at only two times – when no contractions are occurring , and when all tissues are maximally contracting simultaneously .', "At these times Pascal's Law applies , and P\u200a=\u200aForce/area in all chambers .", 'This equation does not apply during the onset and offset of the contraction because of the viscoelastic properties of the tissues undergoing passive stretch .', 'Assuming nearly identical tissues and identical piston areas , the peak pressure throughout the system when all the tissues are contracting simultaneously is equal to the peak pressure ( Pmax ) generated by one tissue in an isolated chamber .', 'When no tissues are contracting , the minimum pressure equals the baseline tension , which is equally expressed on each tissue .', 'If one tissue contracts , the pressure begins to rise in all the chambers .', 'The elasticity of the four tissues that are not contracting slows the rate of pressure development .', 'If another tissue contracts , the elasticity of that tissue is lost , and pressure rises faster .', 'Therefore , we will approximate the system pressure at any time as linearly proportional to the average contractile activity of the regions .', 'Applying this reasoning to the five chamber experiment in figure 2B , if the first tissue contracts maximally , the system pressure will rise to approximately 20% Pmax .', 'The pistons in the other chambers move outward in response to the rising pressure , and the non-contracting tissues are stretched .', 'A stretch-initiated contraction occurs if one of the four remaining tissues is susceptible .', 'Because of hydraulic signaling , the susceptible tissue that contracts next does not need to be physically located adjacent to the tissue that contracted first .', 'With two tissues contracting maximally , the pressure increases to ∼40% Pmax , which further pushes the pistons of the remaining three tissues .', 'With the additional stretch , the next most susceptible tissue may then contract , and so on , until all tissues contract simultaneously and the system pressure equals Pmax .', 'Because tissue contractions are caused by electrical activity , in the simulation we will use the term “activity” to mean both electrical activity and contractile activity of a region .', 'In addition , viscoelastic tissue creates tension passively when stretched , and we will use the term “passive activity” or passive tension specifically as the force generated by a tissue that is not caused by contractile activity .', 'Using this nomenclature: Pressure ( t ) =\u200a∑activity of all regions ( t ) /#regions In a closed container containing an incompressible fluid , pressure ( P ) and wall tension ( T ) are related by the Law of Laplace: T\u200a=\u200aP*r/w The r/w factor accounts for the physical shape of the container , or in this case , the anatomy of the uterus .', 'w is the thickness of the wall and r is the local radius of curvature .', 'r can be measured in perpendicular x , y axes , where 1/r\u200a=\u200a1/rx+1/ry .', 'If rx\u200a=\u200ary , a factor of 2 is introduced in the denominator , making the Law of Laplace for a sphere .', 'If rx is infinity , r\u200a=\u200ary , and it becomes the Law of Laplace for a cylinder .', 'Differences of local r and w mean that there are regional variations due to local uterine anatomy that must be accounted for when calculating either T from P , or P from T . We introduce the “anatomy sensitivity factor” to account for these variations .', 'Each region has its own multiplicative factor corresponding to r/w , and we will assume that it is the same for the entire region , and that it does not significantly change for the duration of the run .', 'For the gravid uterus ( an oblate spheroid ) , the largest rx will be close to the “sphere radius” of the uterus , or ∼10 cm , but as short as a few cm at regions of high curvature .', 'Thus , rx conservatively ranges over about a factor of 3 .', 'w varies by approximately a factor of 2 [18] , and the sphere-cylinder difference ( rx may be very large for an oblate spheroid ) brings in another factor of 2 that associates with w .', 'Using these approximations , the anatomy sensitivity multiplier will vary from 1/4 to 3/1 ( range of the numerator/range of the denominator ) .', 'This results in a skewed distribution of this factor between . 25 and 3 , with most values near 1 .', 'To simulate this , we define the anatomysens ( i , j ) matrix .', 'Each ( i , j ) value of the matrix is the anatomy sensitivity multiplier of the ( i , j ) region , and it is held constant through each run of the simulation .', 'To convert from pressure to the passive activity of the ( i , j ) region , we multiply by anatomysens ( i , j ) .', 'When pressure is calculated from the regional activities , we will divide by the same factor .', 'To set specific values between ∼ . 