At first glance the two don’t have much in common. Peter Arbenz, Professor of Computer Science at the Institute for Computational Science, solves a linear equation system with 1.2 billion unknowns using the supercomputer at the CSCS (Swiss National Supercomputing Centre) in Manno. Ralph Müller, Professor at the Institute for Biomechanics, is researching bone atrophy, osteoporosis, using computer-assisted tomography. (1),(2) But what brings the two partners, dissimilar at first glance, together in a project?

Interesting calculation, important application

„“There are two sides to the project,” says Arbenz. For him, the computer scientist, it is an “interesting calculation”, while for the bone researcher Ralph Müller it is an “important application” in the context of osteoporosis. The sums add up for both of them. Müller’s laboratory produces high-resolution computer tomography images of bones that depict, among other things, the fine trabecular structures. (3) From these it is possible to deduce how far the bone mass has already decreased because of osteoporosis. However, in a second step the biomedical scientists also want to find out how strong the bones are and the maximum load under which they break. The computer scientist Peter Arbenz calculates these values. High-resolution CAT (computer tomography) images are the raw materials for such calculations.

Bone structure converted into voxels

The three-dimensional images of the bone structures are converted in the computer into millions of identical cubes known as voxels. Each voxel has eight corners than can each be displaced in three directions. The displacements occur when pressure is applied to the bone in the simulation. Using the displacements at the corners of the voxels it is possible to calculate in the computer the stresses arising in a bone. However, this leads to a system of linear equations with more than a billion unknowns. The Professor of Computer Science recently succeeded in solving a gigantic system of this kind on the supercomputer at the CSCS in a usable period of time, i.e. in less than ten computing minutes – a world first in osteoporosis research. The keys to success are a suitable simplification of the equation, a good algorithm and a clever pre-conditioner. In addition the data must be arranged skilfully for the parallel computation so the PC needs to exchange as little information as possible. However, the power and above all the memory capacity of 1000 PCs are still necessary to enable this kind of equation system to be solved.

If Arbenz had allowed the complete system matrix to be calculated, this would have needed eight exabytes (ten to the power 18 bytes) of memory, which corresponds approximately to the memory capacity of one billion PCs.

Thousands upon thousands of cubes represent a section from a bone and show the loading by a colour code. (Photo: P. Arbenz / Institute for Computational Science) large

A quantum leap in osteoporosis research

The novel computing method takes the biomechanical engineer Ralph Müller a big step forwards. He says “This has given us a new measure of the strength of bone.” For large bone systems it was previously necessary to perform experimental mechanical tests to reach results of this kind. It was impossible to carry out these tests on patients. The aim is to use the new method in everyday medical work. The idea is that a doctor can make images by using a CAT scan in his surgery, can calculate these on his computer and can discuss them with the patient. As a result the doctor would be able to calculate various scenarios, for example how heavy a shopping bag can be without breaking a patient’s wrist. However, Müller says the calculations could also be used to reveal the progress of treatments.

The two researchers have not yet reached this stage. Even if a supercomputer could come up with the data within a usable period of time, hardly any doctor or hospital has access to such computing power. Arbenz says that “Patients would have to wait much too long for the result of the calculations.” Therefore the aim must be to improve the program to such an extent that it needs even less memory capacity. Arbenz is confident that this will also be successful: “Nevertheless the new approach with its 1000-fold reduction is a quantum leap for Ralph Müller’s group. It opens up a new world of analysis.” The intention in the future is to improve the program to such an extent that it needs even less memory capacity and the data can be processed directly in the doctor’s surgery. Arbenz is confident that this will be successful as well.

Data sets become even bigger

The challenge remains. For example today the biomechanical engineers image only the first centimetre of the forearm. “That is not enough to calculate the strength of the bone,” says Müller. He has in mind imaging about five centimetres of the forearm in a CAT scan and calculating the bone strength with a data set of this kind. The equation will become correspondingly larger as a result. Solving these would probably need several Mannos – or an even better computing method from Peter Arbenz.