Why do mothers never stop grieving for their deceased children? Enduring alterations of brain connectivity and function (2024)

Participants and procedures

Between March 2017 and May 2019, we enrolled eighteen mothers, aged 46–72, each with at least 12 years of education (Table 1). Eligible participants were fluent in English with adequate visual and auditory acuity for testing and no history of significant neurologic disease, MRI contraindications, or medical frailty. The Enduring Maternal Grief group (Grief N = 9) comprised mothers who lost an adult child unexpectedly (e.g., accident, suicide) at least 5 months before enrollment (median time since loss = 38 months, SD = 110.41, range: 5–362). Grieving mothers were referred through a local support group or by other participants. The control group (Control; N = 9) were recruited via community flyers and comprised age-matched women who were parents of a living child close in age to their matched grieving mother’s child at the time of their loss. Controls had never experienced the loss of a child.

All participants underwent a medical screening interview conducted over the phone to check for MRI contraindications and conditions that would affect study eligibility. To meet the eligibility criteria, all participants had to be fluent in speaking and understanding English, have adequate visual and auditory acuity for neuropsychological testing, be in good general health with no diseases expected to interfere with the study, provide pictures of their child that can be shared with the research team for the fMRI task, able to participate for the duration of the study and in all procedures.

Participants were excluded if they displayed any of the following: significant neurologic disease such as Parkinson’s disease, epilepsy, multiple sclerosis, migraine headaches, or brain cyst, tumor or aneurysm; preexisting disability that is so severe that it precludes assessment of dementia (e.g., severe/profound cognitive impairment with multiple disabilities); MRI contraindications, e.g., pacemakers, aneurysm clips, artificial heart valves, ear implants, metal fragments or foreign objects in the eyes, skin or body; Females who are pregnant or trying to get pregnant.

All participants provided written informed consent in accordance with the University of California at Irvine Institutional Review Board and were compensated for their participation. Participants completed a neuropsychological testing battery followed by questionnaires reporting on their grief symptoms. Participants were then given a 30-min break followed by a 1.5-h MRI scanning protocol.

Image acquisition

The MRI session began with acquisition of a structural MRI followed by three runs of the fMRI task, two resting-state scans, and one DTI scan. MRI data were acquired on a 3.0 Tesla Philips Achieva scanner, equipped with a 32-channel sensitivity-encoding (SENSE) head coil at the Neuroscience Imaging Center at the University of California, Irvine. First, a high-resolution three-dimensional (3D) magnetization-prepared rapid-gradient echo (MP-RAGE) structural scan was acquired for co-registration (0.75 mm³, TR/TE = 11/4.4 ms, 200 slices, FOV = 240 × 231 × 105, flip angle = 18 degrees, slice orientation = sagittal). This was followed by task and resting state fMRI (2.5 mm × 2.5 mm in-plane resolution, 2.3 mm slice thickness with a 0.2 gap, TR/TE = 2,500/26 ms, 44 slices, FOV = 180, flip angle = 70 degrees, slice orientation = transverse, 147 dynamic scans per run, number of dummy scans to ensure T1 stabilization = 4). Diffusion data were acquired with a b-value of 800 s/mm², 32 non-collinear directions and a single volume with a b-value of 0 s/mm². (TR/TE = 1,298/49 ms, FOV = 128, 128, 60 mm, voxel size = 1.78 × 1.78 × 2 mm) (Table 2).

Task-activated functional magnetic resonance imaging analysis

Upon enrollment in the study, participants provided 30 images of their child. During the fMRI task, the 30 images of their child were presented randomly intermixed with 30 images of recently deceased celebrities (familiarity control condition) and 30 images of unfamiliar individuals from stock photos (unfamiliar control condition). The photos of their child could be from across the lifespan at any age, subjects typically provided a breadth, but no strict divisions were made. The main stipulation was that the child needed to be front facing and the only person in the photo. Images were either provided digitally, or physical copies were scanned. Appropriate cropping and other small edits were made to ensure photos fit within the criteria for the task. Each of the 90 images was shown three times for 3 s, with a 1-s fixation image between trials (Figure 1A). Participants were asked to rate their emotional response to each image on a scale of 1 to 4 using an MR compatible button box.

