Spanish is a idiom that have a lot of synonyms so you can use se (propagó/difundió/diseminó/extendió/esparció) all these will be well with you phrase.
El veneno se (propagó/difundió/diseminó/extendió/esparció) por todo su cuerpo
Maybe you are thinking why use se before the verb (se extendió). This word in this case is a reflexive pronoun This meaning that the word suggest the action is do itself.