Accurate counts of neurons are essential metrics for understanding the structure and function of the brain (Bonthius et al., 2004; Herculano-Houzel and Lent, 2005). This is particularly important for pre-clinical studies of human disease, as it provides a necessary starting point for assessing neurodegenerative changes on a regional basis (Price et al., 2001; Rosen and Williams, 2001; Bandeira et al., 2009). In addition to absolute counts, measuring neuron density can provide important insights into the structural complexity of local circuits. The distribution of neurons in the mouse brain on a region-by-region basis is also crucial for understanding variation between individuals and strains. The density of neurons can reflect the distinctive cytoarchitecture of brain regions, including laminar organization, size and shape of constituent neurons, and the volume and composition of associated neuropil (Wree et al., 1982; Spocter et al., 2012; Kasthuri et al., 2015). Furthermore, assessing neuronal densities in targeted brain regions under varying conditions may reveal impacts that change the composition of neuropil with or without associated loss (or gain) of neuronal cell bodies (Amunts et al., 1996; Selemon and Goldman-Rakic, 1999). The heterogeneity of neuronal density within a given region can provide insights into the complexity, developmental history, and functional diversity of the region (Peters et al., 1991). Establishing such datasets enables pre-clinical studies of the impact of genetics, environment, and development across the lifespan on brain structure.

To investigate cells numbers and densities in CNS, researchers have developed various quantitative methods, including several stereological approaches (Williams and Rakic, 1988; West, 1999; von Bartheld, 2002; Schmitz and Hof, 2005; Deniz et al., 2018) and approaches that first homogenize brain tissue and dissociate brain cells (Herculano-Houzel and Lent, 2005; Collins et al., 2010; Young et al., 2012). Stereology is a quantitative method for estimating the three-dimensional characteristics of biological structures using two-dimensional histological sections or images and systematic random sampling within delineated brain regions. In traditional approaches to stereology, the specimen is preserved by means of chemical fixation, the brain is removed from skull, sectioned into thin slices (usually 5–50 μm thick), and stained with specific dyes to highlight different cell types. The sections are then viewed under a microscope, and measurements are taken to estimate the cell numbers within delineated brain regions. Both 3D counting and the optical fractionation are alternatives to traditional stereological methods introduced by Abercrombie (1946, reviewed in Rosen and Williams, 2001) that is design-based in its approach to sampling a volume of tissue, counting targeted objects (e.g., neurons), and generating statistics that assess the precision of the counts (West, 1999). These methods are considered unbiased, but still can suffer from bias due to differential z-axis shrinkage and variable penetration of stains. By providing a less biased estimate of structural parameters, these modern stereological methods have contributed significantly to our understanding of many biological systems. However, there are some limitations. Stereological methods require extensive preparation of tissue and the use of microtomes to produce thin tissue sections. This can introduce damaging artifacts, lost sections, and distortions, even in the hands of experts. The results are sensitive to a range of factors, including the choice of chemical fixation, the post-fixation treatment of the specimens, the specific histological protocols used, and the specific features of the design-based approach to sampling and counting. Thus, it has be difficult to determine the accuracy of the measurements obtained in tissue that was subject to such deformation and the range of operational variables employed. Finally, stereological analysis can be a laborious and time-consuming process (Bonthius et al., 2004). When multiple brain regions are analyzed, the time and effort required can increase significantly, and the manual aspect of the process can introduce additional sources of variability.

In contrast, the isotropic fractionator (IF) involves homogenizing a small tissue sample from a region of interest—or the entire brain —and processing it into a uniform suspension of cells. The cells are then stained with a dye and placed into a special counting chamber, where the number of cells in a known volume is counted under a microscope (Herculano-Houzel and Lent, 2005), or by the flow cytometry (Collins et al., 2010; Young et al., 2012). The total number of cells in the brain region can then be estimated by extrapolating the cell density from the counting chamber to the reported or measured volume of the entire brain region. The downsides to isotropic fractionator are similar to stereology. One limitation is that both IF and stereology use the brain which is taken out of the skull and processed, introducing swelling and/or shrinkage, which can affect the accuracy of volume estimation.

