Non-Gaussian Diffusion to investigate bone marrow

Non-gaussian diffusion to investigate bone marrow S. De Santis and S. Capuani Physics Department, University of Rome “La Sapienza”, P.zle A. Moro 2, 00185 Roma, Italy INFM-CNR SOFT, Physics Department, University of Rome “La Sapienza”, P.zle A. Moro 2, 00185 Roma, Italy Enrico Fermi Center Roma, Italy Introduction: Water diffusion in biological systems is often found to deviate from the conventional mono-exponential decay of Stejskal-Tanner equation S(b)=S(0)exp(-bD). As a consequence the behaviour of the signal decay can be interpreted as arising from a non gaussian propagator. As stated by the Continuous Time Random Walk (CTRW) theory, the gaussian approximation fails when the environment in which the spins diffuse is able to trap them, letting the waiting time distribution between two consecutive steps diverge [1]. The solution of the diffusion equation leads to a non linear dependence of the mean squared displacement to the diffusion time ( ) γ t t r ∝ 2 and to a stretched exponential form for the signal decay: S(b)=S(0)exp(-Abγ). By varying the b-value, it is possible