Induction by breaking water

Inducing Labor (for Parents) - Nemours KidsHealth

Stripping Membranes and Breaking Water for Labor Induction, Augmentation

Mathematicians reach a breakthrough in the study of a "dangerous" problem Now, however, Terence Tao has made more progress than anyone else in decades.

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It's common for many pregnant women, especially first-time mothers, to watch their baby's due date come and go without so much as a contraction. The farther away from the expected delivery date (called the EDD) you get, the more anxious you might become. You may start to wonder — is this baby ever going to come?

Late pregnancy can be challenging — you may feel large all over, your feet and back might hurt, you might not have the energy to do much of anything, and you're beyond ready to meet the little one you've nurtured all this time. Which is why waiting a little longer than you'd expected can be particularly hard.

Still, being past your due date doesn't guarantee that your doctor (or other health care provider) will do anything to induce (or artificially start) labor — at least not right away.

Labor induction is what doctors use to try to help labor along using medications or other medical techniques. Years ago, some doctors routinely induced labor. But now it's not usually done unless there's a true medical need for it. Labor is usually allowed to take its natural course. However, in some situations, a health care provider may recommend induction.

Your doctor might suggest an induction if:

your water broke but you are not having contractions
your baby still hasn't arrived by 2 weeks after the due date (when you're considered post-term — more than 42 weeks into your pregnancy)
you have an infection in the uterus (called chorioamnionitis)
you have certain risk factors (e.g., gestational diabetes or high blood pressure)
there is not enough amniotic fluid
there is a problem with the placenta
the baby is not growing appropriately

Induction also can be appropriate under certain circumstances, as with a mother who is full term and has a history of rapid deliveries or lives far from a hospital.

Some mothers request elective inductions for convenience, but these do come with risks. Doctors try to avoid inducing labor early because the due date may be wrong and/or the woman's cervix might not be ready yet.

Some methods of induction are less invasive and carry fewer risks than others. Ways that doctors may try to induce labor by getting contractions started include:

Stripping the membranes. The doctor puts on a glove and inserts a finger into the vagina and through the cervix (the opening that connects the vagina to the uterus). He or she moves the finger back and forth to separate the thin membrane connecting the amniotic sac (which houses the baby and amniotic fluid) to the wall of the uterus. When the membranes are stripped, the body releases hormones called prostaglandins, which help prepare the cervix for delivery and may bring on contractions. This method works for some women, but not all.
Breaking your water (also called an amniotomy). The doctor ruptures the amniotic sac during a vaginal exam using a little plastic hook to break the membranes. If the cervix is ready for labor, amniotomy usually brings on labor in a matter of hours.
Giving the hormone prostaglandin to help ripen the cervix. A gel or vaginal insert of prostaglandin is inserted into the vagina or a tablet is given by mouth. This is typically done overnight in the hospital to make the cervix "ripe" (soft, thinned out) for delivery. Administered alone, prostaglandin may induce labor or may be used before giving oxytocin.
Giving the hormone oxytocin to stimulate contractions. Given continuously through an IV, the drug (Pitocin) is started in a small dose and then increased until labor is progressing well. After it's administered, the fetus and uterus need to be closely monitored. Oxytocin is also frequently used to spur labor that's going slowly or has stalled.

Stripping the membranes can be a little painful or uncomfortable, although it usually only takes a minute or so. You may also have some intense cramps and spotting for the next day or two.

It can also be a little uncomfortable to have your water broken. You may feel a tug followed by a warm trickle or gush of fluid.

With prostaglandin, you might have some strong cramping as well. With oxytocin, contractions are usually more frequent and regular than in a labor that starts naturally.

Inducing labor is not like turning on a faucet. If the body isn't ready, an induction might fail and, after hours or days of trying, a woman may end up having a cesarean delivery (C-section). This appears to be more likely if the cervix is not yet ripe.

If the doctor ruptures the amniotic sac and labor doesn't begin, another method of inducing labor also might be necessary because there's a risk of infection to both mother and baby if the membranes are ruptured for a long time before the baby is born.

