---
title: PETRA-Derived Pseudo-CT for Ultrasound Planning
url: https://www.emergentmind.com/topics/petra-derived-pseudo-ct
type: topic
---

# PETRA-Derived Pseudo-CT for 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 [2508.01050].

## 1. Definition and research setting

PETRA is described as an ultrashort-echo-time sequence used here because of its stronger ability to image bones [2508.01050]. 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 [2508.01050].

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 [2508.01050].

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 [2508.01050]. 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 [2508.01050].

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 $= 0.75 \ \mathrm{mm}$, and field of view matched to CT with in-plane resolution of approximately $0.44 \ \mathrm{mm}$ [2508.01050].

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 [2508.01050].

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 $N$ paired bone voxels $\{(x_i,y_i)\}$, where $x_i$ are normalized PETRA intensities and $y_i$ the CT Hounsfield Units, principal component analysis is performed on the $2 \times N$ data matrix
$$
D = [x-\mu_x; \ y-\mu_y],
$$
with covariance matrix
$$
\Sigma = \frac{1}{N} D \cdot D^T .
$$
The first eigenvector direction $v_1$ is then used to identify the linear trend [2508.01050].

In practice, this reduces to an affine model
$$
y \approx a \cdot x + b .
$$
From the first principal component, the reported in-vivo mapping is
$$
\mathrm{CT} \ (\mathrm{HU}) = a \cdot \mathrm{PETRA} + b,
$$
with
$$
a = -2940.2 \ \mathrm{HU}, \qquad b = 3291.1 \ \mathrm{HU}.
$$
Here PETRA is unitless after normalization and CT is expressed in Hounsfield units [2508.01050].

For direct density mapping including the CT phantom calibration, the reported expression is
$$
\rho = -1076.1 \cdot \mathrm{PETRA} + 2238.7 \qquad (\mathrm{kg} \cdot \mathrm{m}^{-3}) .
$$
The mathematical summary also gives the PCA decomposition as
$$
D = U \Sigma V^T, \qquad v_1 \propto U[:,1],
$$
and states the affine model as
$$
y_i = a x_i + b, \qquad a,b \in \mathbb{R}.
$$
All of these relations are reported explicitly for the PETRA-derived pseudo-CT pipeline [2508.01050].

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 $\rightarrow -1000 \ \mathrm{HU}$,
- head or soft-tissue mask $\rightarrow 42 \ \mathrm{HU}$,
- skull mask $\rightarrow$ Eq. (1) applied to PETRA intensity [2508.01050].

Voxel-wise agreement between pseudo-CT and ground-truth CT is quantified by the mean absolute error and root-mean-square error:
$$
\mathrm{MAE} = \frac{1}{N} \sum_k |\hat{y}_k - y_k| ,
$$
$$
\mathrm{RMSE} = \sqrt{\frac{1}{N} \sum_k (\hat{y}_k - y_k)^2} ,
$$
where $\hat{y}_k$ is the pseudo-CT value and $y_k$ the ground-truth CT value [2508.01050].

For acoustic comparison, the reported focal metrics use subscripts $1,2$ to denote CT and pseudo-CT simulations:

- focal-position error:
$$
r = \| \mathrm{COM}_2 - \mathrm{COM}_1 \|_2 \qquad (\mathrm{mm}),
$$
- peak-pressure error:
$$
\epsilon_p = 100 \cdot \frac{p_2 - p_1}{p_1} \qquad (\%),
$$
- focal-volume error:
$$
\epsilon_V = 100 \cdot \frac{V_2 - V_1}{V_1} \qquad (\%).
$$

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 $0.2 \ \mathrm{mSv}$ [2508.01050]. 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 [2508.01050].

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 $500 \ \mathrm{kHz}$, using $6 \ \mathrm{pts}/\lambda$, $f_c = 1550 \ \mathrm{m/s}$ for soft tissue, and $\rho = 1045 \ \mathrm{kg}/\mathrm{m}^3$. For skull modelling, density was obtained via CT-phantom calibration, speed of sound by
$$
c = 1.33 \ \rho + 166.7 \qquad (\mathrm{m/s}),
$$
and attenuation by
$$
\alpha = 13.3 \cdot f \qquad (\mathrm{dB/cm}) .
$$
These parameters are reported directly for the in-vivo simulation setup [2508.01050].

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

| Metric | Reported value |
|---|---|
| Focal-position error $r$ | $0.48 \pm 0.25 \ \mathrm{mm}$ |
| Peak-pressure error $\epsilon_p$ | $5.1 \pm 4.0 \%$ |
| Focal-volume error $\epsilon_V$ | $5.8 \pm 4.4 \%$ |

These values are presented as evidence that PETRA-derived pseudo-CT yields small errors for in-vivo data [2508.01050]. 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 $120 \ \mathrm{kVp}$, $228 \ \mathrm{mAs}$, and $0.47 \times 0.47 \times 0.5 \ \mathrm{mm}^3$ resolution, together with PETRA [2508.01050]. For this setting, the mapping was fit separately as
$$
\mathrm{CT} = -2815.1 \cdot \mathrm{PETRA} + 2779.4 .
$$
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 [2508.01050].

Hydrophone experiments were performed at $270$, $500$, and $750 \ \mathrm{kHz}$ and $1 \ \mathrm{MHz}$ using H115, H104, and H101 transducers in a $60 \times 60 \ \mathrm{mm}$ scan plane with $0.5 \ \mathrm{mm}$ steps, with water temperature at $20^\circ \mathrm{C}$. In-skull cortical field measurement was obtained via angular-spectrum reconstruction. The k-Wave simulation used $8 \ \mathrm{pts}/\lambda$, $\mathrm{PML}=20 \ \mathrm{pts}$, a GPU cluster, and equivalent-source holograms [2508.01050].

The reported mean $\pm$ standard deviation errors over $3$ skulls $\times 4$ frequencies are:

| Comparison | $r$ | $\epsilon_p$ | $\epsilon_V$ |
|---|---:|---:|---:|
| CT vs experiment | $1.5 \pm 1.2 \ \mathrm{mm}$ | $17.1 \pm 14.6 \%$ | $32.5 \pm 22.5 \%$ |
| pCT vs experiment | $1.6 \pm 1.4 \ \mathrm{mm}$ | $18.2 \pm 17.1 \%$ | $19.2 \pm 15.9 \%$ |
| CT vs pCT | $0.8 \pm 0.6 \ \mathrm{mm}$ | $7.9 \pm 4.9 \%$ | $8.5 \pm 5.5 \%$ |

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 [2508.01050]. 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 $1 \ \mathrm{mm}$, and good acoustic-field agreement of $5$–$20 \%$ in pressure [2508.01050]. Recommended use cases are transcranial ultrasound neuromodulation or ablation planning when CTs are unavailable, frequencies greater than or equal to $500 \ \mathrm{kHz}$ for precise targeting, and workflows requiring rapid MR-only planning and subject safety [2508.01050].

The reported limitations and error sources are MR segmentation quality, with SPM skull mask $\mathrm{DSC} \approx 0.85$, bias-field residuals, registration inaccuracies, CT calibration differences, attenuation modelling uncertainty, and the requirement for in-vivo soft tissue for histogram normalisation [2508.01050]. 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 [2508.01050]. The repository also includes an example EXAR PETRA protocol [2508.01050].

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 [2508.01050].

Source: https://www.emergentmind.com/topics/petra-derived-pseudo-ct