Modelling and numerics for keyhole surgery simulations
Reference no.: PJD1
Supervisor: Dr Penny Davies
Date advertised: 6th February 2007
Please contact Dr Penny Davies for further information.
Laparoscopic or "keyhole" surgery is becoming increasingly popular because it is both beneficial to patients and cost-effective. It differs from conventional surgery in that the surgeon cannot see the tissue being operated on directly but instead views its image on a high quality video monitor.
The surgical instruments are inserted into the patient via tubes through small wounds, and are necessarily both slender (5mm) and long (30cm). The main additional difficulties in this type of surgery are that the surgeon operates from a two dimensional image with a limited field of view and has much less tactile feedback.
The surgical techniques needed to perform this type of operation are obviously very different from those needed for conventional surgery, and it is essential that keyhole surgeons are properly trained.
There is growing interest in the potential for computer simulations to enhance training, in a similar way that flight simulators are used by pilots.
My interests in this field are to develop good mathematical models to capture the mechanical properties of intestinal tissues, and to develop new numerical algorithms for solving the resultant complicated system of PDEs.
The modelling has to be done very carefully to provide realistic results and it is essential that the models are based on sensible physical assumptions and clinical measurements.
Nonlinear elasticity seems to provide a good framework for modelling, and gives a good fit to data for spleen tissue.
The aim is to try to improve the modelling by adding in other physically realistic behaviour.
Once a good mathematical model has been derived and verified, the object is to use it to compute the tissue's behaviour when it is indented with surgical probes.
This involves solving a complicated system of partial differential equations numerically (there aren't "exact" solutions in general). The aim here is to develop efficient numerical methods.