When prostaglandin or oxytocin is used, there is a risk of abnormal contractions developing. In that case, the doctor may remove the vaginal insert or turn the oxytocin dose down. While it is rare, there is an increase in the risk of developing a tear in the uterus (uterine rupture) when these medications are used. Other complications associated with oxytocin use are low blood pressure and low blood sodium (which can cause problems such as seizures).

Another potential risk of inducing labor is giving birth to a late pre-term baby (born after 34 and before 37 weeks). Why? Because the due date (EDD) may be wrong. Your due date is 40 weeks from the first day of your last menstrual period (LMP).

Babies born late pre-term are generally healthy but may have temporary problems such as jaundice, trouble feeding, problems with breathing, or difficulty maintaining body temperature. They may also be more likely than full term babies to have developmental or school problems later on.

Even though inductions do come with risks, going beyond 42 weeks of pregnancy can be risky, too. Many babies are born "post-term" without any complications, but concerns include:

A vaginal delivery may become harder as the baby gets bigger. As babies get bigger, the chance of an injury during delivery, such as a broken bone, increases.
The placenta that helps to provide the baby with nourishment is deteriorating.
The amniotic fluid can become low or contain meconium — the baby's first feces. If the baby breathes in meconium, it can cause breathing problems.

Old wives' tales abound about ways to induce labor, such as the use of castor oil. It is not safe to try to artificially start labor yourself by taking castor oil, which can lead to nausea, diarrhea, and dehydration. And herbs and herbal supplements meant to induce labor can be harmful. Breast stimulation can cause uterine contractions by causing the release of oxytocin. However, some studies have suggested that the baby might have abnormal heartbeats after breast stimulation. Some women feel that having sex in late pregnancy can induce labor, but there is no conclusion on this yet.

Talk to your doctor before doing anything to try to encourage your little one's arrival. Inducing labor is best left to medical professionals — you may cause more harm than good.

As frustrating as it can be waiting for your baby to finally decide to arrive, letting nature take its course is often best, unless your doctor tells you otherwise. Before you know it, you'll be too busy to remember your baby was ever late at all!

Written by WebMD Editorial Contributors

If your doctor or midwife has concerns about your health or your baby's health toward the end of your pregnancy, they might suggest speeding up the process. This is called inducing labor, or induction. Instead of waiting for labor to start naturally, your doctor or midwife will use drugs or a procedure to start it sooner.

Induction can be the right choice for some women, but it has risks. And it doesn’t always work. If it doesn’t, you may need another induction or a c-section. Most experts say it's best to let labor begin on its own and progress naturally unless there's a clear medical reason.

Induction is very common -- 1 out of 4 women in the U.S. starts labor with induction. Many times it's done for medical reasons, but it can be elective.

Why do some women need to have labor induced?

You’re 1-2 weeks past your due date. Studies show that inducing labor at 39 weeks doesn’t raise the risk for having a C-section or birth complications for the baby. After 41 weeks, you and your baby are at greater risk for complications. Being a little "late" isn’t a reason to induce. You also don’t want to be induced too early. Babies born before 39 weeks are more likely to have health problems, longer hospital stays, and time in neonatal intensive care.
Your water breaks but labor doesn’t start. Once your water breaks, you and your baby have a higher risk of infection. You might not need induction right away, though. Check with your doctor or midwife. Sometimes it's still safe to let labor begin on its own. After your water breaks, your doctor will limit the number of vaginal exams performed because of the potential for infection.
A problem puts you or your baby’s health at risk. Examples are infection (chorioamnionitis), too little amniotic fluid (oligohydramnios), and placental abruption. If you have conditions like diabetes, high blood pressure, preeclampsia, or eclampsia, your doctor or midwife might want to induce labor.
If your baby isn’t growing as it should be, or has an abnormal heart rate, your doctor or midwife might want to induce labor.

Some doctors recommend "elective" inductions for non-medical reasons. Maybe you live far from the hospital and your doctor worries that you won't get there in time. Or maybe your doctor asks you to accommodate their schedule. Experts say you should reconsider, though. Because induction poses some risks, experts say that women shouldn't be induced unless it's medically necessary.

