John G. Griffiths

Image guided orthopaedic surgery design and analysis

Within the next few years it is envisaged that a number of computer assisted surgery products will become available. For many surgical procedures, outcome of surgery,, will rely on the accuracy and repeatability with which a computer assisted surgical toolperforms its task. This paper presents a Computer Assisted Orthopaedic System (CAOS) which takes an image guided approach to planning and implementing a trajectory, to assist an orthopaedic surgeon. Accurate delivery of this trajectory is achieved via an intelligent guide. This paper details the design issues and identifies the registration and calibration techniques used by the CAOS intelligent guide. The paper also enumerates, and where possible quantifies, thefactors that influence the accuracy performance of the system. Accuracy trees are used to show the root source of inaccuracies and how they propagate and combine in a system.

Toolpath based on Hilbert's curve

Abstract An algorithm for generating a toolpath for a milling machine is described. The approach to its design was interdisciplinary. The algorithm contains ideas from computer graphics and mathematics, rather than mechanical engineering alone. An artefact described by any set of curved surfaces is carved out of a workpiece in two stages. Horizontal slices are removed to reveal the roughly cut artefact, and a final pass cuts the artefact to within a preset tolerance. The toolpath might seem to be needlessly convoluted, but it has substantial advantages over less sophisticated paths. Its local complexity adapts automatically to the local complexity of the artefact, so that more attention is concentrated on those parts of the artefact which require it. At the roughing out stage, the path efficiently skips over completely worked areas without retracing them with each new horizontal slice. The path minimizes the amount of tool movement which does not cut material, and minimizes the number of occassions on which the tool reenters the material. A prototype system has been developed to demonstrate that the new approach is viable.

Table-driven algorithms for generating space-filling curves

Abstract A simple general method for constructing space-filling curves is presented, based on the use of tables. It is shown how the use of Hilberts curve can enhance the performance of Warnocks algorithm. A procedure is given which generates Hilbert curves or Sierpinski curves. A second procedure is given which generates Warnocks windows in Hilbert order.

A new cutter-path topology for milling machines

Abstract Cutter-path topology is critical to the efficiency and applicability of the milling process. The paper introduces a new cutter-path form that incorporates elements of currently used topologies, and demonstrates its efficiency and applicability to the milling of general free-form shapes using a ball-nosed cutting tool.

Implicit Fitting Using Radial Basis Functions with Ellipsoid Constraint

Implicit planar curve and surface fitting to a set of scattered points plays an important role in solving a wide variety of problems occurring in computer graphics modelling, computer graphics animation, and computer assisted surgery. The fitted implicit surfaces can be either algebraic or non‐algebraic. The main problem with most algebraic surface fitting algorithms is that the surface fitted to a given data set is often unbounded, multiple sheeted, and disconnected when a high degree polynomial is used, whereas a low degree polynomial is too simple to represent general shapes. Recently, there has been increasing interest in non‐algebraic implicit surface fitting. In these techniques, one popular way of representing an implicit surface has been the use of radial basis functions. This type of implicit surface can represent various shapes to a high level of accuracy. In this paper, we present an implicit surface fitting algorithm using radial basis functions with an ellipsoid constraint. This method does not need to build interior and exterior layers for the given data set or to use information on surface normal but still can fit the data accurately. Furthermore, the fitted shape can still capture the main features of the object when the data sets are extremely sparse. The algorithm involves solving a simple general eigen‐system and a computation of the inverse or psedo‐inverse of a matrix, which is straightforward to implement.

Constructive implicit fitting

In this paper, we present a constructive method for fitting both an explicit and an implicit curve or surface to a set of scattered points by using gate functions. With this technique, the data are first partitioned with geometric primitives into small data sets such that each sub-data set can be well fitted by a simple algebraic or non-algebraic shape. These simple shapes are then blended to form an overall fitting for the given data. Compared with some conventional fitting techniques, the proposed method has the following distinct features. First of all, a preset accuracy can always be achieved if the data set is sufficiently finely partitioned. Secondly, a large data set can be dealt with as several small data sets, which can significantly reduce the complexity of the shape to be fitted. Thirdly, the proposed fitting technique can also be used to increase the fitting speed by using simple fitting techniques for each sub-data set. Fourthly, the degree of smoothness of the fitted function can be adjusted to be as smooth as one wishes. Furthermore, the fitting technique provides direct support for parallel computation in curve and surface fitting. When a large data set is partitioned into smaller data sets, these small data sets can then be fitted simultaneously over a parallel system. This will greatly reduce computation time.

A depth-coherence scanline algorithm for displaying curved surfaces

Abstract A scanline algorithm is presented which generates a realistic picture of a solid object bounded by curved surfaces. Externally, a surface is described by parametric equations. The internal representation is comprised of meshes of cubic splines which may be subdivided. Memory is saved by delaying subdivision, and by using a novel garbage collection technique. Time is saved by exploiting depth coherence. A viewpoint and scanline fix a cross-section represented as a set of curves. There are usually only a few of these to compare, and the curve nearest the viewer often remains nearest over much of its length.

Recovery of distal hole axis in intramedullary nail trajectory planning

In intramedullary nail (IMN) surgical operations, one of the main efforts for surgeons is to find the axes of two distal holes. Two distal holes on an intramedullary nail, which are inside the intramedullary canal of a patients femur, can only be seen in a lateral X-ray view. For the standard surgical procedure, the localisation of the distal hole axes is a trial-and-error process which results in a long surgical time and large dose of X-ray exposure. In this paper, an algorithm to derive the 3D position and orientation of the distal hole axis was developed. The algorithm first derives the nail axis through two X-ray images. Then the distal hole axis is calculated through projecting back the hole boundary on the X-ray image from a lateral view to the 3D space. A least squares method is used to determine the centres of the front hole and the back hole through iteration. The algorithm has been tested with real data and it was accurate and robust.

End user issues for computer assisted surgical systems

Orthopaedic implants are manufactured to the highest degree of precision by some of the most precise machines known to man and inserted into patients by some of the most imprecise methods known. Computer assisted systems aim to overcome this dichotomy by improving the planning and implementation of orthopaedic surgery. This can be achieved by providing the surgeon with better information for planning and a more precise means of implementing the surgery. This surgical advancement will change current orthopaedic practice significantly if the appropriate surgical issues are considered during their development. Safety is obviously paramount and is being addressed, as is registration between the real (patient) and the virtual computer world. The more subtle, but nevertheless important, surgical issues have as yet not been fully identified or addressed satisfactorily. The following questions serve to highlight them. Is there an optimal system size, shape, reach, control and positioning in surgery? What are the salient environmental and functional requirements ? Can there be intra-operative computer processing time? How important and what does timelessness, universality, communality and simplicity of the system mean? Should there be a relationship between training, surgical feedback and simplicity? What is partial or total sterilisation ? Can capital outlay and running costs for the system be reduced or avoided by the hospitals? Are computer assisted orthopaedic surgical systems cost effective, necessary, desirable or indeed indicated in current cost containment in the NHS? The above questions are answered in this paper and points which are conducive to a positive response from the end user (surgeons, and hospital management) are discussed.

Removal of hidden lines by recursive subdivision

Abstract A new hidden-line algorithm is proposed for illustrating objects whose faces are plane or nearly plane polygons. The algorithm shows how the number of comparisons between edges and edges, and between faces and segments can be reduced by recursively subdividing the picture before analysing it. The algorithm overcomes some of the shortcomings of purely sorting strategies and it is particularly intended for illustrating complex objects. Illustrations are provided as examples.