. Author manuscript; available in PMC: 2022 Dec 9.

Published in final edited form as: Proc SPIE Int Soc Opt Eng. 2022 Apr 4;12032:1203213. doi: 10.1117/12.2612210

Mapping Pediatric Spinal Cord Development with Age

Ashwin Kumar ^a, Simon Vandekar ^b, Kurt Schilling ^c, Aashim Bhatia ^d, Bennett A Landman ^a,^e, Seth Smith ^c

PMCID: PMC9733418 NIHMSID: NIHMS1804747 PMID: 36506260

Abstract

Pediatric spinal cord morphometry has been relatively understudied because of non-optimal image quality due to the difficulty of spine imaging, rarity of post-mortem analysis, motion artifacts, and pediatric MR imaging research focus on understanding spinal injury or pathology. The pediatric brain has been comparatively well-studied with white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF) differences observed with age and gender. Therefore, a greater understanding of pediatric cervical and thoracic spinal cord morphometry would be beneficial for developing clinically relevant cord growth models. We focused on retrospectively characterizing cervical and thoracic spinal cord growth and morphometry changes in a healthy pediatric population. High resolution multi-echo gradient echo (mFFE) images were acquired from pediatric spinal cord scans from 63 patients (mean: 9.24 years, range: 0.83–17.67 years). The mFFE scans were then registered to the template space for uniform viewing and analysis by using a customized semi-automatic processing pipeline involving Spinal Cord Toolbox (SCT). Jacobian control determinants were calculated, and subsequent WM, GM, dorsal column, lateral funiculi, and ventral funiculi scalar averaging was conducted. Random effects models were used to model age-related Jacobian scalar differences. Observing the growth of cord matter by patient age and vertebral level suggests that the upper cervical spinal cord, specifically C2-C3, and mid-thoracic spinal cord, T3-T8, grow faster than other cervical levels and thoracic levels, respectively. This knowledge will facilitate clinical decision making when considering spine interventions and conducting radiological analysis in children with cervical and thoracic spine abnormalities.

Keywords: Pediatrics, spinal cord development, cord maturation, volume change, random effects, morphometry

1. INTRODUCTION

Study of pediatric spine maturation has focused on cadaver pedicle examination^1,2 and spine CT analysis for disc and pedicle growth^3,4. Pediatric spinal cord development and analysis studies have been limited to pathological-focused features of the cord⁵, longitudinal analysis of specific cord region(s)⁵, and alignment of cervical spine⁶. Unlike the pediatric spinal cord, the adult cord has been well documented across individual segments and cord regions in healthy patients⁷. Similarly, adult and pediatric brains have been well-characterized, including white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF) differences observed with age and gender^7,8. These studies include longitudinal and cross-sectional studies ranging from neonatal to adolescents through Jacobian analysis^7–10. Jacobian analysis can detect morphological changes and measure tissue growth or loss by calculating the rate of Jacobian change, which is measured by computing the amount of deformation required to map the anatomical to template space¹⁰. For instance, pediatric brain age and gender Jacobian analysis has shown extensive WM growth and potential GM shrinkage over time combined with regional growth differences in the lateral ventricles and caudate nuclei between boys and girls⁷. Furthermore, surgeons are often requested to evaluate children in collaboration with radiologists for spine instrumentation and fusion for various indications¹¹. Treatment decision in many cases may be influenced by expected normal spine growth and size based on age¹². Therefore, due to the pediatric spinal cord’s relatively understudied nature, a greater understanding of pediatric cervical and thoracic cord morphometry would be beneficial for developing clinically relevant cord growth models. Our aim was to retrospectively define cervical and thoracic spinal cord morphometry changes in a healthy pediatric population by Jacobian analysis. We studied the growth rates of such cord anatomy as cord matter, GM, WM, lateral funiculi, dorsal columns, and ventral funiculi.