You doctor shouldn’t induce if:

You had C-section before that involved a classical incision or major surgery
The placenta is covering the cervix (placenta previa)
Your baby is in the wrong position (sideways or feet-first)

There are a few ways a doctor or midwife can induce your labor, including:

Stripping the membranes. In this procedure, your doctor or midwife will use a gloved finger to gently separate the amniotic sac from the wall of the uterus at the cervix. This releases hormones that can trigger contractions. You can get it done in your doctor's or midwife's office. It can be uncomfortable. Afterward, you’ll probably go home to wait for contractions. You might have cramping and spotting.Studies disagree about how well membrane stripping works. Considering that and the discomfort it causes, talk over the pros and cons with your doctor or midwife beforehand.
Hormones. At the hospital, your doctor will give you hormones called prostaglandins to open the cervix and trigger contractions. If you’ve had a C-section in the past, your doctor won’t use this treatment, because it raises the risk of uterine rupture.
Mechanical dilation. Another way your doctor or midwife triggers labor is with a balloon catheter. At the hospital, your doctor inserts a thin tube through your vagina into your cervical opening. Then the doctor uses water to inflate the balloon at the end of the tube, causing your cervix to expand.
Medications. The medicine Pitocin (oxytocin) can start contractions. You get this at the hospital through an IV tube in your arm. Your doctor or midwife starts with a small dose and gradually increases it until your contractions are strong and frequent enough for your baby to be born.

Some women go into labor and deliver within a few hours after induction. Others take 1 or 2 days to start labor. If none of these methods starts your labor, and staying the course isn’t a good option, you'll most likely need a C-section, especially if your water has broken.

Induction doesn’t work for everyone, and every pregnant mom’s body reacts differently to induction technique. Generally, inducing labor is safe, but there are risks:

Longer hospital stay. If you're induced, you may be in the hospital longer during labor and delivery. If you wind up needing a C-section after induction, your time in the hospital will be even longer.
Increased need for pain medicine. Inducing labor might cause contractions to come on stronger and more often than they would naturally. You're more likely to need an epidural or another medicine to manage the pain.
Increased risk of infection. Breaking the amniotic sac can lead to infection if you don't deliver within a day or two after induction.
Health problems for your baby. Women who are induced before the 39th week for medical reasons may deliver a baby who has problems with breathing. These babies have a higher risk of long-term developmental problems.
Complications during delivery. Induction, especially with medications, might not be safe for women who’ve had a previous C-section or other surgery to the uterus. They have a higher risk of uterine rupture. Intense contractions also cause the placenta to detach from the wall of the uterus, called placental abruption. Both of these conditions are serious but rare, even with induction.

If your doctor or midwife recommends induction, ask questions. You want to be absolutely sure that it's the best decision for your health and your baby's health.

Tales abound of home remedies that supposedly bring on labor, but there is no scientific evidence to back them up. These methods include:

Having sex
Gently stimulating your nipples
Herbal remedies including blue or black cohosh (some herbs can be dangerous if you don’t use them properly)
Drinking small amounts of castor oil (Recent, well-controlled studies say it’s safe during late pregnancy but castor oil can have unpleasant side effects, like diarrhea. )
Walking

Don’t try any of these methods without first talking to your doctor or midwife. Some can cause side effects or pose risks.

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Take any number. If it's even, divide it by two. If odd, multiply by three, add one. Repeat. Does any number eventually come to 1?

Experienced mathematicians advise beginners to stay away from the Collatz conjecture. They call it the song of the siren: fall under its influence, and you may never get to meaningful work.

The Collatz conjecture is perhaps the simplest unsolved problem in mathematics, and that is what makes it so treacherously attractive.

“This is a very dangerous task. People become obsessed with it, even though it is completely impossible,” said Jeffrey Lagarias, a mathematician at the University of Michigan and an expert on the Collatz conjecture.

But in 2019, one of the best mathematicians in the world dared to approach it, and received the most significant result that has been achieved in several decades.