25 and 3 centered around 1 , we select pseudorandom numbers from a Weibull distribution .', 'This distribution is shaped by three parameters , the first sets the shape , the second the scale , and the third establishes the starting location .', 'Hence , act ( i , j ) =\u200apressure * anatomysens ( i , j ) and pressure\u200a=\u200a∑ ( act ( i , j ) / ( #regions * anatomysens ( i , j ) ) where act ( i , j ) is the contractile activity of the i , j region at a specific time step .', 'Since act ( i , j ) varies over time , the time series is stored in the activity tensor , activity ( i , j , t ) .', 'SQUID data suggest that repetitively active regions maintain the same location , at least on the time scale of the reported experiments ( several contractions ) .', 'Hence , we will also assume the regions are physically stable over the duration of each run of the simulation .', 'When stretched , each region will either increase tension passively , or it may contract if a propagating action potential is initiated .', 'To simulate a stretch-initiated contraction , we assign each region a tension threshold value .', 'An active contraction occurs if the wall tension of a region exceeds its threshold .', 'To emphasize a key element of our model - that propagating action potentials recruit tissue within regions - we will use the more specific term “action potential threshold” to refer to the value of the tension that initiates a contraction .', 'It is unlikely that the action potential threshold is the same for all the regions .', 'Since this is possibly a key factor in the onset of labor , we will again allow flexibility in the simulation by pseudorandomly selecting action potential threshold values from a Weibull distribution .', "When a regional tension exceeds that region's action potential threshold , we simulate the contraction by multiplying the passive tension by the action potential multiplier ( an input variable >1 ) .", 'From isometric muscle bath experiments [19] , it is well-understood that tissue relaxation begins when the burst stops , and there appears to be an upper limit to the duration of a burst .', 'In our simulation , once a regional burst is initiated , it will remain on until either the activity falls below threshold , or the tissue reaches its maximum burst duration ( an input variable ) .', 'We therefore calculate the ( i , j , t ) burst tensor such that each region experiences independent bursting behavior as follows: If act ( i , j ) is below threshold , then burst ( i , j ) =\u200a1 .', 'If act ( i , j ) is above threshold , then bursting occurs and burst ( i , j ) =\u200aaction potential multiplier .', 'However , if the Maximum burst duration is exceeded , then burst ( i , j ) =\u200a1 Immediately following a burst , the tissue relaxes and it is relatively unresponsive to initiation of another contraction .', 'To simulate this refractory period , we apply the refractory multiplier ( input variable , value <1 ) .', 'The refractory period has a defined refractory duration ( input variable ) .', 'If the Maximum burst duration is not exceeded , then refractory ( i , j ) =\u200a1 .', 'If the Maximum burst duration is exceeded , then refractory ( i , j ) =\u200arefractory multiplier .', 'It the Refractory duration is exceeded , then refractory ( i , j ) =\u200a1 .', "Thus , rule 3 corrects each region's contractile activity by the burst and refractory matrices during each time step of the simulation .", 'act ( i , j ) =\u200aact ( i , j ) ×burst ( i , j ) ×refractory ( i , j ) pressure ( t ) =\u200a∑act ( i , j ) / ( # regions * anatomysens ( i , j ) ) at the next time step: act ( i , j , t+1 ) =\u200apressure ( t ) * anatomysens ( i , j ) * burst ( i , j ) * refractoryfactor ( i , j ) where burst ( i , j , t+1 ) =\u200a1 , if act ( i , j , t+1 ) <threshold ( i , j ) .', 'burst ( i , j , t+1 ) =\u200aaction potential multiplier , if act ( i , j , t+1 ) >threshold ( i , j ) .', 'burst ( i , j , t+1 ) =\u200a1 , if duration of the burst>max burst duration .', 'refractoryfactor ( i , j , t+1 ) =\u200a1 , if duration of the burst<\u200a=\u200amax burst duration .', 'refractoryfactor ( i , j , t+1 ) =\u200arefractory multiplier , if duration of the burst>max burst duration .', 'refractoryfactor ( i , j , t+1 ) =\u200a1 , if refractory period duration>max refractory duration .', 'The names and descriptions of the input , calculation , and output variables are in Table 1 .', 'Because there are a number of input variables , we have selected the following short-cut descriptors to allow changing conditions to be easily compared: X . S1YYY: weibullvar1/weibullvar2/weibullvar3; S2ZZZ: weibullvar4/weibullvar5/weibullvar6 .', 'Here X represents a specific set of input variables for row , column , timesteps , initial pressure , minimum pressure , maximum burst duration , refractory duration , action potential multiplier , and refractory multiplier ( see Table 2 ) .', 'S1YYY refers to the anatomy sensitivity ( anatomysens ) seed value between 1000 and 1999 .', 'S2ZZZ refers to the action potential threshold ( burstthreshold ) distribution seed value 2000 through 2999 .', 'Weibull1 to 3 refer to the Weibull parameters for anatomy sensitivity and Weibull4 to 6 for action potential threshold parameters .'], ['Here we describe the behavior of the simulation for specific input values ( Table 2 ) .', 'In figure 3A the default values , 1 . S1000:1 . 