2. METHODS

2.1. Data Criteria

High resolution multi-echo gradient echo (mFFE) scans were retrospectively acquired from pediatric spinal cord scans from 63 patients (mean: 9.24 years, range: 0.83–17.67 years) at the Monroe Carrel Jr. Children’s Hospital. All studies were performed under local institutional review board approval (AAA_171784). Imaging was conducted using a 3T whole-body MR imaging scanner (Philips Healthcare, Best, Netherlands). mFFE volumes consisted of 25–70 mm variable lengths and were imaged in the cervical and thoracic levels. Spinal cord mFFE location distribution varied with many scans located in the cervical or upper thoracic cord regions as shown in Figure 1. Only patients with normal spinal cords (absence of pathology reviewed by a licensed pediatric neuroradiologist [A.B.]) were included in the study.

Figure 1. — Number of subjects distributed across cord vertebral levels with logarithmically scaled colorbar. Note the greater relative concentration of subjects in cervical cord compared to the thoracic cord. The upper (T1-T4) and lower-thoracic (T10-T12) cord regions have more subjects than mid-thoracic cord regions (T5-T10). The maximum (n=44) and minimum (n=1) subject counts were observed in C6 cervical and T9 thoracic cord regions respectively.

2.2. Image Processing and Registration

mFFE scans were pre-processed and registered to the PAM50 template space for uniform viewing and analysis using a customized semi-automatic processing pipeline involving the Spinal Cord Toolbox¹³, Version 5.3 (SCT; https://github.com/spinalcordtoolbox/spinalcordtoolbox). Each axial slice was initially inspected to ensure scans were reflective of cord matter and excluded if low signal or artifacts were present. The pre-processing sequence (Figure 2) for the mFFE scans involved manual centerline identification, automatic cropping, semiautomatic cord segmentation, automatic GM and WM segmentation, manual vertebral labeling, and automatic cord normalization. The spinal cord centerline was manually processed by selecting the center point on axial and coronal slices. Cropping of original mFFE scans to 70 mm radially from centerline increased slicewise processing speed and homogenized planar dimensions. Automatic segmentation algorithms erroneously identified cord matter boundary on 57 subjects (90.47%). Therefore, manual segmentation editing was necessary and required <10 minutes per dataset. GM was automatically segmented¹⁵ and WM segmentation was computed from cord matter and GM segmentation. Automatic vertebral labeling algorithms incorrectly labeled the vertebral discs on all patients given varied availability of vertebral C2-C3 disc. Consequently, a manual slicewise vertebral labeling process was constructed by modifying SCT’s labeling software and inspecting saggital cord slices. Cord matter mean intensity was then linearly normalized to 1000 (arbritarily chosen) for each patient scan to ensure cord matter was visible when comparing patients.

Figure 2. — Overview of mFFE pre-processing and registration pipeline involving SCT and ANTs. Anatomical data was pre-processed to obtain parameters necessary for PAM50 template registration (cord segmentation and vertebral labeling). Registration was split between anatomical data that required vertebral straightening (due to spinal curvature) and data not requiring such straightening. Both data types were then affine and non-linearly registered, in which the latter remained necessary for Jacobian analysis. Extrapolated vertebral regions not bound by vertebral labeling and unreflective of approriate cord regions were sliced. The Jacobian was then voxelwise computed from the mFFE to template deformation fields.

Initial multi-parameter template registration failed due to non-customized parameter variation. Registration to the PAM50 T2*-weighted template¹⁴ was selected from two registration parameters by visual inspection, vertebral straightening (39 patients) and no vertebral straightening (24 patients). This was followed by two affine transformations and a non-rigid transformation. Each registration was visually inspected, and non-vertebrally labeled slices that resulted in extrapolated vertebral registration were removed.

2.3. Jacobian Analysis

In spinal cord registration, the displacement difference is minimized by matching homologous points between the source and target image usually using a cost function or solving a differential equation¹⁰. The obtained displacement function is stored in the deformation field. Valuable information, specifically the Jacobian, can be extracted from the deformation field, which has been shown to identify growth rates in brain white matter⁷. Using the Jacobian as a scalar to analyze spinal cord growth should facilitate extraction of temporal and anatomical differences.

