A mathematical model to foresee diabetic retinopathy progression
Cristina G. Pedraz/DICYT Diabetic retinopathy is a chronic condition linked to diabetes. It refers to the most prevalent vascular disease occurring in the retina and is classified into two types: non-proliferative diabetic retinopathy (it develops first and is characterized by enlarged blood vessels in certain areas) and proliferative diabetic retinopathy (the most severe and advanced type producing new fragile and breakable blood vessels). Development and progression of diabetic retinopathy, a leading cause of blindness worldwide, are related to changes in blood sugar control.
Hyperglycemia (high blood sugar) produces retinal and blood vessel injuries. These injuries are worse and occur frequently in patients with diabetes. Proliferative diabetic retinopathy “may cause blindness during a short period of time”, while in non-proliferative diabetic retinopathy “vision can be maintained through appropriate monitoring, and even is vision is lost, it does not mean an important problem”, as we were told by Javier Finat, responsible for the Grupo MoBiVAP (Universidad de Valladolid, Spain), working on the pathology’s mathematical modeling and that has recently presented this study in one of the research seminars by the Instituto de Oftalmología Aplicada (IOBA), an institute for applied ophthalmology.
“We are working on retinopathy spreading and monitoring modeling using biomedical images. We determine vascular structure of arteries and veins in the retina, and, from this structure, we try to figure information out regarding prone to risk areas.”, he explains to DiCYT.
These prone to risk areas refer to vessels that may get ruptured and cause minor bleeding and microaneurysms (dilation of capillaries that may get ruptured easily). Additionally, they are trying to obtain information “regarding an important common phenomenon that doctors call neovascularization (one of these capillaries gets ruptured and the body produces new capillaries that are very fragile and high blood pressure gets them ruptured”. When a massive rupture occurs, as Finat states, “vision may be lost”.
Why does this happen? Diabetic patients develop pressure variable models that also have an impact on the eye. “Some vessels constrict and, when blood arrives with the same pressure, they get ruptured in the weakest areas.” Nevertheless, “if a prior diagnosis is performed, we are able to foresee its evolution and, from this moment on, we tackle the most sensitive areas”.
Confocal Microscopy Images
To carry out the mathematical modeling of the disease, researchers from the Universidad de Valladolid are using confocal microscopy images (an imaging technique “that enables the reconstruction of three-dimensional structures allowing us to reach the back of the eye”).
The first study on this regard was developed 10 years ago with the participation of researcher Eduardo Cuesta. “We performed an intelligent operation: while an image analysis is carried out, it determines continuity and discontinuity areas (in this case in blood vessels) and, depending on discontinuity, it changes its execution. Consequently, this mathematical operator changes its behavior every time, it is an almost biological operator that changes depending on difficulties encountered.”, he explains.
These propagation models, he adds, are inhomogeneous diffusion models, what in mathematics is called “anisotropic diffusion”, because “they do not behave the same way in all directions. When they encounter elements that from imaging point of view are considered discontinuities, in this case in blood vessels, propagation happens differently and that is why it is called anisotropic (behavior is not homogeneous throughout the space, that is, it is not isotropic)”.
This is a pioneering propagation method in scientific literature developed by Grupo MoBiVAP that is currently being upgraded for making videos and 3D images, and eventually, for 3D videos; the researchers states. “We are proving a small part of the potential of these models for biomedical applications.”, he explains.
Restoration of a Real-Time 3D Video
The major objective is to eventually perform a restoration of a real-time 3D video from these models. According to Javier Final, “when you are to restore a video, you often find blanks you have to fill in, otherwise, blots appear on the screen; these models may be useful in this regard”. Moreover, “when you perform a 3D documentation of an object, there is always some part missing and, with an intelligent propagation mechanism, you may fix both videos and volumes”, he emphasizes.
Therefore, the chief aim is to merge videos and 3D images. “We have to take into account that a normal video contains 20 frames per second, a high-definition video has 30 frames per second and a 3D video, more than 50 frames per second and channels are mixed. Nowadays we need to wear glasses for 3D TV and we have to do without them; we need to figure out how to merge both elements, video and 3D images, so we need the restoration of real-time 3D videos.” Nevertheless, he adds, “solutions in this regard will come up in around three years”.
Diabetic retinopathy is the second leading cause of vision loss in Spain; it is the blindness leading cause at working age affecting about 50% of diabetics. It is a growing problem: it is expected that the diabetic population will double in the next 15 years. Retinopathy is directly linked to the diabetes course time. Figures show that, after 20 years of disease, all diabetes type 1 patients and 80% of diabetes type 2 patients develop retinopathy, but, early diagnosis and an appropriate treatment would prevent 90% of cases of vision loss.