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First 3-D mathematical model of labor contractions

Although researchers have looked for the origins of preterm birth for years, the causes are still unknown. By studying the electrical activity causing contractions, a model exists that may aid in predicting preterm birth.


Arye Nehorai PhD and his team have developed the first 3-D mathematical model of contractions. Contractions begin from a single cell in the myometrium tissue of the uterus.

The coupling of excited to contracting smooth muscle cells in the uterus is basic to any smooth muscle contraction anywhere in the body. Body builders to weekend runners use the same process of exciting muscles cells — then relaxing muscles cells in repetitive sequences throughout the progress of their sport, or simply by standing up and sitting down.

However, the uterine smooth muscle differs from all other muscle types by automatically coordinating the gain and loss of Ca2+ in a consistent manner. This pulsing, repetitive process increases and decreases in order to pull apart the bones of the pelvic girdle — approximately 10cm — just enough for a baby's head to pass between the two. The mother does not control or regulate this process as would an athlete increase or decrease muscle repetitions.

The electrophysiology of the uterine lining is controlled by cells of the sarcoplasmic reticulum. The sarcoplasmic reticulum is similar structurally to the endoplasmic reticulum, but contains different proteins. It stores large amounts of calcium and then releases it when muscles are stimulated. But, the sarcoplasmic reticulum mainly synthesizes and transports proteins to a cell system known as the Golgi apparatus.

Cells of the sarcoplasmic reticulum regulate calcium ion concentration in the cytoplasm of striated muscle cells. These cells increase their amount of calcium (Ca2+) — leading to contraction of cell walls. Cell contraction is then followed by a decrease in the amount of Ca2+ and a subsequent relaxing of the smooth muscle, restoring it to its original shape. The repetition of loading increasing amounts of Ca2+ in and out of uterine smooth muscle cells at increasing levels defines active labor.

The research was published May 28, 2016, in the journal PLoS One.

"We know that cells start the electrical activity, but nothing is known about the positions or numbers — or how cells interact in different places in the uterus.

"In addition, we don't yet know directions of the fibers in the myometrium. [This is] important because electricity propagates along the muscle fibers, and that direction varies among women."


Arye Nehorai PhD, Eugene and Martha Lohman Professor of Electrical Engineering, Chair, Department of Electrical & Systems Engineering in the School of Engineering & Applied Science, Washington University, St. Louis, Missouri, USA


University of Arkansas researchers gained this information by applying sensors to the abdomens of 25 pregnant women. Using 151 magnet-ometers, they measured the strength of the magnetic field in each woman's abdomen — resulting from electrical activity from a contraction — the team then created a precise mathematical model replicating that electrical activity throughout labor.

They plan to use this data to predict which pregnancy contractions are early and weak — or pre-term —and which are valued as active labor, explains Nehorai. Additionally, the 3D information can also estimate position, number and distribution of electrical output by the uterus.


"Our ultimate goal is to share this information with obstetricians and gynecologists so they can take measurements and make a prediction of whether a woman will have preterm or term labor. Creating a realistic, multiscale forward model of uterine contractions, will allow us to better interpret magnetomyography measurements and, therefore, shed light on the prediction of preterm labor."

Arye Nehorai PhD


Abstract
Understanding the mechanisms of uterine contractions during pregnancy is especially important in predicting the onset of labor and thus in forecasting preterm deliveries. Preterm birth can cause serious health problems in newborns, as well as large financial burdens to society. Various techniques such as electromyography (EMG) and magnetomyography (MMG) have been developed to quantify uterine contractions. However, no widely accepted method to predict labor based on electromagnetic measurement is available. Therefore, developing a biophysical model of EMG and MMG could help better understand uterine contractions, interpret real measurements, and detect labor. In this work, we propose a multiscale realistic model of uterine contractions during pregnancy. At the cellular level, building on bifurcation theory, we apply generalized FitzHugh-Nagumo (FHN) equations that produces both plateau-type and bursting-type action potentials. At the tissue level, we introduce a random fiber orientation model applicable to an arbitrary uterine shape. We also develop an analytical expression for the propagation speed of transmembrane potential. At the organ level, a realistic volume conductor geometry model is provided based on magnetic resonance images of a pregnant woman. To simulate the measurements from the SQUID Array for Reproductive Assessment (SARA) device, we propose a sensor array model. Our model is able to reproduce the characteristics of action potentials. Additionally, we investigate the sensitivity of MMG to model configuration aspects such as volume geometry, fiber orientation, and pacemaker location. Our numerical results show that fiber orientation and pacemaker location are the key aspects that greatly affect the MMG as measured by the SARA device. We conclude that sphere is appropriate as an approximation of the volume geometry. The initial step towards validating the model against real MMG measurement is also presented. Our results show that the model is flexible to mimic the limited-propagation magnetic signature during the emergence and decay of a uterine contraction.

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Nov 21, 2016   Fetal Timeline   Maternal Timeline   News   News Archive   

Direction of uterine contractions detected by a SQUID Array for Reproductive Assessment (SARA)

(a) Uterine model of fixed conductivity angles.
(b) Uterine model with random conductivity angles.
Both actions squeeze the fetus down into the birth canal.
Image Credit: Arye Nehorai laboratory, Washington University


 


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