What is Mathematical Modelling?
We keep saying, "Disior software automatically creates mathematical 3D models of tissues visible in medical images." So, what is it and what does it do? Simplified, it is a way to turn something into a virtual model that is made of data points. The points understand where they are, where the neighbour points are, and the laws of nature. This way, they can model things like movement, speed and material behavior.
You get a model that fully represents the reality. It is not an image representation, or a 3D render of reality, but something that is made of data, and has the full data, and it's yours to play with.
Can you give me an example?
In industrial use, mathematical modelling is used in stress and durbility calculations, and to optimize structures. If you want to build a bridge, you need to design it and you need to test it, before you start to build it. How much traffic can it handle? How large a truck can it carry? And what happens to the structures over time? All this can be modelled on your computer.
The same logic applies to modelling tissue. How is a bone fractured? What kind of forces affect the fracture? Is a cast enough to support the fractured system? Or, if it is fixed using plates and screws, what is the optimal setup?
Why should I do it?
Every bone is unique, and so are soft tissue structures. Fracture lines, cavities, tumors, and almost anything, that has a mesurable volume and shape, are unique.
Mathematical modelling allows fast, reliable and reproducible analysis of the key parameters from the area of interest. Since the model measures pre-set reference points, it eliminates both measurement error and manual labor. And, as the software works with data models instead of visual representations, it is not dependent on finding familiar structures. Or on measurer’s accuracy.
And, since it's mathematical modelling, it's not just about measuring things. You can model the system behavior under body movement. The models themselves are created automatically by our software, from your medical images, so there's no engineer or mathematician needed in you clinical routines.
And there's more to the technology!
So far, medical images have been interpreted as images. The original 2D tools were rulers and angle measurers. With 3D, the toolbox grew with surface tracing, volume estimations and shape modelling.
Still, it's reading images and measuring images.
With mathematical modelling, the images become information. You don't need to mark the area or find the boundary - the software does. The data model is a perfect representation of what's in the image, and since it's made by the software, and it is measured by the software, it always happens the same way - resulting in objective and reproducible mesaures.
The variations in sizes and shapes don't matter. The software can't be confused by variations in anatomy. Artificial Intelligence that relies on finding familiar shapes, finds only familiar shapes. And this makes all the difference to the softwares that work with models instead of shapes.