# LesionSCynth: A simple parametric lesion synthesis method to improve spinal cord lesion segmentation in low-data scenarios

Ricky Walsh, Prabhjot Kaur, Davood Karimi, Anne Kerbrat, Simon K Warfield, Francesca Galassi, Benoit Combès

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Ricky Walsh, Prabhjot Kaur, Davood Karimi, Anne Kerbrat, Simon K Warfield, et al.. LesionSCynth: A simple parametric lesion synthesis method to improve spinal cord lesion segmentation in low-data scenarios. 2025. hal-05121315

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# LesionSCynth: A simple parametric lesion synthesis method to improve spinal cord lesion segmentation in low-data scenarios

Ricky Walsh¹,†, Prabhjot Kaur², Davood Karimi², Anne Kerbrat¹,³,
Simon K. Warfield², Francesca Galassi¹,*, Benoit Combès¹,*

¹ Univ Rennes, Inria, CNRS, Inserm, IRISA UMR 6074, Empenn, Rennes, France

² Computational Radiology Laboratory, Boston Children's Hospital and Harvard Medical School, Boston, MA, USA

³ Department of Neurology, Rennes University Hospital, Rennes, France

† Work partly done during exchange at the Computational Radiology Laboratory.

* Equal contribution

Correspondence: {ricky.walsh, francesca.galassi, benoit.combes}@inria.fr

June 19, 2025

**Abstract:**

Detecting multiple sclerosis lesions in spinal cord MRI is a critical but complex task for radiologists and neurologists. While deep learning models have shown promise for this task, training these models requires large manually annotated datasets, which are time-consuming and expensive to create. To reduce the annotation burden, this study proposes LesionSCynth, a parametric framework for synthesising hyperintense lesions in spinal cord MRI. Based on analysis of the intensity distribution of real lesions in sagittal T2-weighted acquisitions, LesionSCynth generates realistic synthetic lesions that can augment small annotated datasets. Segmentation models trained on a combination of these synthetic lesions and 17 real acquisitions achieved notably better performance than those trained on the real lesions alone (0.52 vs. 0.46 FROC, respectively). Notably, models trained with LesionSCynth lesions achieved similar detection performance to a model trained on eight times more real lesions (0.55 FROC for both). Moreover, LesionSCynth outperformed two leading lesion synthesis
methods, LesionMix (0.43) and CarveMix (0.41), in low-data regimes. These findings position LesionSCynth as a practical and effective solution for reducing the annotation burden while improving MS lesion detection and segmentation in spinal cord MRI.

**Keywords:** synthetic data, multiple sclerosis, spinal cord, lesion segmentation, few annotations

# 1 Introduction

## 1.1 Motivation

Multiple sclerosis (MS) is a chronic demyelinating disease of the central nervous system, and is a leading cause of disability in young adults (Jakimovski et al., 2024). A key diagnostic criterion for MS is the presence of white matter lesions in the brain and spinal cord, which appear as hyperintense in T2-weighted (T2-w) magnetic resonance (MR) scans (Thompson et al., 2018). However, accurately identifying these lesions is a complex and mentally demanding task for radiologists and neurologists, and is prone to significant inter-rater variability (Lodé et al., 2025; Walsh et al., 2023).

Automated tools, particularly those based on deep learning, have demonstrated impressive performance for this task, and have been shown to improve the sensitivity of experts for both brain and spinal cord lesions (Combès et al., 2021; Lodé et al., 2025). However, automated lesion segmentation in spinal cord MRI has remained relatively less studied compared to the brain. The narrow, elongated, and mobile anatomy of the spinal cord introduces additional challenges, such as a higher susceptibility to motion and respiratory artefacts, as well as partial volume effects with cerebrospinal fluid (CSF) (Kearney et al., 2015). Moreover, heterogeneity of acquisition protocols for spinal cord MRI, where many different MR sequences can be used for acquisitions (Wattjes et al., 2021), complicates the development of generalisable deep learning models. Training such models requires large, annotated datasets covering the whole range of acquisition protocols, which are often difficult to obtain.

