How do I integrate a BSDF into a ray caster.

Question

I'm trying to implement sub surface scattering at isosurfaces and looked up how a BSDF works mathematically.

Implementing the reflective and diffuse part seems to be quite easy as i just have to evaluate phong at the isosurface intersection, but how do you I apply the transmissive part of the BSDF? In what way do i have to modify the ray direction.

Any pointers to a practical implementation are welcome.

Thanks and So long!