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FIGURE 1

MRI results. (A) Task structure. (B) Child fMRI Response (Child > Celebrity + Random) for Grief (red) and Control (blue) mothers and the spatial overlap of voxels shared between groups (violet). (C) Independent samples t-test results demarcate greater Child fMRI Responses in Grief compared to Controls (red) and Controls compared to Grief (blue). Arrows point to regions with corresponding plots in panel (D). (D) Individual data points of Child fMRI Response magnitude in the dACC/DMPFC (top) and insula (middle) shown with standard deviation crossbars and dotted line illustrates numerical split between groups. The bottom panel of part (D) depicts a correlation between Child fMRI Response magnitude and subjective grief on the PG-13 in the inferior parietal lobule. (E) Midline view of PVT-area resting state functional connectivity analysis seed regions. (F) Resting-state fMRI results of PVT-area functional connectivity in controls (blue) and voxels that showed greater connectivity in controls compared to Grief mothers (cyan). (G) Resting-state fMRI results of PVT-area functional connectivity in Grief mothers (red) and voxels in the amygdala that showed greater connectivity in Grief mothers compared to controls (yellow). (H) Individual datapoints of PVT-area functional connectivity by group. The horizontal line highlights the complete numerical split between the groups. (I) Follow-up correlation analysis of PVT-area functional connectivity and PG-13 subjective grief scores. (J) Rendering of areas of interest in the DTI analysis. (K) Correlation plots between BGQ Total and UF (top) and HC (bottom). (L) Correlation plot shown for BGQ Total and UF: HC GFA ratio. Spearman’s rho (ρ) values are displayed with correlations. (M) Correlation between ACC surface area and subjective grief scores on the BGQ Total. DACC, dorsal anterior cingulate cortex; DMPFC, dorsomedial prefrontal cortex; PVT, paraventricular nucleus of the thalamus; Amyg., amygdala; FC, functional connectivity; PG-13, prolonged grief questionnaire; ACC, anterior cingulate cortex; GFA, generalized fractional anisotropy; BGQ, brief grief questionnaire.

Pre-processing and subject-level general linear model analyses were implemented using FSL FEAT. Each subject’s individual images were motion-corrected, smoothed with a 5 mm Gaussian filter, high-pass filtered, and pre-whitened. Event-related responses were estimated using event-related convolution with an ideal hemodynamic response represented by a double gamma function and its temporal derivative. Functional images were registered to their corresponding T1-weighted anatomical image and then to the standard MNI152 2 mm template. Explanatory variables were modeled for each of the three conditions (Child, Celebrity, Random). The Child Response contrast, i.e., Child > [Celebrity + Random], for each subject was entered into a group-level independent samples t-test in SPM12 (Wellcome Department of Cognitive Neurology, London, United Kingdom). In addition, the Child Response subject-level contrast images were entered into correlational models to demarcate clusters with positive and negative correlations between the fMRI Child Response magnitude and the subjective-grief scores. Task fMRI statistical maps were set to an initial voxel threshold of p < 0.005 (uncorrected). The group comparison and subjective grief correlation result maps were corrected for multiple comparisons to p < 0.05 by enforcing a cluster-forming voxel extent threshold of k = 49 based on Monte Carlo Simulations with 1,000 iterations (Slotnick, 2017). The group comparison contrast (effectively a directional interaction) was inclusively masked with the corresponding group map thresholded at p < 0.005.

Resting state functional magnetic resonance imaging analysis

Resting-state volumes were preprocessed and successfully denoised using the CONN Toolbox (Whitfield-Gabrieli and Nieto-Castanon, 2012) version 19c. The structural images were centered, AC-PC aligned, segmented, and normalized to the MNI template. The functional images were (Kersting et al., 2009) realigned and unwarped, (Gündel et al., 2003) centered and aligned to the AC-PC line, (McConnell et al., 2018) slice-timing corrected, (Arizmendi et al., 2016) segmented and MNI-normalized, and (Zetumer et al., 2015) smoothed with a 6 mm Gaussian kernel. Structural and functional data were resampled to 1 and 2 mm³ voxels, respectively. The pre-processed images underwent despiking followed by nuisance regression (white matter and CSF signal using aCompCor, realignment with first order derivatives, framewise motion estimates, motion artifact scrubbing, and linear detrending) followed by band-pass filtering (0.008 Hz < f < 0.09 Hz). We enforced conservative motion artifact thresholds (Global Signal Change z > 3 and framewise displacement > 0.5 mm). Two Grief participants (aged 54 and 55) and 1 control (age 50.95) were excluded from RSFC analyses for having far fewer valid scans than the rest of participants (more than 30% of the timepoints scrubbed) and instances of max motion > 4 mm (Supplementary Figure 1). Upon removing these three participants from analysis, denoising was successful with no evidence of associations between random permutations of RSFC and the quality control (QC) metrics (valid number of scans, mean or max global signal change or mean motion). All included participants had approximately 12 min of usable data (Controls: Mvalidscans = 292.6; Grief: Mvalidscans = 291.3) and there was no evidence that the number of valid scans or other motion metrics differed between groups.

