Page 68 - Cellular Imaging in Regenerative Medicine, Cancer and Osteoarthritis
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                                Chapter 3
LMD=f.M= v.NL . n.μ = μ . n.NL.m0 =μ .cFe (2) V v m0 V m0
where v is the cell volume, n is the number of SPIOs in a cell, m is the magnetic moment of an SPIO, m0 is the mass of iron per SPIO particle and cFe is the iron concentration in the sample. Any spatial rearrangement of SPIO leaves the iron concentration constant, and also 'R2' if SD is valid.
The difference between cell dilution and cell division sample at a given SPIO concentration (Fig. 4) can be viewed as a simple rearrangement of SPIOs in labeled cells: in the cell dilution samples the SPIOs are concentrated in fewer cells. Also the ‘High’ labeled sample has fewer cells with higher load compared with the ‘Low’ labeled sample at an equal amount of SPIO particles (Fig. 6a). These rearrangements of labeling particles lead to different R2' values and r2' relaxivities. SD theory fails to describe this behavior. The following explains this result: SD increasingly underestimates R2' at higher volume fractions of labeled cells (16,20,29). A rough estimate of the volume fraction range of the magnetic disturbers is 0.3–5% in our cell suspension samples. With the assumption of even distribution of SPIOs to daughter cells, the cell division samples represent a higher volume fraction of magnetic disturbers (here: labeled cells) compared with cell dilution samples; therefore the elevation of R2' values from SD prediction is higher. Similar to this, the ‘Low’ labeled samples have higher volume fractions compared with ‘High’ labeled samples at the same SPIO content, resulting in higher elevation of R2' values.
The SPIO and cell dilution samples exhibit minor deviation from the linear relaxivity–concentration curve (Fig. 3): the relaxivities decrease at lower concentrations. Also, an extrapolation to lower concentration from the data points leads to negative relaxation rates at zero iron concentration. Based on our results and the SD theory, one can predict that the different samples exhibit the same relaxivity when dilute; this relaxivity value is described by the SD theory. With increasing concentrations (as the theoretical prediction underestimates the relaxivity values), the relaxation rates of the samples deviate from the mutual, theoretically predicted value and exhibit higher relaxivity. As our results demonstrate, this relaxivity is dependent on spatial distribution of SPIOs.
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