Dependence of Anisotropy of Human Lumbar Vertebral Trabecular Bone on Quantitative Computed Tomography-Based Apparent Density
Bibliographic record
Abstract
Most studies investigating human lumbar vertebral trabecular bone (HVTB) mechanical property-density relationships have presented results for the superior-inferior (SI), or "on-axis" direction. Equivalent, directly measured data from mechanical testing in the transverse (TR) direction are sparse and quantitative computed tomography (QCT) density-dependent variations in the anisotropy ratio of HVTB have not been adequately studied. The current study aimed to investigate the dependence of HVTB mechanical anisotropy ratio on QCT density by quantifying the empirical relationships between QCT-based apparent density of HVTB and its apparent compressive mechanical properties--elastic modulus (E(app)), yield strength (σ(y)), and yield strain (ε(y))--in the SI and TR directions for future clinical QCT-based continuum finite element modeling of HVTB. A total of 51 cylindrical cores (33 axial and 18 transverse) were extracted from four L1 human lumbar cadaveric vertebrae. Intact vertebrae were scanned in a clinical resolution computed tomography (CT) scanner prior to specimen extraction to obtain QCT density, ρ(CT). Additionally, physically measured apparent density, computed as ash weight over wet, bulk volume, ρ(app), showed significant correlation with ρ(CT) [ρ(CT) = 1.0568 × ρ(app), r = 0.86]. Specimens were compression tested at room temperature using the Zetos bone loading and bioreactor system. Apparent elastic modulus (E(app)) and yield strength (σ(y)) were linearly related to the ρ(CT) in the axial direction [E(SI) = 1493.8 × (ρ(CT)), r = 0.77, p < 0.01; σ(Y,SI) = 6.9 × (ρ(CT)) − 0.13, r = 0.76, p < 0.01] while a power-law relation provided the best fit in the transverse direction [E(TR) = 3349.1 × (ρ(CT))(1.94), r = 0.89, p < 0.01; σ(Y,TR) = 18.81 × (ρ(CT))(1.83), r = 0.83, p < 0.01]. No significant correlation was found between ε(y) and ρ(CT) in either direction. E(app) and σ(y) in the axial direction were larger compared to the transverse direction by a factor of 3.2 and 2.3, respectively, on average. Furthermore, the degree of anisotropy decreased with increasing density. Comparatively, ε(y) exhibited only a mild, but statistically significant anisotropy: transverse strains were larger than those in the axial direction by 30%, on average. Ability to map apparent mechanical properties in the transverse direction, in addition to the axial direction, from CT-based densitometric measures allows incorporation of transverse properties in finite element models based on clinical CT data, partially offsetting the inability of continuum models to accurately represent trabecular architectural variations.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".