PETRA-Derived Pseudo-CT for Ultrasound Planning

• PETRA-derived pseudo-CT is an MR-only workflow that converts ultrashort-echo-time images into CT-equivalent Hounsfield maps using an affine transformation based on paired scans and PCA.
• The method employs a detailed preprocessing pipeline—including registration, bias correction, and histogram normalization—to accurately map normalized PETRA intensities to CT values for acoustic simulations.
• Validation studies demonstrate sub-millimeter focal-position errors and comparable pressure and volume metrics in both in-vivo and ex-vivo settings, supporting its use in precise transcranial ultrasound planning.

Searching arXiv for the cited paper and closely related pseudo-CT/transcranial-ultrasound work. PETRA-derived pseudo-CT denotes a pseudo-computed-tomography workflow in which the ultrashort-echo-time magnetic resonance sequence pointwise encoding time reduction with radial acquisition (PETRA) is converted into a pseudo-CT suitable for transcranial ultrasound simulations. In the reported formulation, paired CT and PETRA scans from human subjects and ex-vivo skulls are used to establish an affine relationship between normalized PETRA intensity and CT Hounsfield Units, after which the resulting pseudo-CT is used for acoustic simulation and validation against CT-based planning and experimental measurements. The approach is presented as a means to reduce subject exposure to ionising radiation while preserving accurate acoustic field prediction for precision focused transcranial ultrasound applications (Miscouridou et al., 1 Aug 2025).

1. Definition and research setting

PETRA is described as an ultrashort-echo-time sequence used here because of its stronger ability to image bones (Miscouridou et al., 1 Aug 2025). Within transcranial ultrasound stimulation and related planning workflows, ultrasound simulations currently depend on converting computed tomography images to acoustic properties. The reported motivation for PETRA-derived pseudo-CT is therefore the replacement of CT acquisition by an MR-based surrogate in settings where ionising radiation is undesirable or unavailable (Miscouridou et al., 1 Aug 2025).

The underlying study acquired a dataset of paired CT and PETRA scans separately for human subjects and ex-vivo skulls, then performed principal component analysis on bone voxels to uncover the affine relationship converting PETRA images to pseudo-CTs. Acoustic simulations based on CTs and pseudo-CTs were performed in k-Plan and k-wave, and the resulting focal metrics were compared in both in-vivo and ex-vivo settings (Miscouridou et al., 1 Aug 2025).

A plausible implication is that PETRA-derived pseudo-CT belongs to the broader class of MR-only planning methods, but its defining feature in this formulation is the use of a simple affine transform derived from PETRA bone signal rather than a data-hungry learned image-to-image translation pipeline.

2. PETRA acquisition and preprocessing

PETRA is specified as an ultrashort-echo-time sequence with approximately $\mathrm{TE} \approx 0.07 \ \mathrm{ms}$ and $\mathrm{TR} \sim 1$–$3.6 \ \mathrm{ms}$, available on Siemens Prisma scanners at $3 \ \mathrm{T}$ with a 64-channel Head/Neck coil (Miscouridou et al., 1 Aug 2025). The sequence uses radial sampling plus a small Cartesian centre-k-space block to avoid the dead-time gap of zero-echo-time methods. The stated advantages for bone imaging are very short $T_2^\*$-sensitive acquisition that preserves cortical bone water signal, efficient low-frequency component capture, a radial pattern robust to motion, and implementation on clinical scanners (Miscouridou et al., 1 Aug 2025).

Typical PETRA parameters are given as $\mathrm{TR} = 1$–$3.61 \ \mathrm{ms}$, $\mathrm{TE} = 0.07 \ \mathrm{ms}$, flip-angle approximately $1$–$2^\circ$, 320 slices per slab, slice thickness $\mathrm{TR} \sim 1$0, and field of view matched to CT with in-plane resolution of approximately $\mathrm{TR} \sim 1$1 (Miscouridou et al., 1 Aug 2025).

The preprocessing workflow for each subject contains four steps:

1. Rigid registration of PETRA to CT using FSL with 12 degrees of freedom and normalized mutual information.
2. N4 bias-field correction using ANTs to remove coil inhomogeneities.
3. Histogram normalisation of PETRA to shift the soft-tissue peak to unity.
4. Head, bone and air segmentation, with CT-based masks by thresholding and morphological operations in k-Plan for precise bone voxels in mapping, and MR-based head and skull masks via SPM12 and MATLAB for pseudo-CT generation in practical non-CT workflows (Miscouridou et al., 1 Aug 2025).

These preprocessing stages are central because the subsequent affine mapping is applied only after intensity normalization and voxel selection. This suggests that the reported PETRA-to-CT relation is not a raw scanner-space correspondence, but a calibrated relation contingent on registration, bias correction, and histogram normalization.

