A robust methodology for in vivo T1 mapping

Abstract

In this article, a robust methodology for in vivo T(1) mapping is presented. The approach combines a gold standard scanning procedure with a novel fitting procedure. Fitting complex data to a five-parameter model ensures accuracy and precision of the T(1) estimation. A reduced-dimension nonlinear least squares method is proposed. This method turns the complicated multi-parameter minimization into a straightforward one-dimensional search. As the range of possible T(1) values is known, a global grid search can be used, ensuring that a global optimal solution is found. When only magnitude data are available, the algorithm is adapted to concurrently restore polarity. The performance of the new algorithm is demonstrated in simulations and phantom experiments. The new algorithm is as accurate and precise as the conventionally used Levenberg-Marquardt algorithm but much faster. This gain in speed makes the use of the five-parameter model viable. In addition, the new algorithm does not require initialization of the search parameters. Finally, the methodology is applied in vivo to conventional brain imaging and to skin imaging. T(1) values are estimated for white matter and gray matter at 1.5 T and for dermis, hypodermis, and muscle at 1.5 T, 3 T, and 7 T.

Figure 1

Influence of SNR and T₁. (a) RMSE of the T₁ estimates using the complex data (RD-NLS) and the polarity-restored magnitude data (RD-NLS-PR), together with the CRLB, for different σ_n. (b) T₁ estimates as a function of true T₁ values. Each column gives a histogram of the T₁ estimate distribution for a given true T₁. The precision worsens as the true T₁ increases.

Figure 2

Brain T₁ maps at 1.5 T. Three slices were imaged and the RD-NLS algorithm was used on the complex data.

Figure 3

Brain T₁ histogram. The three imaged slices were aggregated. Peaks corresponding to white matter (653 ms) and gray matter (1173 ms) are visible. The leftmost peak corresponds to skull and is segmented out when ROIs are specified.

Figure 4

Skin images obtained at 3 T with the SE-IR sequence. Inversion times are (a) 50 ms, (b) 400 ms, (c) 1100 ms, and (d) 2500 ms. The following structures can be recognized: E: epidermis; D: dermis; H: hypodermis; M: muscle.

Figure 5

(a) Map of the a parameter (magnitude) and (b) T₁ map obtained at 3 T with the SE-IR sequence. The a map has contributions from T₂, proton density, and coil sensitivity. The dermis has a low proton density and a short T₂ (32). The coil sensitivity drops as the distance from the skin surface increases. The T₁ map shows the dermis heterogeneity.

Figure 6

ROI in (a) dermis, (b) hypodermis, and (c) muscle. Hypodermis and muscle are segmented using a region growing algorithm. The threshold used is the same for hypodermis and muscle, and the ROIs are independent of the seed position. The dermis is obtained by subtraction, and therefore includes the epidermis.

Figure 7

Histograms obtained in (a) dermis, (b) hypodermis, and (c) muscle at 3 T with the SE-IR sequence. σ is the root mean square deviation about the mode.

Figure 8

Dispersion plot obtained from Table 3. For the hypodermis, T₁ depends linearly on the field strength. A linear trend is also observed in dermis and muscle, but variability is more pronounced.