Ingrid Bergman Petter Lindström, Dr. Petter Lindstrom, a Swedish-born neurosurgeon respected in his field for his pioneering work in so-called bloodless brain surgery, died on May 24 at his home in Sonoma, Calif. He was 93.

Dr. Lindstrom had the misfortune of being better known to the rest of the world as the husband Ingrid Bergman deserted for Roberto Rossellini, who directed her in the movie ''Stromboli.'' The Lindstrom-Bergman marriage lasted 13 years and ended in scandal and a bitterly contested divorce in 1950.

Dr. Lindstrom went on to a long, distinguished career as a teacher and a practitioner who contributed to the technical advances in brain surgery.

Ingrid Bergman wed Mr. Rossellini, but the marriage was annulled in 1960. She later married Lars Schmidt, a Swedish businessman and theatrical producer. She died in 1982.

Dr. Lindstrom's forte was surgery of the deep brain using ultrasound, carried out to leave no lesions or permanent changes in brain function. He performed the procedure on patients with intractable pain; psychoneuroses like obsessive-compulsive disorders, anxiety and depression; and certain types of epilepsy.

Petter Lindstrom was born in Stode, Sweden. He studied dentistry in Heidelberg, Stockholm and Leipzig, where he received a doctorate in dental surgery in 1931. He went into private practice in Stockholm and held an associate professorship at the Karolinska Institute there.He and Miss Bergman married in 1937. Two years later, her acting career took her from Sweden to Hollywood. After Dr. Lindstrom received his medical degree from the University of Rochester in 1943, he joined her on the West Coast and completed three years of residency in neurosurgery at Los Angeles County Hospital in 1947.

Going into private practice in his specialty, he also held teaching and clinical appointments at the University of Southern California and the University of California at Los Angeles.

He was on the staff of several hospitals in the area and had risen to chief of neurosurgery atLos Angeles County Harbor Hospital by 1949.

Moving east in 1952, Dr. Lindstrom took the same position at the Veterans AdministrationHospital in Pittsburgh and continued his research at the University of Pittsburgh. From 1955 to 1964 he was chief of neurosurgery at the Veterans Administration Hospital in Salt Lake City and, as of 1961, a full professor of neurosurgery at the University of Utah. It was in Pittsburgh and Utah that he introduced his ultrasound surgery.

Dr. Lindstrom returned to California in 1964 and filled academic and hospital appointments in San Francisco and San Diego. He retired as a clinical professor from the University of California at San Diego in 1987, and from private practice in 1988.

Dr. Lindstrom is survived by his wife of 45 years, Dr. Agnes Rovnanek Lindstrom; a daughter from his first marriage, Pia Lindstrom of Manhattan, a former film and theater critic for WNBC-TV in New York; three sons and a daughter from his second marriage, Peter, of Ridgecrest, Calif., Michael, of Boise, Idaho, Karl, of Sonoma, Calif., and Brita Lindstrom of San Diego; and eight grandchildren.