Former Theranos executive Ramesh "Sunny" Balwani will be heading to prison later this month after an appeals court rejected his bid to remain free while he contests his conviction for carrying out a blood-testing hoax with his former boss and lover, Elizabeth Holmes.

The Ninth Circuit Court of Appeals' decision late Thursday refusing Balwani's request to delay the start of his nearly 13-year prison sentence still leaves open the question of when he will have to surrender to authorities.

Jeffrey Coopersmith, one of Balwani's lawyers, proposed that Balwani, 57, report to prison April 20 in a motion filed with U.S. District Judge Edward Davila, who presided over Balwani's trial last year and imposed his sentence in December.

Balwani's proposed April 20 reporting date is a week before Holmes, Theranos' founder and CEO, is scheduled to begin a more than 11-year prison sentence after being convicted on four counts of fraud and conspiracy last year.

Holmes, 39, appeared before Davila last month along with her lawyers in an effort to persuade the judge to allow her to remain free while she pursues her own appeal. Davila hasn't ruled on Holmes' request yet.

Davila last month rejected Balwani's request to remain free while he appeals his conviction on 12 counts of fraud and conspiracy and ordered him to report to prison March 16. Balwani then avoided having to report on that date by appealing Davila's ruling against him.

But three judges on the Ninth Circuit Court of Appeals concluded Balwani hadn't provided enough compelling evidence to convince them that his conviction is likely to be overturned.

The ruling means Balwani will soon be traveling to Southern California to serve his time in a facility near a harbor in San Pedro, California, located about 30 miles (50 kilometers) from downtown Los Angeles. The Terminal Island prison has incarcerated several other prominent figures, including gangster Al Capone in the 1930s, apocalyptic cult leader Charles Manson for an auto theft in the 1950s, and LSD evangelist Timothy Leary in the 1970s.

Although they had separate trials, Holmes and Balwani were accused of essentially the same crimes centered on a ruse touting Theranos' blood-testing system as a revolutionary breakthrough in health care. The claims helped the company become a Silicon Valley sensation that raised nearly $1 billion from investors.

But its technology never came close to working like Holmes and Balwani boasted, resulting in Theranos' scandalous collapse and a criminal case that shined a bright light on Silicon Valley greed and hubris.