On September 8, 2019, Terence Tao published a proof showing that the Collatz conjecture is at least "almost" true for "almost" all numbers. And although Tao's result is not a complete proof of the conjecture, it is a very serious breakthrough for a problem that does not reveal all its secrets so easily.

“I didn't expect to solve the problem completely,” said Tao, a mathematician at the University of California, Los Angeles. “But I managed to do more than I expected. ”

Lothar Kollatz probably made the hypothesis of the same name in the 1930s. The challenge sounds like a party trick. Take any number. If it's even, divide it by two. If odd, multiply by three, add one. Get a new number. Apply the same rules for him. The hypothesis tells what will happen if this process is persistently repeated.

Intuition tells you that the starting number affects the final result. Perhaps some numbers will eventually decrease to 1. Perhaps other numbers will increase indefinitely.

However, Collatz predicted that this was not the case. He suggested that if you start with a positive integer, and repeat the indicated sequence long enough, then from any initial number you will come to 1. And when you come to one, you will fall into the trap of the rules of the hypothesis, and enter an infinite loop: 1, 4 , 2, 1, 4, 2, 1, and so on, ad infinitum.

Over the years, many problem lovers have been drawn to the attractive simplicity of the Collatz conjecture, or "3x+1 problem," as it is also called. Mathematicians have already checked a quintillion examples (this is a number with 18 zeros), not finding a single exception to Collatz's prediction. You yourself can try to check a few examples with any of the many "Collatz calculators" available on the Internet. The Internet is full of unsubstantiated amateur proofs of the hypothesis, the authors of which claim that they managed to prove or disprove it.

“You just need to know how to multiply by 3 and divide by 2 and you can start playing with it. And it's very tempting," said Mark Chamberland, a mathematician at Grinnell College, who made a popular YouTube video about the problem called "Easiest of Impossible Problems."

But there is little real evidence.

In the 1970s, mathematicians showed that almost all Collatz sequences - the list of numbers that you get when you repeat the process - end up with a number less than the initial one. This was weak evidence that almost all Collatz sequences lead to 1, but it was there nonetheless. And from 1994 years before Tao's 2019 result, the record for showing the lowest value was held by Ivan Korets. Other works have similarly attempted to attack the problem without approaching its main goal.

"We don't really understand the Collatz question very well, so there hasn't been much work on the subject," said Kannan Soundararajan, a mathematician at Stanford University who worked on the conjecture.

The futility of these attempts has led many mathematicians to the conclusion that this conjecture is simply not available at the current level of knowledge, and that they are better off spending their time on other research.

"The Collatz problem is notorious for its complexity—so much so that mathematicians routinely preface every discussion of it with a warning not to waste time on it," said Joshua Cooper of the University of South Carolina.

Lagarias first became interested in this hypothesis as a student at least 40 years ago. For decades, he was the unofficial curator of everything related to her. He has amassed a library of related papers, and in 2010 published some of them as a book titled: The Decisive Challenge: The 3x+1 Challenge.

“Now I know much more about this problem, and I can still say that it is impossible to solve it,” Lagarias said.

Usually Tao does not waste his time on impossible tasks. In 2006, he received the Fields Medal, the highest honor in mathematics, and is considered one of the finest mathematicians of his generation. He is used to solving problems, not chasing castles in the air.

“These are the risks associated with being a mathematician,” he said. “You can become obsessed with one of the big known tasks that is beyond the capabilities of any person, and waste a lot of time.”

However, Tao is not always able to resist temptations from this area. Every year he spends one or two days on the most famous of the unsolved problems in mathematics. Over the years, he made several approaches to the Collatz conjecture, but without success.

Then in August, an anonymous reader left a comment on Tao's blog. He suggested trying to solve the Collatz conjecture "for almost all" numbers, without trying to fully prove it.

"I didn't answer, but it got me thinking about this problem again," Tao said.

And he realized that Collatz's conjecture was in some ways similar to the special types of equations - partial differential equations - appearing in the most significant results obtained during his career.

Partial differential equations (PDEs) can be used to model many of the most fundamental physical processes in the universe, like the evolution of fluids or the passage of gravitational waves through spacetime. They appear in situations where the future state of the system—for example, the state of a pond five seconds after a stone is thrown into it—depends on the contributions of two or more factors, such as the viscosity and velocity of the water.

