Dynamical systems, chaotic attractors and fractal dimension are mathematical concepts that have been intensively applied in much area of biomedical sciences. Recent studies on chaotic dynamics from Neuro-science and epidemiology lead to the existence of chaotic attractors and the question arises on their finite fractal dimensionality. Fractal dimensionality is accepted as a measure of complexity for systems that cannot be described by integer dimensions. A new idea, detailed in is presented in this review article that allows us to bind from above the fractal dimension of some chaotic attractors.