With New Abortion Restrictions, Ohio Walks Fine Line Michael F. McElroy for The New York Times Madelyn Puterbaugh, 23, said that her birth control had failed and that it was "not the right time" for her to bear a child. CLEVELAND - Angela H., married with two children, became pregnant accidentally and, after a medically difficult time and severe postpartum depression, said neither she nor her family was ready for another child. Andrew Spear for The New York Times Mike Gonidakis, the president of Ohio Right to Life, at his home in Dublin, Ohio, in 2011. Under a law that took effect in Ohio this month, the Cleveland abortion clinic she visited had to offer her a chance not only to view an ultrasound of the fetus but also to watch its beating heart, which she said she resented. "It's a hard decision for anybody to make," she said of abortion, asking that her surname not be published out of privacy concerns. To make it more difficult by passing these laws and making women feel guilty is terrible. Ohio has become a prime laboratory for what anti-abortion leaders call the incremental strategy - passing a web of rules designed to push the hazy boundaries of Supreme Court guidelines without flagrantly violating them. Many of the rules, critics say, are designed to discourage women from getting abortions or to hamper clinic operations, even forcing some to close. The mandated discussion of fetal heartbeats is one of a cascade of abortion restrictions adopted here over the years, from a waiting period to curbs on the medication-induced abortions preferred by many women. The pace has quickened since John R. Kasich became governor in 2011, cementing Republican domination of state politics. Avowedly anti-abortion, Mr. Kasich said through a spokesman that he considered the restrictions he signed this year to be "reasonable." These laws have passed without the national drama provoked by far-reaching abortion bans that were approved, then overturned in court, in states like Arkansas and North Dakota. But taken together, they affect patients and clinics in myriad ways - in the view of proponents, rightly making women think twice before ending a pregnancy and ensuring clinic safety, or, in the view of opponents, imposing heartless obstacles and guilt on women who are seeking a legal procedure. "In Ohio, the last few years have been fantastic if you support the pro-life movement," said Mike Gonidakis, the president of Ohio Right to Life. His group has even lobbied against a more sweeping ban on early-term abortions, incurring the wrath of more restless abortion foes. But he says: "We've been able to craft pro-life laws that can withstand court scrutiny." On Wednesday, the American Civil Liberties Union filed a challenge in state court to the heartbeat mandate and other new restrictions, asserting that they were adopted in violation of the Ohio constitution's "single subject" rule because they were part of an unrelated budget bill. More broadly, abortion-rights advocates call the incremental strategy, now being pursued with variations in many states, an insidious way to limit access to abortion and shame women who in many cases already have to walk past shouting protesters to enter clinics. "If you can't outlaw abortion outright, just make it harder and harder to get," said Chrisse France, the executive director of Preterm, a large, nonprofit abortion clinic on Cleveland's east side that performs about 4,900 abortions a year, mainly for low-income women. They say they're doing this to protect women's health, but some of the laws are actually harmful, and some are just cruel. Conversations with patients at Preterm revealed diverse reactions to the mandated waiting period and counseling, but no sign that any women were changing course. She said she had turned down the chance to view the fetal heartbeat. "I didn't look," she said. I thought I'd be too sad. She proceeded with the abortion, but said she had not minded the required 24-hour wait between the counseling and the procedure. "They gave me a lot to think about," she said, "but it's my choice." Ohio has long required abortion clinics to have a formal transfer agreement with a nearby hospital for emergency care, something physicians say is medically unnecessary because hospitals are already required to treat emergency patients. Now, a new measure bars public hospitals from signing such agreements - a shift that could force two or three of the state's remaining 11 clinics to close because they cannot find willing partners.