Robert S. Ledley, a Georgetown University physicist who was credited with inventing the first full-body CT scanner, a machine that revolutionized medical diagnostics by allowing doctors to gaze inside their patients’ tissues without ever touching a scalpel, died July 24 at the Arden Courts nursing facility in Kensington, Md. He was 86.

His death, of Alzheimer’s disease, was confirmed by his son Fred Ledley. Ledley was a Laurel, Md. resident.

Ledley was trained as a dentist — in case his career in physics didn’t pan out — and became a scientific polymath. In the late 1950s, when most doctors still worked with pen and paper, he became a prominent advocate for using data processors to help diagnose disease.

Then, in 1973, Ledley introduced one of the most powerful diagnostic aides since the discovery of X-rays in 1895. He called his invention the automatic computerized transverse axial scanner (ACTA). It was, in effect, the first machine capable of producing cross-sectional images of any part of the body.

Today, the CT scan is a commonplace medical procedure. (“CT” stands for computed tomography; another moniker is CAT scan, for computer-assisted tomography.) Ledley’s prototype did not include the modern machine’s dreaded tunnel — in his original design, the patient passed through a thinner ring-like scanner — but most CT scanners today rely on his basic concept.

CT technology, originally formulated several years earlier by Nobel Prize-winning scientists Godfrey Hounsfield and Allan M. Cormack, transformed medical imaging. Before the advent of CT scans, doctors relied on X-ray images, which showed only hard tissue such as bone.

CT scans offer near-photographic renderings of soft tissue and organs such as the brain and heart. On X-rays, tumors show up as faint shadows or not at all. With a CT scanner, doctors can use cross-sectional images to pinpoint a tumor’s location — and without subjecting the patient to potentially life-threatening surgery.

When Ledley’s machine began to become widely available in the mid 1970s, the Journal of the American Medical Association called it a “remarkable and fundamentally new technique.” Ledley was inducted into the National Inventors Hall of Fame in 1990 and in 1997 received the National Medal of Technology.

Ledley developed and built his original scanner in a basement laboratory at Georgetown University, with help from a local machinist and a final paint job by a nearby Cadillac dealership.

The machine represented a major improvement on a model built in Britain by Hounsfield, said Joseph November, a University of South Carolina history professor who is working on a biography of Ledley.

Hounsfield’s machine used a tank of water equipped with what November described as a “rubber bladder” — a watertight area within the tank where the patient positioned his head. Only the head, and sometimes extremities such as arms and legs, could be scanned because of the unwieldy water tank.

The technology’s limitation, Ledley discovered, stemmed from a mathematical weakness.

“I couldn’t see any reason why it had to be limited to the brain,” he told The Washington Post in 1990. “Then I realized that the inventor had used the wrong mathematical formula.”

To test the machine, Ledley used calf brains from a Washington area butcher shop.

“One time, late at night . . . I was putting the brain in the skull,” Ledley told The Post. “I guess I was getting a bit sloppy, and a security guard appeared in the doorway and almost passed out. We kept the door shut after that.”

The machine was first used on a patient at the Georgetown University hospital, where a toddler was taken after falling off his bicycle and hitting his head. With the CT scanner, doctors scanned his brain and detected a blood clot that, unnoticed, might have killed the child.

“It was a tremendous feeling,” Ledley told Washingtonian magazine in 1999. “The ACTA scanner had saved its first life.”

In the 1970s, Ledley formed a company, Disco, to produce the scanner. He later sold the company to Pfizer. Today the machine’s prototype is housed at the Smithsonian Museum’s National Museum of American History.

Much of Ledley’s work was conducted from the National Biomedical Research Foundation, a nonprofit organization he founded in 1960 and later ran from Georgetown. The foundation was a headquarters for his efforts to infuse medicine with logic and computer prowess.

The foundation’s work also resulted in the creation of a machine that automated chromosome analysis. It became particularly useful for prenatal detection of conditions including Down syndrome, November said. Without the machine, he said, diagnosis required a geneticist to count chromosomes under a microscope — by hand.

Robert Steven Ledley was born June 28, 1926, in Queens. His father had pursued a doctorate in physics but became an accountant to support his family.

The elder Ledley encouraged his son to pursue a degree in the dependable field of dentistry. As a compromise, Ledley studied dentistry, receiving a D.D.S. degree from New York University in 1948, while also studying physics at Columbia University, where he received a master’s degree in 1949.

He worked and taught over the years at the National Institute of Standards and Technology, where he used one of the early modern computers, as well as at Johns Hopkins University and George Washington University. He joined Georgetown in 1970 and retired in 2005.

Survivors include his wife of 63 years, Terry Wachtell Ledley of Laurel who, according to Washingtonian, “learned mathematics to better decipher her husband”; two sons, Fred Ledley of Boston and Gary Ledley of Philadelphia; and four grandchildren.

Ledley had more than 20 patents and, according to the Hall of Fame, wrote “the first comprehensive textbook for engineers on digital computer engineering.” He also developed skid-resistant crutches.

He credited his training in patient-focused dentistry with making him a better researcher. In the interview with Washingtonian, he recalled an incident when a 300-pound woman became stuck in one of his early scanners. She was able to extricate herself thanks to a safety chain purchased from a hardware store and installed by Ledley.

“If I wasn’t a dentist,” he said, “I wouldn’t have thought of that . . . if I didn’t understand what a medical device was and what a patient is.”