One way to reduce the annotation burden is to synthesise entire images or to insert synthetic lesions into existing ones (Brugnara et al., 2024; Ferreira et al., 2024; Terrassin et al., 2024). Although generative adversarial networks (GANs) and diffusion models create realistic synthetic images, they require large annotated datasets for training, so are not applicable in low-data scenarios. Several non-model-based techniques have been proposed for lesion synthesis, such as CarveMix (X. Zhang et al., 2023) and LesionMix (Basaran et al., 2024). However, these methods typically rely on using existing lesions from the training dataset, and so may overfit to the specific intensity characteristics, especially when only a
small number of real lesions are available.

This study proposes *LesionSCynth*, a parametric method for lesion synthesis in spinal cord MRI, designed to improve the performance of deep learning segmentation models in low-data scenarios, thereby reducing the annotation demand. Based on an analysis of spinal cord lesion characteristics, our approach generates synthetic lesions using real lesion shapes and a modelled hyperintensity profile. During training, we insert synthetic lesions into real MR volumes and use these alongside a small set of real annotated lesions, to aid the model to generalise to a wider distribution of lesion intensity characteristics. The study demonstrates that a simple parametric method incorporating basic priors can lead to impressive improvements in low-data scenarios. Moreover, although the focus here is on spinal cord lesions in sagittal T2-weighted acquisitions, the method could be easily adapted to generate other types of hyperintense or hypointense lesions and to be used in other imaging modalities.

The contributions of the study are threefold: 1) a parametric method of lesion synthesis, which allows a greater variability of intensity characteristics in low-data scenarios and outperforms state-of-the-art lesion synthesis methods – to the best of our knowledge, this is the first study of lesion synthesis for spinal cord lesion segmentation; 2) comprehensive investigations and ablation studies to understand the impact of various design choices in the proposed method; and 3) a thorough evaluation of the effect of the proportion of images with lesions vs. without lesions, and the ratio of real lesions vs. synthetic lesions, across several different training set sizes.

The paper is organised as follows: the next subsection discusses related literature in MS lesion segmentation in spinal cord MRI and in lesion synthesis. Sec. 2 describes the dataset and preprocessing used in this study. Sec. 3 details the lesion synthesis method and the empirical observations on which it is based. Sec. 4 describes the experiments undertaken, while Sec. 5 presents the results of these experiments. Finally, the results and outlook are discussed in Sec. 6.

## 1.2 Related Work

### 1.2.1 MS Spinal Lesion Segmentation

While MS lesion segmentation in brain MRI has been widely studied over the years, with many challenges and open datasets (Carass et al., 2017; Commowick et al., 2016, 2021; Lesjak et al., 2018), spinal cord MRI has remained less studied. A major contribution in this area came from Gros et al. (2019), where the authors trained deep learning models to segment cervical spinal cord MS lesions in axial and sagittal T2-w volumes. These models were then released in the open-source Spinal Cord Toolbox (SCT). However, some
limitations were identified over time; for example, poor performance when applied to the thoracic spinal cord. Recent updates have improved upon this previous version, including a contrast-agnostic model and a model for axial T2-w scans (Karthik et al., 2025). In all cases, training the models required hundreds or even thousands of examples with segmentation masks manually or semi-automatically generated by expert human raters. Such an effort, however, is not always feasible due to time and budget constraints.

Recent studies have begun to explore frameworks that account for the wide range of possible acquisition sequences and resulting variability in image contrast (Benveniste et al., 2024; Walsh et al., 2024). While the approach taken by Walsh et al. (2024) was to use the manual segmentation masks from the T2-w volumes for the corresponding sequences, this is suboptimal as there can be misalignments between the acquisitions, differences in coverage, and the visible extent of the lesion can vary across acquisitions because of limited resolution, partial volume effects, and artefacts. Therefore, to avoid introducing label noise, a set of high-quality manual annotations would be required for each distinct image contrast, which would further increase the annotation burden.

