Measuring the thickness of a tissue can provide valuable clinical information; anatomical structures segmented on medical images can include sub-structures (inclusions) corresponding to a different biological tissue. This article presents a method, based on partial differential equations, to measure the thickness of one specific tissue in this particular configuration. After describing the mathematical formulation of our weighted thickness definition, we show on synthetic geometries in one, and two dimensions that it outputs the expected results. We then present three possible applications of our method on cardiac imaging data: measuring the muscular thickness of a ventricle with fat infiltration; measuring the thickness of an infarct scar; visualising the transmural extent of an infarct scar.