Researchers interested in quantitative susceptibility mapping of bone.

Bone QSM promises to image calcified minerals in bone, but it is challenging, because bone has rapid T2*(~0.2 ms) signal decay that typically cannot be acquired in standard Cartesian acquisitions (TE 2ms). Recently, bone QSM was shown to be feasible using ultra-short echo time radial gradient echo sequences (UTE) [1]. However, in vivo bone QSM remains challenging, as inconsistent field mapping in the presence of rapidly decaying signal and bone marrow fat often causes erroneous susceptibility in cortical bone.

Here we present a robust field mapping in bone based on a realistic biophysical model for fat signal evolution incorporating multiple spectral peaks and negligible T2* decay in UTE. This corrects the prior model for fat signal that assumed single spectral peak and same T2* decay as water within the voxel, enabling robust bone QSM in clinically applicable acquisition times for assessing bone mineralization without the use of ionizing radiation.

Pulse sequence design: A 3D radial UTE sequence was implemented on a 3T scanner (16.0 GE, Waukesha, WI) [2]. The sequence used a nonselective hard pulse to achieve volumetric excitations and two readouts per TR to accelerate acquisition.

Imaging: 4 echoes were acquired with the following scan parameters: FA = 15, FOV = 18 cm, 35000 radial projections, TR = 14 ms, TE = 0.04, 0.24, 3.0, 4.0 ms. Non-isotropic voxel size (0.7$$$\times$$$0.7$$$\times$$$1.4 mm) was used to increase SNR. Total acquisition time was 12 minutes without parallelization.

Reconstruction: For comparison, field estimation was done using standard R2*-IDEAL [3], multi-peak R2*-IDEAL [4] and a tissue dependent R2* multi-peak fat/water decomposition assuming the following signal equation:$$s(\vec{r},t) = \Big(\rho_w(\vec{r})e^{{-R_2^*}_w t} + \rho_f(\vec{r})\sum_n\alpha_{f,n} e^{-i2\pi f_{f,n}t}\Big)\cdot e^{-i2\pi f_s (\vec{r}) t}$$

Here $$$\rho_w$$$ and $$$\rho_f$$$ are the complex amplitudes of water and fat signals originating form the the voxel $$$\vec{r}$$$ at time $$$t = 0$$$, $$${R_2^*}_w$$$ is the water signal decay rate, $$$\alpha_{f,n}$$$ is the relative amplitude of n^th peak in chemical spectrum of fat [4], $$$f_{f,n}$$$ is its resonant frequency shift, and $$$f_s$$$ is the total spatially varying field induced by all susceptibility sources.

The structure of this equation reflects the fact that bone water is the only species that experiences significant decay by the time of the last echo (4ms). Although possible, introduction of the additional parameter to model R2* effects in fat would increase overall complexity of the problem, making it more sensitive to noise [5].

Experiments: Multiple body regions (knees and wrist ) were imaged in 5 healthy volunteers and the acquired data was processed using the proposed technique.

QSM reconstruction using the proposed method was successful in all cases. Comparison of field maps estimated with different techniques and corresponding calculated susceptibility distributions are shown in Fig 1. Systematic overestimations of the fat fraction within bone and tendon areas were observed in maps calculated using conventional estimators. These errors manifested themselves in field and, subsequently, susceptibility maps, leading to significant error in bone and tendon susceptibility values.

Table 1 summarizes results of volunteer scans, showing good intra- and inter-subject agreement of bone susceptibility values (-1.55±0.17 ppm). Fig.2 shows a thin-slice (5 mm) minIP of susceptibility map reconstructed for a knee (left) and wrist (right).

Correct estimation of the susceptibility field map is a crucial step in quantitative susceptibility mapping. Field mapping from rapidly decaying signals of bone is challenging. Water fat separation using standard IDEAL signal models that assign same T2* to both water and fat species leads to erroneous labeling of the water component in the cortical bone (1^st -3^rd columns vs 5^th column in Fig.1). Modeling bone marrow fat with negligible R2* and rapid R2* decay of water dispersed in the calcified matrix more accurately reflects local tissue physics. Also important is that fat inside cortical bone consists of multiple spectral peaks, as suggested by our experimental data (4th vs 5th columns in Fig.1).

Accordingly, our proposed signal model using the tissue specific T2* and multi-peak fat spectrum corrects errors in the standard IDEAL, allowing robust water/fat separation, accurate field estimation resulting in improvements bone QSM (Fig.2, Table 1). Bone QSM using tissue specific R2* and a multi-peak fat spectrum allows robust field estimation and enables consistently higher bone QSM image quality.