Each patient was processed by using a customized processing pipeline involving Advanced Normalization Tools (ANTs). Specifically, ANTs’s createJacobianDeterminantImage function was given the non-zero slices from the displacement field, consisting of displacement differences from the source to target image transformation. For a given source and target image pair and transformation $T = (T_{x}, T_{y}, T_{z})$ , the Jacobian operator (equation 1), $J_{T}$ , and volume change given by the registration transformation can be calculated slice-wise on the displacement field and by the determinant of the Jacobian operator⁹. The Jacobians were slice-wise calculated to reduce extrapolation errors followed by computing partial derivatives to columnwise voxels not part of the transformation. Not computing these images slice-wise would reduce Jacobian clarity as such partial derivatives can either approach infinity or zero, depending on its position in relation to the source image, and thus produce striations in between Jacobian slices. In fact, even after the Jacobians were slice-wise calculated, a partial boundary zone existed outside the CSF outline in nearly every patient. Thus, to homogenize Jacobian map anatomy, a flood-fill algorithm, operating on a recursive stack, was implemented in a custom python script to remove the partial boundary zone.

J_{T} = (\begin{matrix} \frac{\partial T_{x}}{\partial x} & \frac{\partial T_{x}}{\partial y} & \frac{\partial T_{x}}{\partial z} \\ \frac{\partial T_{y}}{\partial x} & \frac{\partial T_{y}}{\partial y} & \frac{\partial T_{y}}{\partial z} \\ \frac{\partial T_{z}}{\partial x} & \frac{\partial T_{z}}{\partial y} & \frac{\partial T_{y}}{\partial z} \end{matrix})

(1)

2.4. Statistical Analysis

Since most patients had scans that spanned multiple vertebral levels, it was necessary to account for dependence due to repeated measurements on a subject. A random effects regression analysis was therefore conducted on the Jacobian data to model the effects on age and vertebral location, including a random intercept for subject. We therefore tested the following models:

$H_{f u l l} : Y_{i} (v) = α_{0} + α (v) + β (v) a g e_{i} + γ_{i} + ε_{i} (v)$
$H_{v} : Y_{i} (v) = α_{0} + α (v) + β \times a g e_{i} + γ_{i} + ε_{i} (v)$

In the first model (H_full), the effect of age on cord size for subject i is a function of vertebral location, v. In the second model (H_v), there is no slowly varying effect of age across the spinal cord and the effect is the same across all cord locations. γ_i is a random effect for subject and ε_i is the error term. The functions α and β are fit with unpenalized natural cubic splines on 4 degrees of freedom to account for smoothness across adjacent vertebra. We further tested the effects across varied cord anatomy, specifically cord matter, GM, WM, lateral funiculi (LF), dorsal columns (DC), and ventral funiculi (VF). Random effects and residuals, ε_i, were evaluated for fit using QQ-plots. Random effect variance and intra-subject error was additionally evaluated. All models were fit using R 4.0.4^16–17.

The cervical cord was analyzed by each vertebral level (C1-C8) due to its large subject count. However, the thoracic cord has a smaller subject count, thereby making individual vertebral level analysis difficult for comparison (Figure 1). Therefore, the thoracic cord was binned for analysis with the upper-thoracic, mid-thoracic, and lower-thoracic cord consisting of T1-T2, T3-T8, and T9-T12 vertebral levels, respectively.

3. RESULTS

Observing the growth of cord matter by patient age and vertebral level suggested that the upper cervical spinal cord, specifically C2-C3, and mid-thoracic spinal cord, T3-T8, have the largest age-related changes (Figure 3 and 4). For each cord feature, we compared model (i) to model (ii). There was evidence for vetrabral differences in age-related changes in total cord volume. Other such cord features as white matter (WM), gray matter (GM), dorsal column (DC), lateral funiculi (LF), and ventral funiculi (VF) showed similar changes (Table 1).

