They're lacking an enzyme needed to break down a chemical in the body. Without that enzyme the chemical accumulates in the brain and is toxic.
When the twins were three-and-a-half months old, their Mom Gabi noticed her son Yoel seemed to be looking through her rather than at her.
Testing revealed a genetic abnormality in both twins.
"I was like in complete shock, you don't expect anything to be wrong," said Ilinietsky.
Children with Canavan Disease often don't live past ten-years-old.
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"They can't do anything on their own, they can't even play. That has to be taught," said Ilinietsky.
The genetic abnormality that causes the disease is most often found in Ashkenazi Jews.
Genetic testing prior to conception would have revealed that Gabi and her husband are both carriers of the gene that causes Canavan Disease, and that each twin had a one in four chance of developing it. Armed with that information, Gabi says she would have chosen in vitro fertilization over natural conception so that the couple's embryos could have been tested before implantation.
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Gabi says Kaiser emailed her about the testing but didn't directly speak with her about it.
Kaiser Permanente sent ABC7 News the following statement:
"Our hearts go out to the Ilinetsky family and we want them to have the support and care they need. We always want what is best for patients, based on their individual needs and evidence of what is effective. Kaiser Permanente provides genetic testing for Canavan disease. We follow recommendations of the American College of Obstetricians and Gynecologists (ACOG) and American College of Medical Genetics (ACMG) and offer Canavan testing to individuals who identify during screening that they are of Ashkenazi Jewish descent."
The Ilinetsky family is sharing their story to encourage everyone to get genetic testing prior to conception.
They also need to raise two million dollars for the twins to participate in experimental gene replacement therapy being pioneered by an East Coast doctor.
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The family has set up a GoFundMe page.
The family has partnered with Chabad of Contra Costa County in order to make donations tax-deductible.
"We are fundraising for research to be translated into the clinical setting with the FDA approval, and at that time of course we'll have patients that will be screened for their enrollment criteria and they'll undergo the procedure," said Dr. Paola Leon who is a Professor of Cell Biology at Rowan University School of Osteopathic Medicine.
In the meantime, the Illinetsky's are hopeful neuromovement therapy will help the twins reach some milestones.
"We'll do whatever it takes," said Ilinetsky.