Given the increasing requirements for time-consuming and expensive manual annotations, the current study proposes a parametric method for lesion synthesis which, given a small set of real annotated lesions, can improve the performance of a deep learning segmentation model.

## 1.2.2 Image Synthesis

deep learning methods have represented the state of the art in image synthesis since the advent of generative adversarial networks (GAN) (Goodfellow et al., 2014) and more recently, diffusion-based models have significantly improved synthetic image generation (Ho et al., 2020). These methods have been applied to numerous medical imaging tasks as a data augmentation technique, for example for MS brain lesion segmentation (Brugnara et al., 2024), brain tumours (Ferreira et al., 2024), and kidney and liver tumours (Chen et al., 2024). However, training these models requires a large amount of annotated images and so they are not applicable for low-data scenarios.

Several non-model-based techniques have been inspired by the MixUp data augmentation technique (H. Zhang et al., 2018). Here, a new data sample is created by taking a linear combination of two existing samples. Although this may be effective for natural image classification, if we combine two medical images in this way, then we lose fine-grained information about local hyperintense regions which would render MixUp suboptimal for MS lesion segmentation. CutMix, based on a similar idea of combining two images from the training set, later achieved superior performance on ImageNet classification over MixUp (Yun et al., 2019). CutMix involves cutting out a random patch of one image and inserting a
patch from another image into this gap, thus maintaining local continuity of information in the image, although creating clear artefacts at the patch boundary.

Several methods for lesion synthesis in medical images are largely inspired by this idea of cutting an area from one image and inserting it into another image in the training set (Basaran et al., 2024; X. Zhang et al., 2023; Zhu et al., 2022). CarveMix (X. Zhang et al., 2023) operates on whole images, by extracting all lesions in a given image and pasting them into another training image, maintaining the original lesion positions. The area copied from one image to another can be smaller or larger than the lesion mask, and this area is determined by the distance to the lesion boundary, with a target distance randomly sampled for each case.

LesionMix (Basaran et al., 2024) includes two branches for data augmentation, one for inserting new lesions in an image, and another for removing existing lesions through inpainting. Given an existing image in the training set to be augmented, the total lesion load is first calculated and compared to a target load which is sampled randomly from some distribution (e.g., the true distribution of lesion load in the dataset, or a uniform distribution). If the current load is lower than the target load, then lesions from other images are iteratively inserted into the current image until the target load is reached. The inserted lesion positions are based on a prior spatial probability map. If the current load is higher than the target load, lesions in the current image are iteratively inpainted until below the target load.

The main drawback of CarveMix, LesionMix, and similar methods, is that when only a small number of manual segmentations of real lesions are available, models may overfit to their intensity characteristics. Moreover, if the intensity profiles of the source and target images differ significantly, these methods can produce unrealistic lesions, or can even create areas of hypointensity where there should be a hyperintense synthetic lesion, which could inject significant noise into the learning process. The z-score normalisation applied by these methods to harmonise intensity distributions between images is not sufficient to eliminate these inverted lesions.

To address these limitations, we propose a method of lesion synthesis which generates lesions with diverse and controlled intensity profiles, even when the number of real annotated lesions is small. The intensity characteristics of the synthetic lesions can be controlled through the parameters of the method, thereby ensuring that inserted lesions are always hyperintense (or hypointense, if used for T1-w contrasts).
# 2 Data

## 2.1 Overview

The dataset used for the experiments in this study included 324 sagittal T2-w acquisitions corresponding to 215 unique patients, with 202 volumes of the upper spinal cord and 122 of the lower spinal cord. The upper acquisitions covered the whole cervical spinal cord and several thoracic vertebrae (ending at T2-T9, depending on the acquisition). The lower acquisitions usually overlapped with the upper acquisitions by several vertebrae, and the coverage typically descended below the lumbar vertebrae.

