How is the "grid of patches" different from one more level of convolution?
For example, a conditional random field could express "either these patches both contain a tumor or none of them does" (which is helpful when there's something suspicious on the patch boundary) and the consequences of committing to either possibility can propagate over the whole field. In contrast, a convolutional layer would have to make the decision independently for each local area.
That approach has the advantage that you'll learn about techniques roughly proportional to their current popularity, but it has the disadvantage that explanations in papers tend to be brief and you have to put them into a coherent whole yourself.
If you prefer textbooks, I heard about http://www.deeplearningbook.org/ but didn't get around to reading it. In addition to neural networks, you'll probably also want to read about classical statistics and probability theory, since that's the origin of concepts like conditional random fields, which can be mixed with neural networks but are unlikely to be covered by literature on deep learning.