Light sheet microscopy (LSM) has emerged as a powerful tool for 3D visualization of targeted populations of cells in intact, cleared tissue samples using fluorescent immunocytochemistry. Recent advances in tissue clearing (Ueda et al., 2020) have enabled the capture of high-quality, countable images in the whole-brain using LSM (Hillman et al., 2019). These intact 3D volumes can then be used for accurate counting of neurons and assessing neuronal densities, providing a more comprehensive and representative view of the brain region of interest. Typically, the whole brain images are registered to a standard reference atlas, such as the Waxholm Space Atlas (WHS) (Johnson et al., 2010) or the Allen Brain Atlas (ABA) (Wang et al., 2020). The combination of the digital images and the standard reference atlas facilitates the segmentation of regions and correction of altered brain morphology, allowing for comparison of neuron numbers and density within and across studies.

Researchers have employed this approach of registering LSM to WHS or ABA atlases in a number of recent studies (Susaki et al., 2014; Menegas et al., 2015; Renier et al., 2016; Zhang et al., 2017; Krupa et al., 2021). Susaki et al. (2014) mapped LSM to WHS space but did not proceed with cytometric quantitative analysis. The remaining studies mapped the LSM images to ABA space for analysis. ClearMap, as described by Renier et al. (2016), utilizes a peak detection algorithm with a threshold determined by comparing manual and machine counting, which may not yield optimal results when applied to complex and heterogeneous neuron distributions. Zhang et al. (2017) employed L1 minimization (Lasso), a machine learning regression method, to detect neurons in the whole brain. However, this method assumes sparsity of objects and a linear relationship between input features and output variables, with all features equally important, which may not hold true in the case of heterogeneous neuron distributions. Krupa et al. (2021) used a 3D Unet for cell detection, but these deep learning methods require large inputs and considerable training time compared to other machine learning methods. Menegas et al. (2015) utilized Ilastics¹ to segment cells in eight brain regions, with separate training for each region.

Registration of LSM images obtained from mouse brains to ABA space for correcting deformation and quantitatively segmenting brain structures and regions has one fundamental deficiency. The ABA atlas was generated from multiple specimens that were imaged after the brains were removed from the skulls (Wang et al., 2020). The lack of skull support and the effects of processing will deform the brain. Furthermore, ABA assembled their atlas from 1,600 animals, which were registered into a volume that does not conform to the size and morphology of the in situ mouse brain—as we demonstrate in this work.

We present a novel approach that is highly reproducible and allows efficient counting across the whole brain. Our method utilizes magnetic resonance histology (MRH), an extension of MRI to microscopic resolution of fixed tissue specimens (Johnson et al., 1993). MRH images are acquired with the brain inside the skull, resulting in a representation that more closely approximates the size and morphology of the in vivo brain (Johnson et al., 2023), as compared to reconstructions from histological methods that require cranial dissection, serial sectioning of the brain, and chemical treatment of thin brain sections. As a result, MRH images can serve as the “gold standard” for correcting ex situ brain morphology. Our workflow offers a powerful combination of morphological correction based on MRH, machine learning-based neuron classification, and post-processing. It provides accurate and detailed neuron counts and calculations of neuronal density, which can be readily derived from different brain regions and specimens. Our method features a large, well-defined field of view in 3D, which allows for a comprehensive analysis of an entire subvolume under study. Moreover, our workflow applies the principles of optical fractionation to systematically sample and count neuron numbers in 3D volumes, which reduces the computational costs and represents a novel digital approach not previously explored.

We present a workflow that corrects the deformation introduced by the chemical treatment of brain tissue for LSM and uses an automated algorithm for neuron segmentation and counting through machine learning and post-processing. To improve the accuracy of the results, we use the MRH of the same specimen as a reference for LSM image morphology, as MRH provides in-skull images of the brain that closely approximate the compartmental configuration and accurate size of the living brain. Our method offers a reliable means of acquiring neuron number and density and requires less human labor and subjective judgment than previous methods. The method exhibits high flexibility, as it requires a much lower amount of pre-training data and demonstrates efficient computational time and performance compared to deep learning methods, as depicted in Supplementary Figure S6. It is also much easier to replicate across multiple brain regions and specimens. By correcting raw images and conducting region segmentation, our method provides improved estimates over previous counting methods. Furthermore, by incorporating the principles of optical fractionation, our workflow provides an unbiased sampling method with equal probability to sample for each section with a relatively low sampling ratio (Supplementary Table S4), resulting in reduced computational costs and representing a novel digital approach that has not been explored before.