Figure 3. — Tissue growth maps at C3 and C7 vertebrae binned by age. Cord growth in the C3 vertebrae is characterized by increased and decreased relative growth in the lateral and ventral funiculi and dorsal columns compared to other anatomy. WM further showed an increased growth rate compared to GM. On the other hand, cord growth in the C7 vertebrae is characterized by a moderate increase in growth across cord regions. Cord growth in the C7 is characterized by increased and decreased relative growth in the gray matter, ventral funiculi, and dorsal columns and lateral funiculi compared to other anatomy. Furthermore, GM and WM growth rates remained relatively consistent. C7 vertebral growth remained lower in magnitude compared to C3 growth.

Figure 4. — Tissue growth maps at T2 and T10 vertebrae binned by age. Cord growth in the T2 vertebrae is characterized by increased growth in the gray matter and ventral funiculi and decreased growth in the dorsal columns compared to other anatomy. GM further showed an increased growth rate compared to WM. On the other hand, cord growth in the T10 vertebrae is characterized by a mild increase in growth across cord regions. Similar to C3 vertebrae, there exists increased and decreased relative growth in the lateral and ventral funiculi and dorsal columns compared to other anatomy. Furthermore, WM showed an increased growth rate compared to GM. T10 vertebral growth remained lower in magnitude compared to T2. vertebral growth.

Table 1.

Vertebral differences in age-related changes in cord matter, gray matter, white matter, dorsal columns, lateral funiculi, and ventral funiculi are indicated based on significant p-values.

	F-value	df1	df2	P-value
Cord Matter	3.390	4.000	397.590	0.010
Gray Matter	4.848	4.000	397.832	0.001
White Matter	3.240	4.000	397.176	0.012
Dorsal Columns	2.513	4.000	397.274	0.041
Lateral Funiculi	3.303	4.000	397.858	0.011
Ventral Funiculi	2.707	4.000	396.680	0.030

Open in a new tab

By linearly modeling the Jacobian determinant by patient age, we observed relatively consistent growth rates across cord anatomy (GM, WM, DC, LF, VF) though whole cord variability existed from the upper cervical to lower thoracic cord as follows: VF (slope=8.41; R²=0.56) grew faster in upper cervical cord regions (C1-C3), DC (slope=7.46; R²=0.47) grew slower in mid-cervical cord regions (C4-C5), LF (slope=7.46; R²=0.22) grew slower in lower cervical cord regions (C6-C8), WM (slope=5.26; R²=0.21) and LF (slope=4.85; R²=0.16) grew slower in upper-thoracic cord regions (T1-T2), and GM (slope=5.09; R²=0.35) grew slower in mid-thoracic cord regions (T3-T8) relatively compared to other cord regions. Differences between cord anatomy across each vertebral level are presented as follows: VF (slope=8.41; R²=0.56) and GM (slope=7.23; R²=0.50) grew the fastest and slowest in upper cervical regions (C1-C3), VF (slope=8.45; R²=0.58) and LF (slope=8.53; R²=0.48) grew the fastest and DC (slope=7.46; R²=0.47) grew the slowest in mid-cervical regions (C4-C5), VF (slope=7.11; R²=0.45) and DC (slope=6.43; R²=0.40) grew the fastest and slowest in C6 cervical region, VF (slope=5.54; R²=0.25) and LF (slope=4.89; R²=0.20) grew the fastest and slowest in C7 cervical region, GM (slope=5.20; R²=0.22) and DC (slope=4.04; R²=0.16) grew the fastest and slowest in C8 cervical region, GM (slope=5.84; R²=0.28) and VF (slope=5.82; R²=0.24) grew the fastest and LF (slope=4.85; R²=0.16) grew the slowest in upper-thoracic cord regions (T1-T2), LF (slope=6.19; R²=0.39) and GM (slope=5.09; R²=0.35) grew the fastest and slowest in mid-thoracic cord regions (T3-T8), DC (slope=0.89; R²=0.01) and GM (slope=0.70; R²=0.01) grew the fastest and slowest in lower-thoracic cord regions (T9-T12).

