Figure 3: a) FA and b) TR sequences at initiation and after optimisation for multi-component MRF. Optimisation was performed for tissue parameters {$$$T_{1}^{a}$$$, $$$T_{2}^{a}$$$, $$$M_{0}^{a}$$$} = {700ms, 60ms, 0.3} and {$$$T_{1}^{b}$$$, $$$T_{2}^{b}$$$, $$$M_{0}^{b}$$$} = {1100ms, 102ms, 0.3} with the constraints mentioned in the Methods section. Different initialisation of the optimisation problem returned the same result.

Figure 5: Relative CRB values were calculated using the multi-component Fisher matrix for a conventional MRF sequence (row 1) and an optimised sequence (row 2). The difference is shown in row 3 by subtracting the second row from the first. The rCRB is defined as $$$\text{rCRB} = \frac{\text{CRB}}{\sigma^2 \theta^2}$$$ where θ represents T₁^a, T₂^a or M₀^a. Tissue parameters for one tissue (superscript a) were fixed at T₁^a = 800 ms, T₂^a = 80 ms, while T₁^b and T₂^b for the second tissue (superscript b) vary. In the centre red dot the 2 tissues are exactly the same, resulting in a singularity.