We focused on delineating the circuitry of paraventricular thalamic nucleus (PVT), in view of its established and emerging roles in the encoding and integration of emotionally salient long-term memories (Do Monte et al., 2016; Kark et al., 2021; Kooiker et al., 2021) and the influence of these memories on behaviors during emotional conflicts (Choi et al., 2019). We assessed the impact of maternal grief on resting-state functional connectivity (RSFC) of the PVT. The PVT-area seed was created using the left and right Pv.nii.gz files received in 0.5 mm MNI-space (Krauth et al., 2010; Jakab et al., 2012). We first combined the left and right PVT seeds from the atlas using imcalc in SPM12 and then slightly dilated the bilateral PVT seed using MRICRON (Dilate drawing feature¹). In CONN, all seed regions were inclusively masked with subject-level structural gray matter segmentation masks to ensure signal extraction from gray matter. For one grief participant with a wider third ventricle width, the PVT seeds were slightly nudged away from x = 0 using MRICRON to fall on the paraventricular gray matter. This approach was based on our recently published work demonstrating the intrinsic structure and connectivity of the PVT in humans (Kark et al., 2021). Given the small size of the PVT and to address potential confounding effects of neighboring nuclei, we created a midline subnuclei control seed encompassing all midline nuclei using the Thalamus Atlas of the Swiss Federal Institute of Technology (ETH) in Zurich and University of Zurich, Switzerland (Krauth et al., 2010; Jakab et al., 2012). Subject-level seed-to-voxel PVT RSFC maps were calculated, controlling for the midline subnuclei, and subsequently entered a group-level independent samples t-test in SPM12. Group-level analyses were spatially constrained to key nodes of PVT functional connectivity (Kark et al., 2021; Kooiker et al., 2021), which include the orbitofrontal cortex, cingulate cortex, amygdala, hippocampus, striatum, and the insula, to increase the sensitivity of the analysis and thresholded at p < 0.05 uncorrected.

Diffusion weighted imaging analysis

As the potential impact of maternal grief could involve altered structural connectivity of salient nodes in several “emotional” circuit, we assessed the integrity of several white matter tract ROIs including the cingulate gyrus (CG), hippocampal cingulum (HC), and uncinate fasciculus (UF) (Figure 1J). Like our prior work (Granger et al., 2021), data were analyzed using DSI-Studio,² corrected for motion using FSL’s eddy_correct algorithm, and reconstructed using DSI Studio Q-spin Diffeomorphic Reconstruction (QSDR) algorithm which computes orientation distribution functions in MNI space (Yeh and Tseng, 2011). White matter tract integrity was measured by extracting generalized fractional anisotropy (GFA) from each of the three ROIs (obtained from the Johns Hopkins white matter atlas in DSI studio) and averaging across hemisphere. One Grief subject (age 58) was excluded from the GFA analyses because of a suboptimal template fit (R² value of 0.63), as recommended by the software developers. Like our previous work, corticolimbic circuitry imbalance was calculated as the ratio of UF GFA: HC GFA (Granger et al., 2021).

Structural morphometry

Using the Freesurfer 6.0 and the DKT atlas (Fischl et al., 2002, 2004), we quantified cortical surface areas of seven regions of interest (e.g., cingulate, prefrontal regions) and subcortical volumes of seven regions of interest (e.g., striatal regions, amygdala, hippocampus). An affine registration with Talairach space is followed by an initial volumetric labeling and correction for variation in intensity due to the B1 bias field. After this, a high dimensional non-linear volumetric alignment to the Talairach atlas was performed, followed by pre-processing, and finally the volume was labeled. Combining across hemisphere, we assessed subcortical volumes (accumbens_area, Amygdala, caudate, putamen, amygdala, hippocampus, Thalamus_ Proper) and surface areas (entorhinal_area, parahippocampal_ area, insula_area, anterior cingulate [caudalanteriorcingulate_ area+rostralanteriorcingulate_area], medialorbitofrontal_area, ventro-lateral PFC [parsopercularis_area+parsorbitalis_area+ parstriangularis_area], and middle-frontal/DLPFC areas [ros tralmiddlefrontal_area+caudalmiddlefrontal_area]). Volumes were reported as a percentage of the total gray matter volume and surface areas are reported in mm².

