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A mathematical description of the changes of quantitative MPM parameters in ex-vivo whole brain human brains during fixation and hydration
Francisco J Fritz1, Tobias Streubel1, Herbert Mushumba2, Klaus Püschel2, and Siawoosh Mohammadi1,3,4
1Institut für Systemischeneurowissenschaften, Universitätsklinikum Hamburg-Eppendorf, Hamburg, Germany, 2Rechtsmedizin, Universitätsklinikum Hamburg-Eppendorf, Hamburg, Germany, 3Department of Neurophysics, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany, 4Max Planck Research Group MR Physics, Max Planck Institute for Human Development, Berlin, Germany

Synopsis

Keywords: Multi-Contrast, Modelling, Fixation, Postmortem whole human brain, Hydration

Motivation: Relaxation rates in the in-vivo human brain are strongly different to their counterparts in formalin-fixed postmortem tissue.

Goal(s): To model the changes of the relaxation rate parameters for different tissue stages from in-vivo to ex-vivo: unfixed, during fixation and during hydration.

Approach: The multi-parameter mapping (MPM) protocol was used to measure the changes of five whole-human brains across the aforementioned tissue stages, and different saturation models were tested to describe relaxation parameter changes during fixation.

Results: The MPM parameters varied strongly per tissue stage, and a mathematical description of the change of the MPM during fixation was found.

Impact: We characterised the MPM parameters during the fixation and hydration process across the entire brain and propose a mathematical model to describe the changes. This information could facilitate translating microstructure-mapping methods from fixed ex-vivo tissue samples to in-vivo application

Introduction

Quantitative Magnetic Resonance Imaging (qMRI) provides indirect proxies for tissue microstructure like myelin and iron content. Multi-parameter mapping (MPM7) is a useful qMRI method, yielding in particular the following three qMRI parameters: longitudinal (R1) and effective relaxation rates (R2*) and magnetic transfer saturation (MTsat). One approach to directly estimate iron and myelin content from qMRI is to linearly map histology data and R1 and R2* relaxometry from MRI on the same formalin-fixed post-mortem tissue voxelwise1,2,3. However, this mapping doesn't apply to in-vivo MPM parameters due to various factors affecting the tissue state like excision, paraformaldehyde (PFA) fixation and hydration4,5,6. This study aims at quantifying the changes in MPM parameters from in-vivo measurements to postmortem measurements in whole human brains, covering in-situ measurements, fixation, and hydration. Additionally, we tested different saturation models to describe the MPM parameters changes during fixation.

Methods

Table 1A details the information about the in-vivo cohort and postmortem specimens, while Table 1B details the MR data acquisition and preprocessing. Two analysis were performed across the white matter, cortical and deep gray matter. These regions are referred hereafter as tissue classes (Figure 1B).

Comparison of the different tissue conditions: we estimated the mean values of the MPM parameters for each tissue class (Figure 1B) acquired at five distinct tissue stages: in-vivo, in-situ, fixed at a common time (i.e., 93-95 days in fixative, c-PFA) and last measured time point (i.e., 93-620 days, l-PFA) across specimens, and following hydration (i.e., > 2 weeks in PBS). The difference of the mean values between consecutive tissue stages was also estimated.

Fixative modelling: the temporal evolution of the median estimated MPM parameters were modelled using two saturation models within all tissue classes across all ex-vivo brain specimens. The first saturation model (M1) postulates that the changes in relaxation rates between the unfixed tissue ($$$R_{t0}$$$) and fixed tissue can be expressed through an exponential saturation process, resulting in the following model:
$$M1=R_{t0}+\Delta R_s(1-exp(-t/\tau_s))$$
where $$$\Delta R_s$$$ is the saturation change [1/seconds] and $$$\tau_s$$$ is the saturation time [days]. The second saturation model (M2) proposes that the fixation process in the tissue unfolds in two stages instead12. That model is:
$$M1=R_{t0}+\Delta R_s(1-exp(-t/\tau_s))+\Delta R_l(1-exp(-t/\tau_l))$$
where $$$\Delta R_s$$$ and $$$\Delta R_l$$$ are the short and long saturation changes [1/seconds], and $$$\tau_s$$$ and $$$\tau_l$$$ are the short and long saturation times [days], respectively. To evaluate which model best describes the temporal changes in MPM parameters due to fixation, we calculated the Bayesian Information Criterion (BIC13) per tissue class.

Results

Figure 2 compares MPM parameters across different tissue stages and classes. It also shows the percentual difference between tissue stages. From in-vivo to in-situ condition, R2* and MTsat varies strongly for each tissue class. During fixation, R1 increases the most (>200%), followed by R2* (~45%) and MTsat (~15%). Over longer times (l-PFA), R1 continues increasing while R2* and MTsat remain stable. During hydration, R2* decreases (<25%) while R1 slightly increases and MTsat remains constant.