Random effects testing for cord matter, GM, WM, DC, LF, and VF all resulted in p < 0.001 or significant p-values and variance proportion values 0.68, 0.70, 0.65, 0.65, 0.61, and 0.63 respectively. This indicated significant correlation between vertebral measurements (cord matter intraclass correlation coefficient ICC= 0.68).

Correlation analysis was further conducted to better understand Jacobian variability. Correlation differences between cord anatomy across each vertebral level and patient age are presented as follows: WM and VF had the largest and LF had the smallest correlation for upper-cervical regions (C1-C2), WM and VF had the largest and DC had the smallest correlation for upper- and mid-cervical regions (C3-C4), VF had the largest and DC had the smallest correlation for mid-cervical regions (C5-C6), GM, WM, and VF had the largest and DC had the smallest correlation for C7 cervical region, GM had the largest and LF had the smallest correlation for lower-cervical and upper-thoracic regions (C8-T2), DC had the largest and LF had the smallest correlation for mid-thoracic regions (T3-T8), and there was consistently poor correlation in the lower-thoracic cord (T9-T12).

The lower-thoracic cord in general had reduced growth rates compared to the upper- and mid-thoracic cord. In fact, the lower cervical spinal cord (C7-C8) had similar growth rates to the upper- and mid-thoracic cord.

4. CONCLUSION

Through Jacobian and random effects analysis, we observed overall growth of the pediatric cervical and thoracic cord with age across cord anatomy. Our data showed variability in whole cord growth, specifically increased growth in the cervical cord compared to the thoracic cord. Such cord regions as the upper cervical (C2-C3) and lower-thoracic cord (T9-T12) grow faster and slower respectively compared to other vertebral cord regions. Moreover, lower-thoracic cord regions (T9-T12) tend to grow slower compared to upper- and mid-thoracic cord regions (T1-T8) and upper- and mid-thoracic cord regions (T1-T8) grow slower compared to the upper– and mid-cervical cord (C2-C6).

Pediatric cervical spine morphometric analysis has indicated the C2 body as the largest segment for vertical growth³, which corresponds to our analysis suggesting that C2-C3 growth is greater relative to other vertebral regions. Furthermore, the majority of pediatric spinal canal grows by 4 years⁷, our analysis similarly showed cord matter to have significant growth until 4 years of age followed by consistent increasing growth till adulthood. In fact, spinal cord and brain maturation have some similarities, wherein larger age-related WM changes were observed compared to GM⁷. WM changes in the pediatric spinal cord have been shown to correspond with age-related DTI changes, specifically FA increase with age¹⁸.

Some caution is necessary when interpreting our results. Though the data was binned to better compare thoracic and cervical cord regions greater variability may exist. Compared to longitudinal studies, cross-sectional studies do have more limited conclusions as each subject represents a single time point. Furthermore, the relative Jacobian correlation in the thoracic cord was reduced compared to the cervical cord. Our results can be further supported by analyzing gender related differences and comparing age and gender changes with cord maturation.

ACKNOWLEDGEMENTS

This research was supported, in part, by the Surgical Outcomes Center for Kids at Monroe Carell Jr. Children’s Hospital at Vanderbilt; the Section for Surgical Sciences at Vanderbilt University Medical Center; National MS Society RG-1501–02480; National Institute of Neurological Disorders and Stroke awards 5R01 NS104149, 1R01 NS117816–01A1 and 1R01 NS109114; Vanderbilt Undergraduate Summer Engineering research stipend; and the Vanderbilt Chancellor’s Scholarship.