Neuropsychological and self-report measures

Participants completed a battery of tests including the Mini Mental State Exam [MMSE] (Folstein et al., 1975); the Wechsler Digit Span Forward and Backward, The Controlled Oral Word Association Test (COWAT), Semantic Verbal Fluency (Animals), Trail Making Test A and B, and the Rey Auditory Verbal Learning Test (Schmidt, 1996). They also completed self-report assessments of depressive symptoms (Beck Depression Inventory–II [BDI]) (Beck et al., 1996), anxiety-related symptoms (Beck Anxiety Inventory [BAI]) (Beck and Steer, 1993), sleep quality [Epworth Sleepiness Scale] (Johns, 1991) and Pittsburgh Sleep Quality Index [PSQI] (Buysse et al., 1989). Additionally, the Grief group completed two subjective grief assessments: The Prolonged Grief Disorder-13 scale (PG-13) (Prigerson et al., 2009) and the Brief Grief Questionnaire (BGQ) (Shear and Essock, 2002).

The PG-13 is a diagnostic tool (Prigerson et al., 2009) to assess if respondents meet criteria for Prolonged Grief Disorder (PGD). The PG-13 considers PGD experiencing daily separation distress for at least 6 months post-loss, daily or pervasive cognitive, emotional, and behavioral symptoms, and self-reported impairment in functional areas of living (e.g., social, occupational, domestic responsibilities).

The BGQ is a reliable and valid tool for assessing subjective grief (Shear and Essock, 2002). The BGQ asks responders to rate the extent to which they feel cut off or distant, avoid things related to the person who died, experience bothersome thoughts or images, have trouble accepting the death, and how much grief still interferes with their life (0 = not at all, 1 = somewhat, 2 = a lot). On the BGQ, a score of 8 or higher indicates likely complicated grief, scores ranging from 5 to 7 are considered subthreshold, and a score less than 5 is considered unlikely complicated grief.

Data analysis and visualization

Our general approach was to first test hypothesized regions and circuits in group-level t-tests. For all group comparisons, we calculated independent samples t-test statistics (assuming unequal variances) and Hedge’s g. We subsequently tested across-subject correlations within the Grief group using Spearman’s rho (ρ). The 3D statistical brain maps were visualized for figures using MRIcroGL³ and MRICRON.⁴ Group comparison plots were created using beeswarm.m.⁵

Heightened salience network responses to picture of the deceased child

In-scanner emotionality ratings were entered into a 2 × 3 repeated measures ANOVA with the between subject factors of group (Grief, Controls) and the within-subject factor of stimulus type (random, celebrity, child). There was evidence for a stimulus by group interaction [F_(2,32) = 6.42, p = 0.005]. Both groups of mothers rated viewing images of their children with similar levels of emotionality (M = 3.92, SE = 0.20) but the Grief mothers rated the images of deceased celebrities as relatively less emotional compared to the control mothers (t_(10.27) = 3.98, p = 0.002, Hedges’ g = 1.79 [0.56 2.96]). The in-scanner emotion ratings for images of their child were at ceiling for both groups, thus we were not able to parametric modulation of the Child Response by emotionality rating.

In both grieving and control mothers, the viewing images of their children was associated with activation of mPFC, precuneus, lateral occipital cortex, and the ventral visual stream (Figure 1B, violet). In the Grief group, activation of anterior and posterior cingulate was noted. Unexpectedly, the dorsomedial thalamus including the paraventricular thalamic nucleus (PVT) was robust (Figure 1B, red), as well as brain stem regions. Notably, activation of the PFC robustly distinguished the groups: In the Control group only, mPFC activation was spatially expansive and extended anteriorly toward the frontal pole, and additionally involved the lateral PFC, orbitofrontal cortex and middle temporal gyrus (Figure 1B, blue).