8/1/0 . 3; S2000:4/0 . 6/0 . 4 , reveal a pressure profile suggestive of patterns commonly seen using pressure catheters on women in labor .', 'Contractions are regular , although show some variability of the period between contractions .', 'Peak heights vary slightly .', 'Each contraction arises spontaneously .', 'Pressure rises slowly at first , then accelerates .', 'There is a pseudo-plateau , then a pseudo-symmetrical falling phase .', 'Of note , the refractory time is set at 20 iterations , yet the number of steps between some contractions is ∼40 .', 'In figure 3B , the action potential multiplier is reduced to 2 from 3 .', 'Only small localized contractions are seen and coordinated organ-level contractions are lost .', 'This behavior is what might be anticipated following exposure to nifedipine , which blocks L-type calcium channels and inhibits contractions in tissue strips in a dose-dependent manner [20] .', 'However , reducing the action potential multiplier further to 1 . 5 ( simulating increasing the concentration of nifedipine ) results in a paradoxical reappearance of coordinated contractions ( Fig . 3C ) .', 'In isometric contractility experiments , the primary effect of oxytocin exposure is an increase of force production .', 'To simulate this effect , we step-wise increased the action potential multiplier from 1 . 5 to 2 , then 4 , then 8 ( Fig . 4A , B , C , D , respectively ) .', 'We also simulate a different patient by increasing the number of regions ( using 5 rows and 5 columns ) and changing the pseudorandom seeds , which assigns different anatomy sensitivity and action potential threshold matrices .', 'When the action potential multiplier is 1 . 5 , no coordinated contractions are seen .', 'Increasing this value to 2 resulted in the appearance of irregular and infrequent contractions .', 'At 4 , the contractions became more regular , with increased force and frequency .', 'At these settings , the time between contractions is near the limit of the refractory duration .', 'Doubling the action potential multiplier to 8 resulted in only subtle changes of the contraction pattern .', 'Next we demonstrate that it is possible for the simulation to generate contractions that are initiated by multiple pacemakers .', 'In this run , the rows and columns are set to reflect 25 regions ( rows\u200a=\u200acolumns\u200a=\u200a5 ) and the random number seeds for anatomy sensitivity and action potential thresholds are set to 1474 and 2500 , respectively .', 'Regular contractions are seen with only slight variations of the interval between contractions ( Fig .', '5A .', 'The color animation of the regional activities reveals that the first region to demonstrate significant activity that continues through a global contraction is not always the same ( Fig . 5 B , C , D ) .', 'The likelihood that a region becomes active is increased with a high value of anatomic sensitivity , but a low value of action potential threshold .', 'Therefore , to approximate the overall , or “total” , sensitivity of each region , we divided the anatomic sensitivity by the action potential threshold for each region .', 'The most sensitive region is in row 5 , column 1 ( total sensitivity\u200a=\u200a4 . 003 ) .', 'The second most sensitive region is in row 3 , column 5 ( total sensitivity\u200a=\u200a2 . 024 ) , and the third is in row 5 column 3 ( total sensitivity\u200a=\u200a1 . 975 ) .', 'The pacemaker for the 4th contraction ( Fig . 5B , Step 98 ) is the region in row 5 , column 3 , the pacemaker for the 5th contraction ( Fig . 5C , Step 122 ) is the region in row 5 , column 1 , and the pacemaker for the 6th contraction ( Fig . 5D , Step 151 ) is the region in row 3 , column 5 .', 'An isolated tissue strip can be simulated with rows\u200a=\u200acolumns\u200a=\u200a1 ( Fig . 6 ) .', 'Here we specifically set the anatomy sensitivity to a value near 1 ( 0 . 991 , using anatomy seed 1341 ) , since under isometric conditions the anatomy sensitivity equals 1 exactly .', 'The value for threshold is 0 . 558 ( threshold seed 2987 ) .', 'Repetitive trials reveal that the tissue will only contract if the minimum pressure is above 0 . 6 , even if the initial pressure is above threshold ( Fig . 6B ) .', 'Therefore , minimum pressure is the key factor for determining if regional contractions will occur .', 'When rows\u200a=\u200a1 , columns\u200a=\u200a2 there are two regions , which simulates two mechanically linked tissue strips ( Fig .', '7 [16] .', 'The anatomy seed and Weibull parameters are set to reflect both tissues with similar anatomy sensitivity values near 1 ( 0 . 