Figure 3 shows the temporal evolution of each MPM parameter per specimen and tissue classes. Furthermore, the figure depicts the curve representing the winning model for each tissue class and MPM parameter (black curves) based on the BIC values (Table 2A). The fitted values of the winning model are listed in Table 2B.

All winning models captured the temporal evolution of the MPM parameters due to fixation, particularly M1 for R1 and M2 for R2*. However, the temporal evolution exhibited greater variability between brain specimens for R2* in dGM and MTsat in WM, making it challenging to describe these temporal changes with one single model. None of the proposed model was capable of describing the initial 10-15 days overshoot of MTsat values during fixation, which was particularly pronounced in white matter (bottom, right subplot).

Discussion and conclusion

Our study confirmed changes in relaxation rates during fixation4,5,6,8 and hydration. Moreover, we found mathematical models describing the MPM parameter changes during fixation. This model allows relating MPM parameters at different fixation times and after hydration to their in-vivo counterparts. Two important limitations are (1) the model describe fixation effects in 4% PFA and may not be applicable to other fixatives, (2) using the same in-vivo MPM protocol for ex-vivo samples may introduce parameter estimation bias. In summary, our model bridges the gap between in-vivo and fixed ex-vivo MRI, enabling potential in-vivo applications of MRI-based microstructure mapping derived from fixed ex-vivo samples like estimating iron and myelin from relaxometry parameters2,3.

Acknowledgements

This work was supported by the German Research Foundation (DFG Priority Program 2041 "Computational Connectomics”, [MO 2397/5-1; MO 2249/3–1; KI 13372-2; WE 5046/4-2; MO 2397/5-2; MO 2249/3], by the Emmy Noether Stipend: MO 2397/4-1 and MO 2397/4-2) and by the BMBF (01EW1711A and B) in the framework of ERA-NET NEURON and the Forschungszentrums Medizintechnik Hamburg (fmthh; grant 01fmthh2017). The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n° 616905.

References

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[9] Emmenegger, T.M., David, G., Ashtarayeh, M., Fritz, F.J., Ellerbrock, I., Helms, G., Balteau, E., Freund, P., Mohammadi, S., 2021. The Influence of Radio-Frequency Transmit Field Inhomogeneities on the Accuracy of G-ratio Weighted Imaging. Frontiers in Neuroscience 15, 770. https://doi.org/10.3389/fnins.2021.674719

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Figures

Table 1: Summary tables for the specimens used (A), acquisition and analysis (B) of the multiparametric mapping (MPM7) measurements. Echo times (TE) in (B) describes: first echo:echo steps:final echo. TR: repetition time and FA: flip angle.

Figure 1: (A) Illustration of the image coregistration pipeline for one brain specimen with the MTsat images depicting the different steps. In-situ measurement is not affected by steps B and C (except for threshold) since this brain was used as reference for both manual and automatic registrations. (B) Illustration of the regions of interest (ROIs) used for analysis. (A) Brain tissue classes covered the cortical (red) and deep (green) gray matter, and white matter (yellow).

Figure 2: Comparison of the three MPM parameters (R1, R2*, and MTsat) for four tissue stages: in-vivo, in-situ (unfixed postmortem), fixed in a common time point (93 to 95 days, c-PFA) and the last measurement before hydration (up to 600 days, l-PFA), and hydrated (PBS). This comparison was assessed in the deep cortical gray matter (dGM, left column), cortical gray matter (cGM, middle column) and white matter (WM, right column). Percentual differences between states are displayed. Abbreviations: c/l-PFA = (common/last)-paraformaldehyde; PBS = phosphate-buffered-saline.

Table 2: Summary tables of the BIC values for each fitted model (M1 and M2). (A) and the fitted parameter of the model (Equation 1 or 2) with the lowest BIC (or winning model, B). Each table reports their corresponding values per tissue class (cGM: cortical grey matter, dGM: deep grey matter, WM: white matter) and MPM parameter. Abbreviations: c/l-PFA = (common/last)-paraformaldehyde; PBS = phosphate-buffered-saline.

Figure 3: Temporal evolution of the median MPM parameters during fixation across all brains (coloured markers) for three brain tissue classes. Additionally, the curve of the winning saturation model (black curves, see Fig. 5) is plotted for each tissue class (columns, left to right: deep cortical gray matter (dGM), cortical gray matter (cGM), white matter (WM)) and MPM parameter (rows, top to bottom: R1, R2*, and MTsat).

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)
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DOI: https://doi.org/10.58530/2024/3668