Calcium phosphate cement (CPC) is a widely used material for bone defect restoration. To monitor the dynamic interactions of bone and CPC, different studies estimated their MR properties, such as T₁ and T₂^* relaxation times.^1,2 While decent MR images of CPC and bone have been achieved at high field, their T₂^* quantification remained unsatisfactory with a mono-exponential (ME) fit for the multi-echo time (TE) gradient echo (GRE) signals. A likely reason is that Gaussian rather than Lorentzian functions are more suitable for characterizing the intra-voxel frequency distributions at high field, so that ME is inadequate for signal decay modeling.³ Recent studies proposed a Gaussian augmentation of the mono-exponential (GAME) model, outperforming the ME model in characterizing GRE signals especially at high field.^3,4 Therefore, in this study we compared ME and GAME fits for the multi-TE GRE signals of bone material acquired at 11.7T to determine the optimal model in the derivation of their transverse relaxation properties.

Materials.

CPC consists of 59.1wt% alpha-tricalcium phosphate, 1.5wt% carboxymethyl cellulose (Cambioceramics, Leiden, The Netherlands) and 39.4wt% cryo-grinded poly-lactic-co-glycolic acid particles (PURASORB, Purac, Groningen, The Netherlands). One human molar tooth, surrounded with 5% gelatine in a falcon tube, was drilled with a vertical hole on the occlusal surface and filled with CPC (~10mm³).

Experiments.

Ultra-short TE (UTE) measurements were performed on a 11.7T MR-system (Biospec, Bruker, Germany) using a quadrature ¹H volume coil with 40mm inner diameter. 15 TEs from 28-508µs with increments of 10-100µs, TR=18ms, FA=11° and image resolution=0.3mm³ were applied.

Data Analysis.

The acquired multi-TE UTE data were, respectively, fitted using ME and GAME models in Matlab (Mathworks, Natick, MA) with unconstrained nonlinear optimization. The equation $$$S\left(TE\right)=S_{0}\times e^{\frac{-TE}{T_2^*}}$$$ was used as ME model to extract the pseudo-spin density S₀ and T₂^* relaxation time. Additionally, the equation $$$S\left(TE\right)=S_{0}\times e^{\frac{-TE}{T_2^\prime}}\times e^\frac{-\frac{TE^{2}}{\sigma^{2}}}{2}$$$,⁴ was applied as GAME model for data fitting, where S₀, and the irreversible and reversible transverse relaxation time T₂^' and σ were then obtained. The Gaussian half-width-at-maximum (HWHM) is $$$\frac{\sqrt{2\log_{e}{2}}}{\sigma}$$$.

Regions of interest (ROIs) in CPC and the tooth components (i.e., enamel and dentine) were manually outlined. Goodness of fit for each model was evaluated by calculating the sum of squared errors (SSE) and R-squared values.

A representative UTE tooth image acquired at TE=28µs shows anatomical details such as dentine, enamal and CPC (Fig.1A). Axial images of three consecutive slices at the blue line in Fig.1A are shown in Fig.1B-D. Different ROIs (pink) for CPC were selected in each image and their transverse relaxation times (i.e., T₂^*,T₂^' and σ) were estimated using ME and GAME models (Fig.1B-D). Compared to ME modeling (blue), the GAME modeling (red) performs much better with significantly smaller SSE (p<0.03) and higher R-squared values (p<0.01;Fig.2).

In addition to CPC regions, the signal decays in dentine and enamel were also fitted by GAME and ME models. A slightly better performance is found for dentine (Fig.1E) and a comparable performance for enamel (Fig.1F).

Parametric maps from the ME and GAME fits are shown in Fig.3 for a typical image slice through the tooth. Transverse relaxations in the CPC region from the ME fit (Fig.3B) have different proportions of irreversible and reversible relaxation contributions, which can be separated by GAME fit (Fig.3C,D). In comparison, σ in most dentine and enamel regions are approaching to infinite and thus the transverse relaxations in these regions are dominated by an irreversible relaxation contribution.

We demonstrate that the GAME model performs robustly in GRE signal fitting of bone material at high field, as has also been observed in other tissues at high field.^3,4 The ME model is not sufficient to fit decays of at least CPC material, showing a distinct curvature on semi-log plots (Fig.1B-D). Compared to the tooth components, the CPC region might have more complex susceptibilities caused by increased interfaces of air/CPC and CPC/tooth. The correspondingly induced susceptibility gradients with strong magnitude and high-order variations at high field might be responsible for the curve-shaped signals in CPC, which require a proper fit with an extra Gaussian function.

In conclusion, this study demonstrates that a GAME rather than ME model is suitable for proper modeling of the time course of GRE in CPC and dentine at ultra-high field. This method might also be valuable for high field relaxometry studies of other bone tissues.