986 and 0 . 989 , respectively ) .', 'The left and right tissues have action potential thresholds of 0 . 428 and 0 . 670 , respectively , and the minimum pressure is set to fall between these values ( 0 . 5 ) .', 'In Fig . 7A the tissues appear to oscillate out of phase .', 'The activity animation reveals that with these settings , the two regions are not ever highly active simultaneously ( not shown ) – first the “left” tissue becomes active , and then the “right” .', 'This pattern correlates well with experimental observations ( Fig . 7B ) [16] .', 'However , when the simulation is run with the starting pressure increased to 1 ( Fig . 7C ) , the regions oscillate at the same time and the expressed pressure is large .', 'It is also possible to coordinate the contractions by reducing the refractory duration to 10 ( Fig . 7D , the starting pressure was returned to 0 . 5 ) .', 'In addition to the special cases where only one or two regions were simulated , changing the number of regions has important effects on the expression of contractions .', 'To correlate the total force production as a function of the number of regions , we calculated pseudo- “Montevideo units” ( pMV\u200a=\u200apeak force * # contractions in 300 time steps ) and plotted this value as a function of the number of regions ( Fig . 8 ) .', 'In figure 3B with 16 regions , reducing the value of the action potential multiplier to 2 from 3 , the regional oscillations fail to create enough pressure to trigger a coordinated organ-level contraction .', 'Continuing with these input values , global contractions are expressed when the number of regions is increased to 18 ( 6 rows , 3 columns ) , and the pMV units remain high through 30 regions .', 'At 32 regions , the pMV units drop , and remain low through 42 regions .', 'When the number of regions is 49 and above , the Montevideo units again increase .', 'To ensure that the fall of force production between 32 and 42 regions was not the result of a large change of sensitivity as the number of regions varied , for each run we averaged the total sensitivity of all the regions to obtain the mean total sensitivity .', 'While mean total sensitivity varies slightly , the onset of global contractions at 18 regions and the mid-range dip of force production at 32 to 42 regions does not appear to be attributable to changing sensitivities .'], ['It is possible to measure the apparent speed that an action potential propagates through the human uterus using surface EMG .', 'Two or more pairs of EMG electrodes are placed on the abdominal surface , then the distance between the electrode pairs is divided by the time between the onset of electrical activity .', 'Speeds have been reported to average in excess of 50 cm/sec [4] , which is nearly more than an order of magnitude greater than the speeds measured in rodent in vitro [11] .', 'This discrepancy has been explained [5] by assuming the tissue-level action potential travels long distances at much slower speeds , but they are measured as faster because the initiation point is presumably in between or lateral to the electrodes .', 'In our model , a single action potential does not travel great distances .', 'We propose that high speeds are artifacts of measurement that arise when electrodes record from two regions that are separated by a relatively long distance , and the regions are independently recruited by mechanotransduction at nearly the same time because the regions sense the same intrauterine pressure .', 'Recently , however , action potential propagation velocities ( speed and direction ) were measured in term pregnant women in labor [23] .', 'Using a 2-dimensional array over a 14 cm×14 cm grid of electrode pads , the average speed over 35 contractions was 2 . 18±0 . 68 cm/sec .', 'The maximum measuring distance was 17 . 5 cm on the diagonal , but only 3 velocities were measured near the diagonals .', 'Most measurements were over distances between 3 . 5 and 7 cm .', 'From our model this most likely represents measuring the action potential propagation velocity within one region .', 'In small arteries , pressure-dependent contractions regulate local blood flow by what is referred to as the myogenic response [17] .', 'In brief , acutely increasing intravascular pressure results in acute contraction of the artery wall , which narrows the lumen and helps maintain the flow of blood through the artery at a constant rate .', 'In our model of the laboring uterus , acutely raising intrauterine pressure results in an acute contraction of the uterine wall , which further increases pressure and recruits more regions to participate in the contraction .', 'In this sense , the physiological process we propose for the uterus closely parallels the myogenic response of the artery , with the