When comparing groups directly, we observed that, compared to controls, activation in grieving mothers was reduced in the mPFC (MNI_xyz = −10, 54, 0; k = 19) at a reduced voxel extent threshold minimum, as well as in the precuneus and lateral occipital cortex (Figure 1C, blue). Conversely, activation was increased in grieving mothers within dorsal anterior cingulate (dACC), dorsal medial prefrontal cortex (dmPFC), anterior insula (AI), medial portions of the visual cortex, and inferior parietal lobule (IPL) (Figures 1C,D). Of these the IPL correlated positively with assessment of severity of the grief (PG-13 scores, Figure 1D, bottom). At a reduced voxel extent threshold minimum (k = 10) for Grief > Controls, clusters were also observed in the striatum (MNI_xyz = 16, 2, 2; k = 27), including the caudate and putamen, and the midbrain (MNI_xyz = -2, -24, -28; k = 56), including the substantia nigra/ventral tegmental area (SN/VTA).

Heightened resting state functional connectivity of the paraventricular thalamic nucleus circuit

We assessed the resting state functional connectivity (RSFC) of the PVT structure in the Grief group compared with controls. In the controls, one-sample t-tests yielded the expected PVT circuitry, reproducing prior work (Kark et al., 2021), including hippocampus, amygdala, nucleus accumbens (NAc), anterior cingulate cortex (ACC), and ventral tegmental area (VTA) (shown in blue in Figure 1F). This first analysis established the ability to detect PVT region RSFC with expected targets in our relatively small sample (Table 3 and Figures 1E–I). In the Grief group, the PVT was functionally connected to amygdala, hippocampus, ACC, and VTA (shown in red in Figure 1G). Examining group differences using independent samples t-tests distinguished the Grief and Control groups: Compared to grieving mothers, control mothers showed relatively greater PVT functional connectivity with the ACC, hippocampus, and insula (shown in cyan in Figure 1F). Compared to control mothers, connectivity of PVT with the VTA and bilateral amygdala was greater (shown in yellow in Figure 1G and plotted in Figure 1H). PVT-amygdala functional connectivity of individual grieving mothers correlated with their subjective prolonged grief score (ρ = 0.76) (Figure 1I). Notably, we observed a complete numerical split between the groups in PVT functional connectivity with the amygdala (Figure 1H).

Imbalance in corticolimbic white matter tract integrity

Although DTI scan head motion was greater in the Grief group compared to controls, BGQ Total scores and UF:HC ratios were not related to head motion across subjects (Supplementary Figure 4). Grieving mothers had a lower hippocampal cingulum (HC) GFA [t_(11.54) = 2.18, p = 0.051, CIs (−0.037, 2.037), Hedges’ g = 1.02] and uncinate fasciculus (UF) GFA [t_(11.675) = 1.41, p = 0.184, CIs (−0.342, 1.625), Hedges’ g = 0.66] values compared to the controls, but the differences did not reach statistical significance. While the effect sizes were medium-large, it is important to note that sample size is a limitation. There was no pattern toward a GFA difference of the cingulum [t_(14.796) = 0.73, p = 0.48, CIs (1.29, 0.63), Hedges’ g = 0.34]. Of note, higher levels of subjective grief (BGQ Total) were associated with reduced HC-GFA (Figure 1K, top), greater UF-GFA (Figure 1K, bottom), and thus an increase ratio of UF/HC GFA (Figure 1L).

No major structural magnetic resonance imaging differences between groups

Whereas significant differences in functional connectivity and long-range corticolimbic white matter tracts distinguished grieving mothers and controls, we did not detect group differences in volume or surface areas of the tested brain regions (Supplementary Figures 2, 3). Higher levels of subjective grief were associated with reduced cortical surface area over the ACC (Figure 1M).

Impaired learning efficiency, verbal memory, and executive function

The groups did not differ on the MMSE. Tests of working memory or phonemic and semantic verbal fluency also did not differ between groups. In tests of episodic memory, grieving mothers performed worse than controls on multiple measures of the RAVLT across item recall trials (Figure 2A), including the Last Learning Trial (A5), Immediate Recall, Delayed Recall, and an increased number of Recognition False Alarms (Figure 2B), which drove down Corrected Recognition Scores (Hits—FAs) (Figure 2A). Grieving mothers retained fewer items in memory, even when correcting for the number of items learned (i.e., Long Term Retention). Across participants (N = 7), higher levels of subjective grief were associated with the Learning Over Trials (LOT) index, a measure of learning efficiency (Figure 2C).

