# Optimization of acquisition schemes towards a better estimation of microstructure parameters in diffusion MRI

Constance Bocquillon, Isabelle Corouge, Emmanuel Caruyer

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Constance Bocquillon, Isabelle Corouge, Emmanuel Caruyer. Optimization of acquisition schemes towards a better estimation of microstructure parameters in diffusion MRI. ISMRM 2025 - Workshop on 40 years of diffusion: Past, Present & Future Perspectives, Feb 2025, Kyoto (Japan), Japan. 2025. hal-05368999

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Submitted on 17 Nov 2025

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# Optimization of acquisition schemes towards a better estimation of microstructure parameters in diffusion MRI

Constance Bocquillon¹, Isabelle Corouge¹, and Emmanuel Caruyer¹

¹University of Rennes, INRIA, CNRS, INSERM, IRISA UMR 6074, Empenn ERL U-1228, Rennes, France.

**Target audience:** This work will benefit people interested in microstructure, acquisition design, using diffusion tensor distribution or working in multidimensional diffusion MRI.

**Purpose:** Unlike traditional measurements by diffusion tensor imaging, multidimensional diffusion MRI allows the estimation of additional microstructural parameters in order to better describe the different contributions to the signal. We propose to evaluate our sensitivity to reconstruct the parameters of diffusion tensor distributions (DTD) [1] using b-tensor acquisitions and to optimize the choice of acquisition schemes for this reconstruction.

**Methods:** We generated a superset of cylindrical b-tensors ($b_{max}=2000s/mm^2$; step of 100s/mm$^2$) from which we selected the final scheme. The optimization criterion evaluates the ability to discriminate DTDs generated from a set of values of our microstructure parameters of interest: microscopic anisotropy (µFA), tensor size variance ($C_{MD}$) as well as the orientation parameter (OP). The microscopic anisotropy ranges from 0 to 1 where 0 corresponds to spherical microscopic tensors, and 1 corresponds to a distribution of sticks-like tensors. The tensor size variance describes the variance of the mean diffusivity of the microscopic tensors. It starts at 0 where all the microscopic tensors have the same size and increases with the size disparities. The orientation parameter ranges from 0 to 1 where 0 corresponds to fully randomly oriented tensors and 1 to fully aligned ones.

Inspired by fingerprinting methods [2], we generated a dictionary of signals where the columns are the representatives of the DTDs and the rows are the b-tensor encoded acquisitions of the superset. To do this, we divided the parameter space according to the resolution that could be achieved using the signal on each parameter of interest. That division was inspired by octrees and is represented in Figure 1.

For a given acquisition scheme, we consider that two DTDs can be discriminated if the distance between their corresponding vector of signals is greater than a threshold (here 1/SNR). We tested two optimization algorithms to find, among all subset of b-tensors, the subset that maximises the number of distinguishable DTDs. The first one is a greedy algorithm. We simply selected the best shape – the one increasing the most the number of new pairs of DTDs that could be discriminated – available until we selected the desired number of shapes. The second is a permutation approach. We generated a number of random initial selections (here 100) and we permuted the weakest shape in the selection – the one increasing the least the number of new pairs of DTDs that could be discriminated – with the next best one available until we reached a local maximum. We only keep the best scheme generated out of these repetitions.

Finally, we estimated each DTD parameter using the QTI+ [3] implementation in Dipy [4]. We compared the parameter estimation results with the scheme Q3 optimized for this purpose [5].

**Results:** We generated schemes selecting 4 shapes of b-tensors, using 30 directions each in order to compare the results with the 120 acquisitions from Q3. We also made sure to keep the same range of b-values. The repartition is detailed in Table 1. We estimated DTDs parameters using each of these schemes. Figure 2 shows the estimation error in µFA on its full range with an SNR of 30, a high OP and a medium $C_{MD}$. Figure 3 shows the estimation error in OP in its full range with an SNR of 30, a high µFA and a medium $C_{MD}$.

