volatility - SKEW and VIX relations?

My question is about the CBOE published index VIX and SKEW.

To start with, I consider working on the variance dynamics. I calibrate the market data (such as VIX and VIX futures) into the Heston model. After that it's not hard to derive the dynamics of VIX.

But how about SKEW, how could I relate the Heston Model to it? Or I shall employ further stochastic models for the higher moments of the underlying log return?