Although this dataset does not represent a 'low data' setting, it allowed us to examine the impact of lesion synthesis at different dataset sizes. Not all researchers have easy access to a dataset of this size, however, so our method could be directly applicable in those cases. Moreover, even if a dataset of this size is available, lesion synthesis may still be useful when attempting to improve generalisation of a segmentation model to other scanners, or even to different MRI sequences.

Approximately half of the data came from the French MS Registry (OFSEP) (Vukusic et al., 2020) and this was supplemented by acquisitions from three clinical studies: EMISEP (NCT02117375), MS-TRACTS (NCT04220814), and MAPMS (NCT04918225). Written informed consent was obtained from all participants for being included in the study. The study was approved by the relevant ethics committee and is compliant with French data confidentiality regulations.

The volumes were acquired with scanners from three brands, Siemens (84%), GE (10%), and Philips (6%), and 16 scanner models are represented in the dataset. The median in-plane dimension was 512 and the median number of slices was 15. The 10th percentile, median and 90th percentile of the slice spacing were 2.75mm, 3.00mm, and 3.60mm, and of the in-plane spacing were 0.42mm, 0.59mm, and 0.80mm, respectively.

Among the subjects for whom we know the MS type, 70% were diagnosed with relapse-remitting MS, 18% had a progressive disease course, 3% had clinically isolated syndrome, and 9% of subjects in the dataset were healthy control subjects.

99 of the 324 volumes have no lesions present, with 26 of these coming from healthy control subjects. Among the 225 volumes with lesions, the median number of lesions was 3. The full distribution of lesion counts is shown in Fig. 1A. Lesion load, similarly to lesion count, had a skewed-right distribution with a range of [15, 4200]mm³, median lesion load of 332mm³, and first and third quartiles of 146mm³ and 705mm³, respectively. Fig. 1B shows that this skewed distribution is present in both upper and lower
<figure><img src="image_2.png" /><figcaption>Figure 1: Lesion counts and distribution of lesion load per MR volume across the whole dataset. The lesion load distribution shown includes only volumes containing at least one lesion. The dashed lines represent the 1st quartile, median, and 3rd quartile.</figcaption></figure>

acquisitions.

To create manual annotations, each sagittal T2-w acquisition was reviewed by one of six expert neuro-radiologists and neurologists. These experts also had access to supplementary acquisitions (e.g., STIR, axial T2-w, or axial T2*-w) for each subject, as well as clinical information. The segmentation masks created by these experts were then validated and adjusted where necessary by a senior neurologist with 10 years' experience in reading spinal cord MRI. In a second round, a deep learning segmentation model was trained on the manual annotations, and the predicted segmentations were reviewed by the senior expert, who decided whether to include or reject the proposed lesions.

## 2.2 Training and Test Sets

The data splits were chosen to be consistent with previous projects on the same data (e.g., Lodé et al. (2025)), where a subset of 217 volumes was split into folds for 5-fold cross validation. Three folds were used for training in each run, one fold was used as a validation set, and the remaining fold functioned as a held-out test fold. Experiments were conducted with different training set sizes (see Sec. 4.2); for the largest training set size, we included all remaining volumes in the dataset not contained in the subset of 217 volumes mentioned above.

To supplement the 40-50 volumes in the test folds, and to increase the statistical confidence of our results, we supplemented these with an additional dataset created by Lodé et al. (2025). This included
100 sagittal T2-w volumes (50 upper, 50 lower) obtained from OFSEP. The final test set used for each run of each experiment thus contained 140-150 volumes. The annotations for the additional 100 volumes were created with the input of 20 experts with a range of experience. Each expert reviewed each acquisition together with a corresponding STIR acquisition in two sessions, with and without the aid of an automated segmentation tool, and clicked areas of the acquisition where they suspected lesions. Final segmentation masks were created by a radiology resident and validated by a neurologist with 10 years' experience. To create these masks, the annotators reviewed the T2-w and STIR volumes, the inputs of the 20 experts and automated segmentation tool, supplementary acquisitions for the patient (such as axial T2-w or T2*-w) and clinical information. Discrepancies were adjudicated by a third expert, a neuroradiologist with six years' experience.

