AFAIK, the computational model that more closely mimics the human neural networks is Numenta's hierarchical temporal memory (which has not yet received much attention from the machine learning community). In their models, they explicitly model and implement dendrites and other biological concepts.

A computational model that attempts to closely mimic the human neural networks is Numenta's hierarchical temporal memory (which has not yet received much attention from the machine learning community). In their models, they explicitly model and implement dendrites and other biological concepts.