3. PCA-derived affine mapping

The pseudo-CT generation pipeline is based on principal component analysis on paired bone voxels. Given $\mathrm{TR} \sim 1$2 paired bone voxels $\mathrm{TR} \sim 1$3, where $\mathrm{TR} \sim 1$4 are normalized PETRA intensities and $\mathrm{TR} \sim 1$5 the CT Hounsfield Units, principal component analysis is performed on the $\mathrm{TR} \sim 1$6 data matrix

$\mathrm{TR} \sim 1$7

with covariance matrix

$\mathrm{TR} \sim 1$8

The first eigenvector direction $\mathrm{TR} \sim 1$9 is then used to identify the linear trend (Miscouridou et al., 1 Aug 2025).

In practice, this reduces to an affine model

$3.6 \ \mathrm{ms}$0

From the first principal component, the reported in-vivo mapping is

$3.6 \ \mathrm{ms}$1

with

$3.6 \ \mathrm{ms}$2

Here PETRA is unitless after normalization and CT is expressed in Hounsfield units (Miscouridou et al., 1 Aug 2025).

For direct density mapping including the CT phantom calibration, the reported expression is

$3.6 \ \mathrm{ms}$3

The mathematical summary also gives the PCA decomposition as

$3.6 \ \mathrm{ms}$4

and states the affine model as

$3.6 \ \mathrm{ms}$5

All of these relations are reported explicitly for the PETRA-derived pseudo-CT pipeline (Miscouridou et al., 1 Aug 2025).

A plausible implication is that the method emphasizes parametric interpretability: the image-to-image conversion is expressed as a low-dimensional linear relation on bone voxels rather than as a black-box synthesis model.

4. Pseudo-CT volume construction and quantitative measures

Using MR-derived masks only, pseudo-CT volume creation assigns each voxel according to three classes:

• background or air mask $3.6 \ \mathrm{ms}$6,
• head or soft-tissue mask $3.6 \ \mathrm{ms}$7,
• skull mask $3.6 \ \mathrm{ms}$8 Eq. (1) applied to PETRA intensity (Miscouridou et al., 1 Aug 2025).

Voxel-wise agreement between pseudo-CT and ground-truth CT is quantified by the mean absolute error and root-mean-square error:

$3.6 \ \mathrm{ms}$9

$3 \ \mathrm{T}$0

where $3 \ \mathrm{T}$1 is the pseudo-CT value and $3 \ \mathrm{T}$2 the ground-truth CT value (Miscouridou et al., 1 Aug 2025).

For acoustic comparison, the reported focal metrics use subscripts $3 \ \mathrm{T}$3 to denote CT and pseudo-CT simulations:

• focal-position error:

$3 \ \mathrm{T}$4

• peak-pressure error:

$3 \ \mathrm{T}$5

• focal-volume error:

$3 \ \mathrm{T}$6

These definitions matter because the reported validation focuses not on conventional image-similarity alone, but on task-level equivalence in acoustic field prediction.

5. In-vivo validation for transcranial ultrasound planning

The in-vivo study included 7 subjects scanned with PETRA and low-dose CT of less than $3 \ \mathrm{T}$7 (Miscouridou et al., 1 Aug 2025). The PETRA acquisition was low flip-angle and 3D distortion corrected, and pseudo-CT to CT mapping was obtained by PCA on CT-derived skull masks (Miscouridou et al., 1 Aug 2025).

Acoustic simulation followed a k-Plan to k-Wave workflow with 4 sonications per subject, targeting left and right visual and motor cortex sites at $3 \ \mathrm{T}$8, using $3 \ \mathrm{T}$9, $T_2^\*$0 for soft tissue, and $T_2^\*$1. For skull modelling, density was obtained via CT-phantom calibration, speed of sound by

$T_2^\*$2

and attenuation by

$T_2^\*$3

These parameters are reported directly for the in-vivo simulation setup (Miscouridou et al., 1 Aug 2025).

The corresponding in-vivo acoustic errors between CT and pseudo-CT were:

Metric	Reported value
Focal-position error $T_2^\*$4	$T_2^\*$5
Peak-pressure error $T_2^\*$6	$T_2^\*$7
Focal-volume error $T_2^\*$8	$T_2^\*$9

These values are presented as evidence that PETRA-derived pseudo-CT yields small errors for in-vivo data (Miscouridou et al., 1 Aug 2025). A plausible implication is that the conversion preserves the skull-dependent acoustic parameters sufficiently well for high-precision neuromodulation planning at the tested frequency.

