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Quantification of tissue shrinkage due to formalin fixation of entire post-mortem human brain

Tobias Streubel¹, Francisco Javier Fritz¹, Herbert Mushumba², Klaus Püschel², and Siawoosh Mohammadi¹
¹Institute for Systems Neuroscience, University Medical Center Hamburg-Eppendorf, Hamburg, Germany, ²Institute of Legal Medicine, University Medical Center Hamburg-Eppendorf, Hamburg, Germany

Synopsis

This work investigates tissue shrinkage during fixation and how it is related to associated changes in three quantitative MRI parameters (longitudinal relaxation $$$R_1$$$ and effective transverse relaxation $$$R_2^*$$$ rates, and magnetization transfer saturation rate MT). We proposed a new model to estimate tissue shrinkage from brain volume changes and found that shrinkage was $$$7.7\%$$$. No apparent relation between changes in MT and tissue shrinkage were found, whereas it was remarkable for $$$R_1$$$ and $$$R_2^*$$$, indicating that mostly the extra-axonal space is reduced during fixation.

Introduction

One prominent marker for myelin volume fraction (MVF) is the magnetization transfer saturation rate (MT)^1,2 as acquired, e.g. with the Multi-parameter mapping (MPM) protocol³. A typical approach to validate this marker, would be comparing ex vivo MRI and histology of the same fixed human brain tissue sample. However, potential changes in volume between the in vivo and fixed ex vivo situation due to the fixation process⁴ must be considered for a proper validation. Previous experiments performed in mice brains showed that tissue shrinkage due to fixation^4,5 is between 4% and 10% of the total volume. However, the temporal change of tissue shrinkage and how it is related to the observed changes in quantitative MPM parameters (longitudinal relaxation $$$R_1$$$ and effective transverse relaxation $$$R_2^*$$$ rates, and MT) is unknown. In this work, we model the temporal evolution of the tissue shrinkage during fixation for the whole human brain. To estimate the extend of tissue shrinkage and investigate how it affects qMRI parameters, we longitudinally analyzed two human brains, firstly measured in situ (inside the skull) and later in ex vivo, immersed in 4% paraformaldehyde (PFA) using the MPM protocol.

Methods

Subjects: Two human post-mortem brains dissected at autopsy with prior informed consent (WF-74/16), as described in table 1, were fixed with 4% paraformaldehyde (PFA) in aqueous solution, as commonly used for ex vivo histology^6–8.
MRI: Measurements were performed on a 3T PRISMA fit MRI (Siemens Healthcare, Erlangen, Germany), using the Siemens 32-channel receiver (Rx) head-coil. To ensure reproducibility in brain positioning, a custom-made sample holder was used. Whole brain MR images were acquired using the MPM³ protocol, based on calibration⁹ and spoiled multi-echo fast-low-angle-shot (FLASH¹⁰) sequences, including three different weightings (MT-, PD- and T₁-weighting). The following sequence parameters were used: isotropic resolution of (0.8 mm)³, flip angle of 6° (MT- and PD-weighted) and 21° (T₁-weighted), 8 echoes (2.34 to 18.44 ms, in steps of 2.30 ms), readout bandwidth of 488 Hz/pixel, and repetition time of 25.00 ms.
Analysis: In order to estimate the relative tissue shrinkage ($$$r\Delta V$$$) during the fixation process, we created a brain mask from the gray matter (GM) and white matter (WM) tissue probability maps, generated from the MT and R₁ maps acquired at each time-point using SPM12¹¹. For improved segmentation, the MT map from each time point was registered to the in situ brain using a rigid-body co-registration. To quantify the relative change $$$r\Delta V(d_k)$$$ at time-point $$$d_k$$$, we compared the volumes (represented by the total number of voxels $$$N(d_k)$$$) at $$$d_k$$$ with the volume of the in-situ time point $$$d_0$$$.$$(1)r\Delta V(d_k)=\frac{N(d_0)-N(d_k)}{N(d_0)}\times100$$
A spherical model for the tissue shrinkage: We assumed that the continuous reduction of the brain volume due to fixation can be approximated by the relative volume change of a sphere (Fig.2). The relative change of the sphere as a function of time is as follows:$$(2)rV(T_i)=\frac{V(T_0)-V(T_i)}{V(T_0)}=1-\frac{V(T_i)}{V(T_0)}$$, with $$$\frac{V(T_i)}{V(T_0)}=\frac{\left( r_0-\sum_{k=1}^i\Delta r(T_k)\right)^3}{r_0^3}=\left(1- \sum_{k=1}^i\frac{\Delta r(T_k)}{r_0}\right)^3$$$.
Here, we heuristically assumed that the relative decrement of the radius as a function of time can be described by an exponential: $$(3)\frac{\Delta r(T_K)}{r_0}=\delta\exp^{\left(\frac{T_k}{T_c}\right)}$$ with $$$\delta$$$ being a heuristic dimensionless decrement and $$$T_c$$$ being time at which 65% of the relative change took place. Consequently, we fitted the following function, depending on two parameters (\delta,T_c) to the measured relative volume change of the brain:$$(4)rV(T_i)=1-\left(1-\sum_{k=1}^i\delta\exp^{\left(\frac{T_k}{T_c}\right)}\right)^3$$

