An apricot kernel is a single seed found inside the stone of an apricot. Billed as a new “superfood,” some people believe that apricot kernels have cancer-fighting and detox-enhancing properties.

Twice, Jason Vale was diagnosed with cancers that should have killed him. But 30 years after the first tumor was found in his chest when he was 18, Vale is still alive. The reason for his survival is ...