exception that the artery contraction is tonic and the myometrial contraction is phasic .', 'Despite this difference , we propose that the term “myometrial myogenic response” should be used to refer to the process of generating large intrauterine pressures by synchronizing uterine wall contractions via mechanotransduction .', 'In a more limited sense , it can also be used to describe the mechanism of stretch-initiated contractions .', 'The key purpose of introducing this terminology is to help differentiate the mechanisms used to rapidly coordinate uterine contractions from the mechanotransduction mechanisms used to regulate gene expression over longer time frames .', 'Elementary CAs are well-defined mathematical constructs previously used to investigate the emergent properties of complex systems [24] .', 'There are only 256 possible rules and Wolfram places each into one of four classes based on the expression of complex behavior .', 'Starting values are not considered in the classification of the rule .', 'However 
['Introduction', 'Methods', 'Results', 'Discussion']
['The mechanisms used to coordinate uterine contractions are not known .', 'We develop a new model based on the proposal that there is a maximum distance to which action potentials can propagate in the uterine wall .', 'This establishes “regions” , where one action potential burst can rapidly recruit all the tissue .', 'Regions are recruited into an organ-level contraction via a stretch-initiated contraction mechanism ( myometrial myogenic response ) .', 'Each uterine contraction begins with a regional contraction , which slightly increases intrauterine pressure .', 'Higher pressure raises tension throughout the uterine wall , which initiates contractions of more regions and further increases pressure .', 'The positive feedback synchronizes regional contractions into an organ-level contraction .', 'Cellular automaton ( CA ) simulations are performed with Mathematica .', 'Each “cell” is a region that is assigned an action potential threshold .', 'An anatomy sensitivity factor converts intrauterine pressure to regional tension through the Law of Laplace .', 'A regional contraction occurs when regional tension exceeds regional threshold .', 'Other input variables are: starting and minimum pressure , burst and refractory period durations , enhanced contractile activity during an electrical burst , and reduced activity during the refractory period .', 'Complex patterns of pressure development are seen that mimic the contraction patterns observed in laboring women .', 'Emergent behavior is observed , including global synchronization , multiple pace making regions , and system memory of prior conditions .', 'The complex effects of nifedipine and oxytocin exposure are simulated .', 'The force produced can vary as a nonlinear function of the number of regions .', 'The simulation directly links tissue-level physiology to human labor .', 'The concept of a uterine pacemaker is re-evaluated because pace making activity may occur well before expression of a contraction .', 'We propose a new classification system for biological CAs that parallels the 4-class system of Wolfram .', 'However , instead of classifying the rules , biological CAs should classify the set of input values for the rules that describe the relevant biology .']
['How does the pregnant uterus coordinate a kilogram of smooth muscle tissue into repetitive , synchronous , organ-level contractions of human labor ?', 'Action potential propagation recruits tissue for contraction over short distances , but a single action potential sweeping through the uterus cannot explain organ-level function .', 'Multiple action potentials seem to arise simultaneously , and apparently spontaneously , in different “regions” of the uterine wall .', 'We interpret the existence of regions as a consequence of there being a maximum distance a single action potential can travel .', 'To explain the synchronization of regional contractions , we use a second mechanism: initiation of contractions by stretch .', 'Because the uterus is pressurized , contraction of the first region raises the intrauterine pressure slightly , which stretches the entire uterine wall .', 'The stretch recruits another regional contraction , which generates more pressure .', 'This positive feed-back recruits most regions into simultaneous activity .', 'With this mechanism we simulate the contraction patterns of human labor , and show how contractions emerge from complex interactions .', 'We explain why the decades-long search for the uterine pacemaker has failed , and why drugs that stimulate or inhibit tissue contractions have enigmatic effects at the organ-level .', 'This simulation , for the first time , successfully links tissue experiments to clinical obstetrics .']
['medicine and health sciences', "women's health", 'maternal health', 'obstetrics and gynecology', 'pregnancy']