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FIGURE 2

Neuropsychological changes in learning, memory, and executive functioning. (A) Mean RAVLT word list scores by group: Learning trials (A1–A5), interference list (B1), immediate and delayed recall, and corrected recognition (# of correct hits–# of incorrect false alarms). Standard error bars and individual datapoints are shown. (B) Individual datapoints for RAVLT false alarms shown with SD crossbars. (C) Correlation between BGQ and learning efficiency (LOT index five Total of trials (I to V)–(5X [A1])). (D) Individual datapoints for Trails B shown with SD crossbars. (E) Correlation between Trails B performance, in seconds, and subjective grief on the BGQ. RAVLT, rey auditory verbal learning test; FAs, false alarms; LOT, learning over trials.

Whereas, group differences in psychom*otor performance on Trails A were non-significant, we observed evidence for reduced executive function performance on the Trail Making Test B in the Grief group (Figure 2D). Across participants (N = 7), poorer Trails B performance was closely linked with higher levels of subjective grief (Figure 2E). Groups did not differ on self-reported sleep measures. Yet, grieving mothers scored higher than controls on the BDI and BAI (Table 1).

Acknowledging prior work that grief is a unique condition from mood or anxiety disorders, we utilized the diverse items on the BDI-II (cognitive, affective, and somatic symptoms) to further understand symptoms driving BDI-II scores in this sample. Item scores on the BDI-II were compared between the two groups and sorted in descending order based on effect size (Hedge’s g). The “difficulty concentrating” item emerged as the most consistent symptom of the Grief group with the largest between-group effect size. Only one of the control mothers indicated mild concentration difficulty, by contrast, all eight of the Grief mothers with BDI-II data reported at least mild (n = 4) or moderate (n = 4) difficulty concentrating (see heat map of item scores by participant and group in Supplementary Figure 5). All the Grief mothers also reported mild levels of tiredness and fatigue, and anhedonia symptoms appeared elevated in those with higher PG-13 scores (participant columns sorted by PG-13 scores, see x-axis in Supplementary Figure 5). Interestingly, the mothers with the two highest subjective grief scores had no overlap of their moderate symptoms on the BDI-II except for difficulty concentrating.

Of note, grieving mothers who felt overwhelmingly bitter and had trouble accepting loss reported the highest levels of grief. On the BGQ, all seven of the mothers endorsed either “Somewhat” or “A lot” when asked with how much grief interfered with their life and how much they were experiencing bothersome images or thoughts of their child when they died or thoughts about the death. Feeling cut off or distant from people, family, or friends was the least severe symptom (n = 3 “Not at all”, n = 4 “Somewhat”).

On the PG-13 survey (n = 7 total), six Grief mothers reported weekly (n = 3) or daily (n = 3) intense feelings of emotional pain, sorrows, or pangs of grief. Six reported weekly (n = 2) or daily (n = 4) yearning or longing for their lost child. Only two reported avoidance of reminders. Six of the seven Grief mothers with the PG-13 data reported a pronounced reduction in functional areas of life (item 13). Of these seven mothers, one also met criteria for prolonged separation distress (criterion based on items 1–3), one met the PG-13 criteria for frequent cognitive, emotional, and behavioral symptoms (items 4–12), and two met criteria for both—indicative of PGD based on the PG-13. Naturally, those two mothers had the highest PG-13 scores (45 and 47), and both reported “overwhelming” feelings of bitterness about their loss (versus the five others who reported “somewhat” bitter or less). There two mothers also indicated trouble accepting the loss and confusion about their role in life since the loss.

Consistent with prior work, there was insufficient evidence for a link between time since loss or age at the time of loss and subjective grief, suggesting subjective grief did not decrease with time. In fact, the mother with the highest subjective grief scores had lost her son about 30 years prior to testing.

¹http://people.cas.sc.edu/rorden/mricron/index.html

²http://dsi-studio.labsolver.org

³http://www.mccauslandcenter.sc.edu/mricrogl/home

⁴http://people.cas.sc.edu/rorden/mricron/index.html

⁵https://github.com/ihstevenson/beeswarm

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