I can think of a few ideas, you may need to experiment with these to find what works..
Once the network is trained on general data, you may try fine-tuning the network using the specific patient's data alone. This involves retraining the existing network on the patient's data, but using options that minimize how much the weights change. You may try to reduce the number of training iterations or the gradient step-size used or both.
The aim is to produce a network whose weights derive mostly from non-specific data, but has been customized particularly to be good at the select patient's data.
Alternatively, you could try the sample weighting technique. This involves giving additional weightage to some examples over others for calculating the loss function during training. There are many things you could try for this, such as modifying the architecture or writing a custom training script. The easiest way I can think of is to duplicate the patient's example multiple times in the training data itself and then train the network as normal. I would be cautious though, to avoid overfitting in the network.
Hope it helps!