  Purpose: In surgical navigation, pre-operative organ models are presented to
surgeons during the intervention to help them in efficiently finding their
target. In the case of soft tissue, these models need to be deformed and
adapted to the current situation by using intra-operative sensor data. A
promising method to realize this are real-time capable biomechanical models.
  Methods: We train a fully convolutional neural network to estimate a
displacement field of all points inside an organ when given only the
displacement of a part of the organ's surface. The network trains on entirely
synthetic data of random organ-like meshes, which allows us to generate much
more data than is otherwise available. The input and output data is discretized
into a regular grid, allowing us to fully utilize the capabilities of
convolutional operators and to train and infer in a highly parallelized manner.
  Results: The system is evaluated on in-silico liver models, phantom liver
data and human in-vivo breathing data. We test the performance with varying
material parameters, organ shapes and amount of visible surface. Even though
the network is only trained on synthetic data, it adapts well to the various
cases and gives a good estimation of the internal organ displacement. The
inference runs at over 50 frames per second.
  Conclusions: We present a novel method for training a data-driven, real-time
capable deformation model. The accuracy is comparable to other registration
methods, it adapts very well to previously unseen organs and does not need to
be re-trained for every patient. The high inferring speed makes this method
useful for many applications such as surgical navigation and real-time
simulation.
