MRI Study of Temperature Dependence of Multi-exponential Transverse Relaxation Times in Tomato

Abstract

The effects of the temperature on the multi-exponential transverse relaxation signal of fruit tissues were studied by MRI at 1.5 T, with tomato as an example of fleshy fruits. The relative importance of chemical exchange mechanisms was investigated by comparing the results obtained from tomatoes with those obtained from aqueous solutions made up to simulate the vacuolar water pool. A more extended analysis of the effects of chemical exchanges on transverse relaxation time distributions was performed using the two-site Carver and Richards’s expression, by fitting the experimental dispersion curves with the theoretical model. At temperatures between 7 and 32 °C, the transverse relaxation signal in tomato pericarp was multi-exponential, indicating that cell membranes acted, at least partially, as barriers to diffusive exchanges of water molecules between cell compartments. Unexpectedly, the transition from two to three peaks in the T₂ distribution occurred between 7 and 15 °C for most of the tomatoes analyzed. Further, the relaxation time of the vacuolar water pool of the tomato pericarp remained mostly stable with temperature, which was contrary to expectations when only chemical exchange mechanisms were taken into account. It was deduced that additional mechanisms compensated for the expected increase in T₂ in the tomato pericarp. The hypotheses were discussed, in which the loss of the water magnetization at the membranes was assumed to be produced either by diffusive exchanges between compartments or by chemical exchanges between protons from water molecules and solid membranes.

Appendix

The effects of chemical exchange between two spin species (a, b) in homogeneous sugar systems can be estimated using the theoretical dispersion curves (variation of relaxation rate with interpulse spacing of the Carr–Purcell–Meiboom–Gill (CPMG) pulse sequence) provided by the Carver and Richard’s equations and corrected by Hills [32, 41]:

• $\frac{1}{{T_{2} }} = - \frac{1}{{{\text{TE}}}}\ln \lambda _{1} ,$

• $\ln \lambda _{1} = - {\text{TE}}\frac{{\alpha _{ + } }}{2} + \ln \left[ {\sqrt {D_{ + } \cdot \cos h^{2} \xi - D_{ - } \cdot \cos ^{2} \eta } + \sqrt {D_{ + } \cdot \sin h^{2} \xi + D_{ - } \cdot \sin ^{2} \eta } } \right],$

  with:

• TE: echo time (time between two 180° RF pulses)

• $\alpha _{ + } = \frac{1}{{T_{{2a}} }} + \frac{1}{{T_{{2b}} }} + k_{a} + k_{b} ,$

• $\alpha _{ - } = \frac{1}{{T_{{2a}} }} - \frac{1}{{T_{{2b}} }} + k_{a} - k_{b} ,$

• $T_{{2a}}$ and $T_{{2b}}$: transverse relaxation times of the water protons and the exchangeable protons of the solute, respectively.

• $\tau _{a}$ and $\tau _{b}$: lifetimes of states a and b, respectively.

• $k_{a} = \frac{1}{{\tau _{a} }}$ and $k_{b} = \frac{1}{{\tau _{b} }}$: exchange rates at sites a and b, respectively $\left( {k_{a} = \frac{{P_{b} }}{{P_{a} }}k_{b} } \right).$

• $P_{a}$ and $P_{b}$: fractions of the total proton population at sites a and b, respectively.

• $\left( {P_{a} = 1 - P_{b} } \right)$ and $P_{b} = \frac{{{\text{number}}\;{\text{of}}\;{\text{exchangeable}}\;{\text{protons}}\;{\text{of}}\;{\text{the}}\;{\text{solute}}}}{{{\text{number}}\;{\text{of}}\;{\text{protons}}\;{\text{exchangeable}}\;{\text{in}}\;{\text{the}}\;{\text{solution}}\left( {{\text{solvent}} + {\text{solute}}} \right)}},$

• $2D_{ + } = 1 + \frac{{\psi + 2\Delta \upomega ^{2} }}{{\sqrt {\left( {\psi ^{2} + \zeta ^{2} } \right)} }},$

• $2D_{ - } = - 1 + \frac{{\psi + 2\Delta \upomega ^{2} }}{{\sqrt {\left( {\psi ^{2} + \zeta ^{2} } \right)} }},$

• $\Delta \upomega = \omega _{b} - \omega _{a}$: chemical shift difference given in units of radial frequency rad s⁻¹.

• $\psi = \alpha _{ - }^{2} - \Delta \upomega ^{2} + 4k_{a} k_{b} ,$

• $\zeta = 2\Delta \upomega \cdot \alpha _{ - } ,$

• $\xi = \left( {\frac{{{\text{TE}}}}{{2\sqrt 2 }}} \right)\left[ {\psi + \left( {\psi ^{2} + \zeta ^{2} } \right)^{{\frac{1}{2}}} } \right]^{{\frac{1}{2}}} ,$

• $\eta = \left( {\frac{{{\text{TE}}}}{{2\sqrt 2 }}} \right)\left[ { - \psi + \left( {\psi ^{2} + \zeta ^{2} } \right)^{{\frac{1}{2}}} } \right]^{{\frac{1}{2}}} .$

  The chemical shift $\Delta \upomega$ is given in units of radial frequency (rad s⁻¹): $\Delta \upomega = 2\pi \times B_{0} \times \updelta \upomega$, where δω is the chemical shift difference between the two sites a and b in ppm.