Results

We determined volume of the in-situ brains and compared it to literature for in vivo human brains¹². Subject 1 had a small brain (0.8l), the brain size of subject 2 (1.2l) was comparable to typical in vivo brains (1-1.5l). From our model, we estimated the relative tissue shrinkage ($$$7.7\pm 2\%$$$ at time point 126), the critical day ($$$T_c = 18$$$) and the radius decrement ($$$\delta=0.15\%$$$). The high tissue shrinkage values for the first brain on later time points (orange circles in Fig.3) have been identified as outliers (Fig.4). Figure 5 depicts the scatter plot of the temporal evolution of the quantitative MPMs against the estimated curve of relative tissue shrinkage. No apparent relation between MT and tissue shrinkage was observed, whereas $$$R_1$$$ and $$$R_2^*$$$ showed a continuous dependency on tissue shrinkage which saturated after the critical time $$$T_c = 18$$$ rapidely for $$$R_2^*$$$ and slowly for $$$R_1$$$.

Discussion and Conclusion

In this work, two questions were answered: (1) What is the tissue shrinkage in human brains during fixation? (2) What is the relation between tissue shrinkage and changes in $$$R_1, R_2^*$$$, MT? To estimate tissue shrinkage due to fixation, we introduced a forward model for this phenomenon and found that shrinkage was $$$7.7\%$$$ of total brain volume. No apparent relation between changes in MT and tissue shrinkage were found, whereas it was remarkable for $$$R_1$$$ and $$$R_2^*$$$. One might speculate that the observed volume changes due to fixation occurred mainly in the extra-axonal space, because the shrinkage-sensitive $$$R_1$$$ and $$$R_2^*$$$ parameters would be sensitive to changes in the extra-cellular space while MT is more sensitive to the macromolecular space. To generalize our observations the tissue shrinkage of more brains need to be investigated.

Acknowledgements

This project was funded by the ERA-NET NEURON (hMRI- ofSCI) and the Bundesministerium für Bildung und Forschung (BMBF; 01EW1711A and B) and the Deutsche Forschungsgemeinschaft (grant MO 2397/4-1) and the Forschungszentrums Medizintechnik Hamburg (fmthh; grant 01fmthh2017).

References

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Figures

Table 1: Overview of two post-mortem brains which were included in our study. At day 0 the measurement was performed in situ (unfixed and in the skull). All other time points were acquired ex vivo with the brain being embedded in 4% PFA.

Fig.2: Illustration of the tissue shrinkage model. Volume changes as a function of time in fixative ((a) being an early and (b) a later time point) have been modeled by a sphere with a continuously decreasing radius $$$r_i = r_0 -\Delta r(T_i)$$$ (c). The temporal behavior of the volume change can be modeled by an exponential decrease of radius-change: $$$\Delta r(T_i)=\sum_{k=1}^i\Delta r\exp\left(-\frac{T_k}{T_c}\right)$$$. Note that the volume changes in (b) and (c) were exaggerated for demonstration purpose.

Fig. 3 (a) Tissue shrinkage as a function of time in fixative. Subject 1 (red crosses): 14 time-points in fixative, 1 in situ. Subject 2 (blue circles): 59 time-points in fixative, 1 in situ. Outliers marked with orange circles. Highlighted are estimated volume changes determined from a good segmentation (magenta arrow) and bad segmentation (orange arrow), which are depicted in Figure 4.

Fig.4: Example for (a) good and (b) bad segmentation. Outliers are marked with orange arrows.

Fig. 5: Dependency of qMRI maps ($$$R_1,R_2^*$$$and MT) on tissue shrinkage assessed by scatter plot. A continuous dependency of the relaxation rates $$$R_1$$$ (a) and $$$R_2^*$$$ (b) from tissue shrinkage rate was observed, whereas MT showed no apparent depenency. The critical time-point $$$T_c = 18[d]$$$ is illustrated by a red x. After this day, 65% of the tissue shrinkage rate took place.

Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)

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