6133 A novel approach to give more insides on anomalous diffusion processes: diffusion MR signal at varying of diffusion time versus signal at varying of gradient strength S. Capuani 1,2 , M. Palombo 1 , S. De Santis 1 , and A. Gabrielli 3 1 Physics Department Sapienza University of Rome, Rome, Italy, 2 CNR IPCF UOS Roma, Rome, Italy, 3 CNR ISC, Rome, Italy Introduction: Experimental evidences reported in the last years demonstrate a deviation from the monoexponential decay (S(b)=S(0)exp(-bD), of the PFG (Pulse field gradient) signal as a function of b-value increasing in biological tissues. There are two ways for changing the b-value: i) to modify the gradient strength g, or ii) to modify the diffusion time Δ. Different approaches have been used to investigate anomalous diffusion in heterogeneous systems with the common goal to identify new sources of contrast (different from those offered by conventional diffusion approaches) and obtain new microstructural information from biological tissues [1-6]. Currently, there are two main approaches to assess anomalous diffusion : 1) methods based on the PFG obtained by varying g (as an example the Bennet [1] and Hall [2] approach), and 2) methods obtained by varying Δ (i.e. those introduced by K pf [7] and Özarslan [3]). Approaches 1) and 2) are based on models and concepts that, sometimes, seem to be in contradiction with each other. Specifically, Bennet [1] and Hall[2] approach produces inconsistent procedure when compared to that proposed by Özarslan [3]. We developed and applied a new methodology based on Continuous Time Random Walk (CTRW)[8] to investigate the type of anomalous diffusion information obtenaible using methods based on PFG signal at varying of Δ and/or g. We measured the two temporal and spatial fractional exponents α and μ, respectively based on PFG experiments performed in controlled samples and human tissues with different (expected) diffusional characteristics. On the basis of our experimetal results and physical interpretation of α and μ indeces (as provided by the CTRW theoretical model), we belive that our novel approach may improve the usfulness of anomalous diffusion to investigate biological systems. Morover, our work can explain some apparent inconsistencies in previous methods, and allows a critical revision of previous literature in anomalous diffusion applied to biological tissues. Materials and Methods: styrene beads suspensions (Microbeads AS, Norway) in water at high “sphere packing” characterized by mean diameters of 0.05, 0.3,3.0, 6.0, 10, 15, 20, 30, 40, 80 and 140 micrometers, were used to produce phantoms in which water can probe the micro structural dimensions typically observed in biological tissues. Specifically, eight 10mm capillaries were filled with mono-dispersed beads in de-ionized water and Tween 20 (samples: 0.05µm,0.3 µm, 6µm, 10µm, 15µm, 20µm, 30µm), while three other capillaries were filled with poly-dispersed beads of mixed sizes, to obtain samples at different degrees of disorder. Finally, one sample with free water was also used as control. Two excised tissues of human meningioma characterized by different features and several bone marrow and spongy bone specimens extracted from different calf femur locations were put into a 8mm NMR tube to be investigated. Taking into account the CTRW [8], and considering that the PFG signal decay function is the Fourier Transform (FT) of the motion propagator (MP), to study sub- diffusive processes for which the mean-square displacement (MSD) of diffusing particles grows sub-linearly in time, it is possible to assume the following asymptotic behavior for the FT of the MP: ) exp( ) , ( 2 α α t k K t k W - ∝ when ) /( 1 2 α α t K k << and where k= 1/(2π)gδϒ and 0<α<1. (1) Conversely, to study super-diffusive processes characterized by a divergence of the jump length variance, it is possible to use the following function: ) exp( ) , ( t k K t k W μ μ - ∝ where 0<μ<2. (2) When a competition between subdiffusive and superdiffusive processes occurs, it is possible to introduce a pseudo-MSD as follows: μ α / 2 t MSD ∝ for which 2α/μ grater or smaller than 1 defines superdiffusion and subdiffusion processes respectively. All measurements were performed on a Bruker 9.4T Avance system, operating with a micro-imaging probe (10 mm internal diameter bore) and equipped with a gradient unit characterized by a maximum gradient strength of 1200 mT/m, and a rise time of 100 μs. A spectroscopic PGSTE with δ=4.4ms, g=0.10T/m (i.e. k=22481m -1 ) TR=2.5s and 48 values of Δ in the range (0.020-1.0s) was used for collecting data to fit with equation (1) and for extracting the α value. Vice-versa, a spectroscopic PGSTE with Δ/δ=80/4.4ms, TR=2.5s and 48 gradient amplitude steps g from 0.026 to 1.02T/m was used to collect data fitting with the function (2), to obtain a measure of the μ value. Results: α and μ values measured along x axis, for all eleven samples investigated, are displayed in Fig.1. As expected, μ and α of free water are equal to 2 and 1 respectively, defining Brownian motion. μ increases as beads sizes decrease. Conversely α does not depend on beads sizes. Finally, α decreases as the degree of the disorder increases, while μ does not discriminate between ordered (black points in Fig. 1) and disordered (red points in Fig. 1) samples. μ versus γ graph, where γ is the stretching exponential parameter introduced by the stretching exponential model of anomalous diffusion [1,2] is displayed in Fig.2. This result demonstrates that μ=2γ, as expected from the theory[8]. Results obtained in excised tissues demonstrate that anomalous diffusion indices α and μ reflect some additional microstructural information which cannot be obtained using conventional diffusion methods based on Gaussian diffusion. Discussion and Conclusion: Experimental data illustrated in Fig. 1, demonstrate that anomalous diffusion indices α and μ reflect some additional microstructural information which cannot be obtained using conventional diffusion procedures based on Gaussian diffusion. α, which is obtained using PFG signal at varying of time Δ, can provide information on the degree of disorder within the investigated systems. Indeed, the monodispersed samples constituted by an ordered distribution of equal size beads, are characterized by an equal value of α. Conversely, the disordered samples including beads with different sizes are characterized by lower values of α. μ values, which are obtained using PFG signal at varying of g, show an exquisite sensitivity to discriminate the pore sizes due to packing beads in which water diffuses. Moreover, as demonstrated in Fig. 2, the μ parameter is equal to the γ parameter extracted by Bennet [1] and Hall[2], and is also equal to the β anomalous diffusion parameter introduced by Magin [4,5]. Conversely approaches as those used by K pf [7] and Özarslan [3] investigate subdiffusion processes, thus measuring α parameter or some its derivations[3]. References: : [1] Bennet KM et al. MRM 2006;56:235-240. [2] Hall MG and Barrick TR.. MRM 2008; 59: 447-455. [3] Özarslan E et al. JMR 2006;183:315- 323. [4] Magin RL et al. JMR 2008;190:255-270. [5] Zhou, XJ et al. MRM 2010;63:562-569. [6] De Santis et al. MRM 2010 in press. [7] K pf M et al. Biophys J 1996;70:2950-2958. [8] Metzler R, Klafter J. Phys Rep 2000;339:1-77. Fig.1 α vs μ graph for ordered samples including monodispersed beads in water (black symbols) and for disordered samples (red symbols). Blue star indicates the control sample with free water. Dashed line represents the Brownian (or Gaussian) diffusion region. Fig.1 Fig. 2 μ vs γ graph for samples of monodispersed microbeads in water of different sizes.