It would seem that complex PDEs have little in common with such a simple arithmetic question as the Collatz conjecture.

But Tao understood that they had something in common. In PDE, you can substitute values, get different values, repeat the process - all to understand the future state of the system. For any given PDE, mathematicians need to know whether the initial input values will lead to infinite output values, or whether the equations will always produce final values, regardless of the initial ones.

Terence Tao, inspired by a comment on his blog, made the biggest progress in decades on the Collatz conjecture

For Tao, this goal was of the same order as whether you always get the same value (1) from the Collatz process, regardless of the initial value. As a result, he realized that techniques for studying PDEs might be suitable for studying the Collatz conjecture.

One particularly useful technique uses a statistical way to study the long-term behavior of a small number of initial values (something like a small number of initial pond water configurations) and extrapolates the result to the long-term behavior of all possible initial pond configurations.

In the context of the Collatz conjecture, imagine that we started with a large sample of numbers. Our goal is to study how these numbers behave when we apply the Collatz process to them. If almost 100% of the numbers in the sample end up at 1 or very close to 1, we can conclude that almost all numbers will behave the same way.

But for this conclusion to be valid, the sample must be very carefully selected. This task is similar to taking a sample of voters in a US presidential election. To carefully sample the entire population, weighted proportions for Republicans and Democrats, men and women, and so on, must be used.

Numbers have their own "demographic" parameters. Odd and even numbers, numbers that are divisible by 3, and numbers that differ from each other in even trickier ways. By creating a sample of numbers, you can make sure that it includes certain types of numbers, and does not include others, according to a weighted principle - and the better you choose the weights, the more accurate your conclusions about all the numbers in general will be.

Tao's problem was much more difficult than just understanding how to create an initial sample of numbers with the right weights. At each step of the Collatz process, the numbers you are working with change. One obvious change is that almost all of the numbers in the sample are decreasing.

Another, perhaps less obvious, change is that the numbers may start to cluster. For example, you can start with a nice even distribution of numbers from one to a million. But after five iterations, the numbers are likely to concentrate on a few small intervals on the number line. In other words, you can start with a good sample, which after five steps will be hopelessly distorted.

"You can usually expect the distribution after iteration to be completely different from the initial one," Tao said. However, his key idea was how to create a sample of numbers that for the most part retain their original weights in the Collatz process.

For example, Tao's initial sample is weighted so that there are no numbers that are divisible by three, since the Collatz process eliminates such numbers pretty quickly anyway. Some of the other weights chosen by Tao turn out to be more difficult. He favors numbers whose remainder after division by 3 is 1, and moves away from numbers whose remainder after division by 3 is 2.

As a result, the sample with which Thao begins retains its character even after the start of the Collatz process.

"He found a way to continue this process so that after a few steps it was still clear what was going on," said Soundararajan. “When I first saw this work, I was very happy and thought it was amazing.”

Tao used his weighting technique to prove that almost all initial values - at least 99% - end up with a value very close to 1. This allowed him to conclude that 99% of the initial values, large, than a quadrillion end up with values less than 200.

This is perhaps the strongest result in the long history of this hypothesis.

“This is a great breakthrough in our knowledge of what's going on with this task,” Lagarias said. “This is definitely the best result in a very long time.”

Tao's method is almost certainly not able to get to the full proof of the Collatz conjecture. The reason is that its initial sample is still slightly distorted after each step. The distortion will be minimal as long as the sample still contains many different values far from 1. But in the Collatz process, all the numbers in the sample begin to converge towards the same number, and a small distortion becomes larger - just as a small error in the calculation of the result of a vote does not have large value in the case of a large sample, but greatly affects the result when the sample is small.

Any proof of the full conjecture is likely to be based on a different approach. In summary, Tao's work is both a triumph and a warning to all who are interested: once you feel like you've cornered a problem, it slips away.

“You can get as close to the Collatz conjecture as you like, but it still remains elusive,” Tao said.

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