6. Ex-vivo validation against hydrophone measurements

The ex-vivo study used 3 human calvaria with high-dose CT acquired at $\mathrm{TR} = 1$0, $\mathrm{TR} = 1$1, and $\mathrm{TR} = 1$2 resolution, together with PETRA (Miscouridou et al., 1 Aug 2025). For this setting, the mapping was fit separately as

$\mathrm{TR} = 1$3

The need for a separate ex-vivo fit is explicitly stated in the discussion, which notes that ex-vivo mapping must be refit because in-vivo soft tissue is required for histogram normalisation (Miscouridou et al., 1 Aug 2025).

Hydrophone experiments were performed at $\mathrm{TR} = 1$4, $\mathrm{TR} = 1$5, and $\mathrm{TR} = 1$6 and $\mathrm{TR} = 1$7 using H115, H104, and H101 transducers in a $\mathrm{TR} = 1$8 scan plane with $\mathrm{TR} = 1$9 steps, with water temperature at $3.61 \ \mathrm{ms}$0. In-skull cortical field measurement was obtained via angular-spectrum reconstruction. The k-Wave simulation used $3.61 \ \mathrm{ms}$1, $3.61 \ \mathrm{ms}$2, a GPU cluster, and equivalent-source holograms (Miscouridou et al., 1 Aug 2025).

The reported mean $3.61 \ \mathrm{ms}$3 standard deviation errors over $3.61 \ \mathrm{ms}$4 skulls $3.61 \ \mathrm{ms}$5 frequencies are:

Comparison	$3.61 \ \mathrm{ms}$6	$3.61 \ \mathrm{ms}$7	$3.61 \ \mathrm{ms}$8
CT vs experiment	$3.61 \ \mathrm{ms}$9	$\mathrm{TE} = 0.07 \ \mathrm{ms}$0	$\mathrm{TE} = 0.07 \ \mathrm{ms}$1
pCT vs experiment	$\mathrm{TE} = 0.07 \ \mathrm{ms}$2	$\mathrm{TE} = 0.07 \ \mathrm{ms}$3	$\mathrm{TE} = 0.07 \ \mathrm{ms}$4
CT vs pCT	$\mathrm{TE} = 0.07 \ \mathrm{ms}$5	$\mathrm{TE} = 0.07 \ \mathrm{ms}$6	$\mathrm{TE} = 0.07 \ \mathrm{ms}$7

The study states that the similarity of the experimental errors for both methods validates the use of PETRA-derived pseudo-CT as an alternative to CT for precise acoustic field predictions (Miscouridou et al., 1 Aug 2025). This suggests that, in the tested ex-vivo setting, modelling and measurement discrepancies are of comparable order for CT-based and PETRA-based planning.

7. Advantages, limitations, and implementation

The stated benefits of PETRA-derived pseudo-CT are elimination of ionising radiation, high bone contrast with direct HU mapping, simple affine conversion without large training sets, comparable focal-position accuracy of less than $\mathrm{TE} = 0.07 \ \mathrm{ms}$8, and good acoustic-field agreement of $\mathrm{TE} = 0.07 \ \mathrm{ms}$9–$1$0 in pressure (Miscouridou et al., 1 Aug 2025). Recommended use cases are transcranial ultrasound neuromodulation or ablation planning when CTs are unavailable, frequencies greater than or equal to $1$1 for precise targeting, and workflows requiring rapid MR-only planning and subject safety (Miscouridou et al., 1 Aug 2025).

The reported limitations and error sources are MR segmentation quality, with SPM skull mask $1$2, bias-field residuals, registration inaccuracies, CT calibration differences, attenuation modelling uncertainty, and the requirement for in-vivo soft tissue for histogram normalisation (Miscouridou et al., 1 Aug 2025). These constraints indicate that the method depends not only on the affine PETRA-to-CT relation itself, but also on the quality of masking, normalization, and acoustic property calibration.

Implementation is described as open-source at https://github.com/ucl-bug/petra-to-ct, provided as a MATLAB toolbox under an MIT license and including registration scripts, bias correction calls, mask generation, PCA fitting, and pseudo-CT volume creation (Miscouridou et al., 1 Aug 2025). The repository also includes an example EXAR PETRA protocol (Miscouridou et al., 1 Aug 2025).

In summary, the reported formulation combines PETRA acquisition, preprocessing, PCA-based affine mapping, and acoustic validation to establish PETRA-derived pseudo-CT as an MR-only substitute for CT in transcranial ultrasound planning, with sub-millimeter focal-position agreement in-vivo and closely matched ex-vivo experimental errors relative to CT-based simulation (Miscouridou et al., 1 Aug 2025).