**Discussion:** While the permutation approach produces the highest level of errors, the acquisition scheme generated from the greedy algorithm perform as well as the reference scheme or better.

Our approach is promising and can be further improved in several ways. Our current work is to adapt the number of directions based of the b-value and the shape of the b-tensor. Future work will consider the impact of the shape and its b-value on the echo time (TE) of the waveform to ensure improvements on the final acquisition time.

**Conclusion:** The acquisition schemes greatly influence the estimation of microstructure parameters. Our approach allows us to generate acquisition scheme optimized towards the reconstruction of selected parameters and could be implemented for others models with a reasonable number of parameters in order to generate acquisition schemes specifically tailored for the reconstruction of their parameters. Moreover, such optimized acquisition protocols can be implemented on a clinical MR scanner.

**References:**

[1] Westin CF, Knutsson H, Pasternak O, et al. Q-space trajectory imaging for multidimensional diffusion MRI of the human brain. Neuroimage. 2016;135:345-362.

[2] Rensonnet G, Scherrer B, Girard G, et al. Towards microstructure fingerprinting: Estimation of tissue properties from a dictionary of Monte Carlo diffusion MRI simulations. Neuroimage. 2019;184:964-980.

[3] Herberthson M, Boito D, Haije TD, et al. Q-space trajectory imaging with positivity constraints (QTI+). Neuroimage. 2021;238:118198.

[4] Garyfallidis E, Brett M, Amirbekian B, et al. Dipy, a library for the analysis of diffusion MRI data. Front Neuroinform. 2014;8:8.

[5] Morez J, Szczepankiewicz F, den Dekker AJ, et al. Optimal experimental design and estimation for q-space trajectory imaging. Hum Brain Mapp. 2023. 44(4):1793-1

<figure><img src="image_2.png" /><figcaption>Figure 1: Division of the parameter space in boxes of DTD with generated signal according to the achievable resolution.</figcaption></figure>

<table><caption>Table 1: Repartition of the b-tensor encoded acquisitions. Q3 is the reference scheme, PTE corresponds to planar b-tensors, OTE to oblate b-tensors, STE to spherical b-tensors and LTE to linear b-tensors.</caption><thead><tr><th colspan="5">Q3</th></tr><tr><th>b (s/mm²)</th><th>PTE</th><th>OTE</th><th>STE</th><th>LTE</th></tr></thead><tbody><tr><td>100</td><td>7</td><td>-</td><td>-</td><td>9</td></tr><tr><td>800</td><td>9</td><td>-</td><td>-</td><td>50</td></tr><tr><td>2000</td><td>-</td><td>-</td><td>30</td><td>15</td></tr></tbody><tbody><tr><th colspan="5">Greedy algorithm</th></tr><tr><th>b (s/mm²)</th><th>PTE</th><th>OTE</th><th>STE</th><th>LTE</th></tr><tr><td>1000</td><td>30</td><td>-</td><td>-</td><td>-</td></tr><tr><td>1200</td><td>-</td><td>30</td><td>-</td><td>-</td></tr><tr><td>1300</td><td>-</td><td>-</td><td>-</td><td>30</td></tr><tr><td>2000</td><td>-</td><td>-</td><td>-</td><td>30</td></tr></tbody><tbody><tr><th colspan="5">Permutation algorithm</th></tr><tr><th>b (s/mm²)</th><th>PTE</th><th>OTE</th><th>STE</th><th>LTE</th></tr><tr><td>1100</td><td>-</td><td>30</td><td>-</td><td>-</td></tr><tr><td>1200</td><td>30</td><td>-</td><td>-</td><td>30</td></tr><tr><td>1300</td><td>-</td><td>-</td><td>-</td><td>30</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>Figure 2: µFA estimation error at SNR 30 with a high OP. In blue, the reference scheme; in orange, the greedy algorithm result; in green, the permutation algorithm result.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 3: OP estimation error at SNR 30 with a high µFA. In blue, the reference scheme; in orange, the greedy algorithm result; in green, the permutation algorithm result.</figcaption></figure>