A human heart left on a commercial airliner provides a glimpse into the nation’s transplant system, which relies on an obscure network of nonprofit organizations to collect and transport human organs and tissue.

The heart traveled in the cargo compartment of a Southwest Airlines flight from Sacramento to Seattle on Sunday. It was supposed to be picked up in Seattle but remained on the plane when the aircraft left for Dallas. There are conflicting accounts of what went wrong, and an investigation is underway.

Southwest realized the problem about 90 minutes into the flight to Dallas. The pilot issued an announcement to passengers, made a hairpin turn and headed back to Seattle.

Passengers were at first confused, then generally supported returning to deliver the heart, in case it was needed to save a life, one passenger, Andrew W. Gottschalk, has told media outlets.

As it turned out, the heart was headed to a “tissue processor” in Renton, Wash., a suburb of Seattle, where the valves could be removed for transplant, according to an official with LifeNet Health, a nonprofit organization in Virginia Beach that runs the facility. Tissue processors prepare heart valves, skin, bone and other body parts — but not solid organs — for use in medical procedures.

Initial testing indicates no damage to the valves, which have been removed, said LifeNet Vice President Doug Wilson. “They are in high demand, so they will likely be transplanted as soon as that testing is complete,” he said.

Sen. Todd C. Young (R-Ind.), who has been looking into the transplant system, said Friday that the incident “strikes me as another example of a need for more oversight of the entire organ donation system. That system has operated in the darkness for decades, and Congress and the administration need to fix this.”

LifeNet Health and Sierra Donor Services, which collected the heart from a donor, are two of 58 “organ procurement organizations” (OPOs) chartered by the federal government to collect hearts, kidneys, livers, pancreases and other human organs.

They also collect human tissue and often sell it to tissue processors, which is sometimes their primary method of raising revenue. It is illegal to sell organs at a profit in the United States, but OPOs may charge significant markups on tissue such as heart valves, corneas and bone. Some OPOs, such as LifeNet Health, perform both tissue collection and processing.

The OPOs whisk solid organs to transplant centers for implantation into critically ill patients. The United States has a severe shortage of transplant organs, and speed is critical in keeping them suitable for recipients. Last year, 31,608 organs were transplanted. More than 114,000 people are on waiting lists for organs; 33 die in need of organs each day.

The OPOs’ task of transporting organs and tissue involves a number of crucial steps that often rely on airlines and couriers. All of them are potentially subject to human error.

OPOs are lightly regulated by the federal Centers for Medicare and Medicaid Services, which has repeatedly found that many do a poor job of recovering enough organs to meet the need. For the first time in more than a decade, the government is attempting to shut down one OPO for failing to recover enough organs: LiveOnNY, which collects body parts in the New York metropolitan area. Each OPO has a monopoly over a portion of U.S. territory.

Enforcement of OPO safety standards is generally left to the United Network for Organ Sharing, an umbrella nonprofit that coordinates the system. It is difficult to determine how often problems occur because UNOS’s records are hidden from scrutiny by the public or Congress. But some incidents have emerged.

In 2014, for example, a human pancreas was left sitting in a container on a counter for nearly two hours at the Life Alliance Organ Recovery Agency, the Miami OPO, according to records obtained by The Washington Post. A spokeswoman for the organization said the organ was successfully transplanted. The courier responsible for the mistake was “reeducated about the proper delivery procedure, and there have been no repeat issues,” she said.

In 2013, a kidney that was not accepted for transplant was returned to the wrong location at Oregon Health and Science University, according to federal records. Mike Seely, executive director of the Pacific Northwest Transplant Bank, the OPO in Portland, Ore., said that “the courier failed to follow their internal policies” but that no recipient’s health was jeopardized. The OPO “conducted follow-up with the courier” to prevent future incidents, he said.

Greg Segal, co-founder of Organize, an activist group that is critical of OPOs, said Friday that “the cases the public hears about are really only the tip of the iceberg . . . Organs are lost every day. And every time they are, a patient on the waiting list dies unnecessarily.”

The group worked with the Department of Health and Human Services in 2015 and 2016 to try to reform the transplant network.

The Association of Organ Procurement Organizations declined to comment.

At the moment, it’s unclear who was responsible for Sunday’s incident and why it wasn’t discovered until the plane was in the air to Dallas. Sierra Donor Services, the OPO that provided the heart, said a courier did not show up in time to collect the heart. Wilson, the LifeNet spokesman, said that Southwest failed to take the heart off the plane and that the error was discovered by its courier. Southwest acknowledged that its crew did not remove the heart from the cargo compartment but is not sure how the error was discovered.

“We don’t know all the details,” Wilson said. “We are doing an investigation to make sure this doesn’t happen again.”