To validate the method, we used the workflow to analyze 13 regions in different divisions of 5 C57BL/6 J specimens. The results, as shown in Figure 5, demonstrate the variability in neuron density across regions within the same animal and across animals for the same regions. In the Supplementary materials, we conducted a systematic search of the literature providing neuron counts of the same regions for comparison with our method. As our method produces regional neuron density as its direct output, we assessed the accuracy of our results in terms of density. For most cortical regions, our findings were consistent with those of previous studies or fell within the range of previously reported results. However, in some regions, e.g., LGd, PSV, VISp, TH, and BLA, our results showed a higher neuron density than what was reported in earlier studies. This is likely due to our utilization of the morphology-corrected space for calculating neuron density. This space closely approximates the volume and morphology of the brain confined within the skull, which may have contributed to the observed differences in density measurements. In certain regions where our density measurements were markedly different from those reported in previous studies, such as the facial motor nucleus, we manually counted the sub-regions to validate the neuron distribution. Our findings indicated that the neuron distribution in this region was indeed sparse, with a density measurement about six times lower than that reported in the Blue Brain Map (BBM) (Ero et al., 2018). We hypothesize that this discrepancy may be due to differences in data quality or acquisition methods between studies. BBM estimated neuron counts using a transfer function and Monte Carlo method applied to the ABA Nissl atlas. The authors only used whole-brain values from literature, such as the total number of cells and neurons in the mouse brain, to constrain their estimates of cell densities in each brain region. Further investigation is required to elucidate the causes of the observed discrepancy. Nonetheless, our method, which directly measures regional neuron density, provides a reliable alternative to indirect methods such as those used by BBM, and can contribute to a more accurate appreciation of brain structure.

Our method has two limitations. In those regions in which the cell density is so high that the resolution of the LSM we acquired is not sufficient to differentiate countable cells (e.g., dentate gyrus, granule cell layer of cerebellar cortex), the random forest classifier and watershed algorithms will fail, and hence the performance hinges on the volume filter, which approximates the neuron count by partitioning the volumes of nested neurons based on the average neuron size (Supplementary Section S7). A second limitation is that performance is dependent on the quality of the raw data. In cases where the tissue preparation and scanning are suboptimal, the method will not function properly. Although the data provided by LifeCanvas, which we used for our study, are generally of high quality, there are occasionally regions with poor image quality (as shown in Supplementary Figure S7), which can limit the method’s reliability. Advanced imaging techniques such as expansion microscopy, as demonstrated by Wassie et al. (2019) or acquisition with higher power objectives will address resolution questions and are likely to produce reliable and accurate counts of neurons using our workflow.

The application of stereology to counting cells has a venerable history. As acquisition methods have improved the methods to count cells have been adapted to the newer data. The advent of tissue clearing and volume light sheet imaging yield opportunities for significant improvement in precision and accuracy. This is particularly important in our studies of the mouse brain as we seek apply this workflow to quantitative studies of the mophological and cytological impacts of neurodegeneration and aging. Correction for tissue changes, use of a more accurate label set, and automation described in this work will provide crucial tools in quantitative neuropathology.

The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found in the article/Supplementary material.

The animal study was approved by Duke Institutional Animal Care and Use Committee. The study was conducted in accordance with the local legislation and institutional requirements.

YT: Designed and coded the workflow, conducted the evaluation, and wrote the manuscript. GJ: Conceived the project, guided YT, and contributed to manuscript writing. RW: Offered valuable expertise and guidance in stereology. LW: Provided valuable expertise and guidance into neuron density, neuroscience, and strategy. GJ and RW: Provided funding and contributed to manuscript writing. All authors participated in manuscript revisions, reviewed, and approved the final submission.

This work was supported by National Institute of Aging R01AG070913 to GJ and RW.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.