REFERENCES

[1].Nuckley DN, et al. , “Developmental biomechanics of the human cervical spine,” Journal of biomechanics 46(6), 1147–1154 (2013). [DOI] [PubMed] [Google Scholar]
[2].Vara CS and Thompson GT, “A cadaveric examination of pediatric cervical pedicle morphology,” Spine 31(10), 1107–1112 (2006). [DOI] [PubMed] [Google Scholar]
[3].Johnson KTJ, et al. , “Morphometric analysis of the developing pediatric cervical spine,” Pediatrics 18(3), 377–389 (2016). [DOI] [PubMed] [Google Scholar]
[4].Ferree BAF, “Morphometric characteristics of pedicles of the immature spine,” Spine 17(8), 887–891 (1992). [DOI] [PubMed] [Google Scholar]
[5].Boese CB, et al. , “Spinal cord injury without radiologic abnormality in children: a systematic review and meta-analysis,” Journal of trauma and acute care surgery 78(4), 874–882 (2015). [DOI] [PubMed] [Google Scholar]
[6].Pesenti SP, et al. , “Cervical facet orientation varies with age in children: An MRI study,” JBJS 100(9), e57 (2018). [DOI] [PubMed] [Google Scholar]
[7].Hua XH, et al. , “Detecting brain growth patterns in normal children using tensor‐based morphometry,” Human brain mapping 30(1), 209–219 (2009). [DOI] [PMC free article] [PubMed] [Google Scholar]
[8].Huster RJH, et al. , “Morphologic asymmetry of the human anterior cingulate cortex,” Neuroimage 34(3), 888–895 (2007). [DOI] [PubMed] [Google Scholar]
[9].Aljabar PA, et al. , “Assessment of brain growth in early childhood using deformation-based morphometry,” Neuroimage 39(1), 348–358 (2008). [DOI] [PubMed] [Google Scholar]
[10].Chung MK, et al. , “A unified statistical approach to deformation-based morphometry,” NeuroImage 14(3), 595–606 (2001). [DOI] [PubMed] [Google Scholar]
[11].Anderson CR, et al. , “Long-term maintenance of cervical alignment after occipitocervical and atlantoaxial screw fixation in young children,” Pediatrics 105(1), 55–61 (2006). [DOI] [PubMed] [Google Scholar]
[12].Hwang SW, et al. , “Outcomes of instrumented fusion in the pediatric cervical spine,” Spine 17(5), 397–409 (2012). [DOI] [PubMed] [Google Scholar]
[13].De Leener BD, et al. , “SCT: Spinal Cord Toolbox, an open-source software for processing spinal cord MRI data,” Neuroimage 145(A), 24–43 (2017). [DOI] [PubMed] [Google Scholar]
[14].De Leener BD, et al. , “PAM50: Unbiased multimodal template of the brainstem and spinal cord aligned with the ICBM152 space,” Neuroimage 165, 170–179 (2018). [DOI] [PubMed] [Google Scholar]
[15].Perone SP, et al. , “Spinal cord gray matter segmentation using deep dilated convolutions,” Scientific reports 8(1), 1–13 (2018). [DOI] [PMC free article] [PubMed] [Google Scholar]
[16].Bates D, et al. , “Fitting Linear Mixed-Effects Models Using lme4.” Journal of Statistical Software 67(1), 1–48 (2015). [Google Scholar]
[17].Kuznetsova A, et al. , “ImerTest Package: Tests in Linear Mixed Effects Models.” Journal of Statistical Software 82(13), 1–26 (2017). [Google Scholar]
[18].Reynold BB, et al. , “Quantification of DTI in the pediatric spinal cord: application to clinical evaluation in a healthy patient population.” American Journal of Neuroradiology 40(7), 1236–1241 (2019). [DOI] [PMC free article] [PubMed] [Google Scholar]

PERMALINK

Mapping Pediatric Spinal Cord Development with Age

Ashwin Kumar

Simon Vandekar

Kurt Schilling

Aashim Bhatia

Bennett A Landman

Seth Smith

Abstract

1. INTRODUCTION