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If the noise effect can not be neglected, we can further get the diffusion approximation beyond Eq. 3 (see Additional file 1 for details).
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Using the Eq. (37), we get the self-diffusion coefficient D. Using the obtained value of D in the equation to have a new value of (varLambda), and by solving the cubic equation, we get the velocity auto-correlation function D t).
In summary, IVIM MR imaging could get the perfusion and diffusion information of gliomas simultaneously and might enable a noninvasive method in differentiating grade LGG from HGG gliomas.
It is not easy to calculate directly the diffusion coefficient with photobleaching tools, however, we can promptly get the absolute value of diffusion coefficient with FCS instrument.
After these processes, using DTIFit within the FMRIB's diffusion toolbox, the images were calculated to get the FA, λ1 (longitudinal diffusivity) (the magnitude of diffusion along the principal diffusion direction) and λ23 (radial diffusivity) (the magnitude of diffusion in the two orthogonal directions perpendicular to the principal diffusion direction) maps.
While the image shown in (d) is the image we will ultimately get if we let the diffusion go on for a long enough diffusion time.
To get the rapid vertical molecular diffusion, the vertical difference procedure uses implicit numerical method.
With this map we solve numerically the diffusion equation to get the Green functions G s d, k B (t ).
This supported that the cell entrapped in CA matrices did not substantially get the limitation of the substrate diffusion resulting in high glucose removal as described in earlier section.
Despite this, one can still get the ratio of the spin diffusion coefficient to the mobility of the photoinduced spin-polarized carriers by fitting the experiment data using Eq. 1. Fig. 3 ACPGE and AHE currents corresponding to the extreme points as a function of wavelength, respectively.
Thirty cases have been simulated to get the accurate average value of diffusion coefficients.
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