## 2.3 Preprocessing

The volumes were preprocessed in a similar way to previous studies (Gros et al., 2019; Walsh et al., 2023, 2024), and full details for the preprocessing used in this study are given in the supplementary material. Briefly, volumes were resampled to 0.5mm³ isotropic spacing. Each axial slice was cropped to (48, 48) voxels around the spinal cord with the aid of spinal cord segmentation masks obtained with the Spinal Cord Toolbox (SCT) (De Leener et al., 2017). These axial slices were stacked along the z-axis, leading to a 'straightened' spinal cord representation. The resulting length of the preprocessed images along the z-axis ranged from 187 to 909, with a median of 478 voxels (239mm).

# 3 Synthetic Lesion Generation (LesionSCynth)

We aim to build a simple parametric process to generate altered versions of the training data that includes prior knowledge of lesion appearance. This section provides a principled description of such a parametric generating process to add an arbitrary number of synthetic lesions to acquisitions using a limited number of lesions provided in the training set. The subsequent sections of the paper will describe how this process was used to increase the diversity of lesions when training a U-Net model. The overall process is illustrated in Fig. 2 and detailed below.
<figure><img src="image_3.png" /><figcaption>Figure 2: Examples of synthetic lesions. A) Sagittal cross-section of image with no real lesions (patch size: 16 × 27.5mm), B) Masks of two lesions to be inserted. C) Result of multiplying intensity of all voxels inside masks by a factor of 1.2. D) Application of spatial Gaussian function ($\sigma = 1 \times 2.5mm$) to the intensity increase. E) Application of blur to the output of D) with radius=1mm and $\sigma = 0.333mm$.</figcaption></figure>

### 3.1 Lesion Intensity Profiles

**Lesion-to-normal-appearing-tissue Contrast** The main defining feature of MS lesion appearance is its contrast relative to surrounding tissue. Here, we describe a method to compute and analyse the contrast of a given lesion relative to its neighbouring normal-appearing tissue. For a lesion $p$, we have a manual binary segmentation mask $M_p$. To obtain the mask of the lesion neighbourhood on each slice, we first dilated $M_p$ in each sagittal slice using a disk structuring element with a radius of 5 voxels, and then subtracted the original $M_p$. To prevent hyperintense CSF being included in the neighbourhood, we removed any voxels outside the spinal cord by multiplying the result with the spinal cord mask after applying an erosion using a disk of radius 1 voxel. The resulting neighbourhood mask for lesion $p$ is denoted $M_p^*$. The contrast ratio, $C_p$, between the lesion and the surrounding normal tissue is calculated as:

$$C_p = \frac{\frac{1}{|M_p^*|} \sum_{v \in M_p^*} I_v - \frac{1}{|M_p|} \sum_{v \in M_p} I_v}{\frac{1}{|M_p^*|} \sum_{v \in M_p^*} I_v} \quad (1)$$

where $I_v$ is the intensity at some voxel $v = (i, j, k)$ and $|M_p|$ is the number of voxels in mask $M_p$.

Fig. 3 displays the distribution of $C$ from the 847 lesions in the dataset. Overall, we observed that the contrast between mean lesion intensity and neighbourhood follows an approximate normal distribution. Lesions with low and negative contrast in Fig. 3 typically occur when: 1) the neighbourhood includes voxels with CSF partial volume effects, despite efforts to exclude them 2) the lesion is not clearly distinguishable in the sagittal T2-w acquisition but appears more clearly in other acquisitions, or 3) the
manual segmentation either misses some hyperintense regions or includes voxels with lower intensity. Examples are given in the supplementary material.

<figure><img src="image_4.png" /><figcaption>Figure 3: Distribution of contrast between mean lesion intensity and mean neighbourhood intensity. The sample mean is 0.17 and the sample standard deviation is 0.11.</figcaption></figure>

A simple approach to take into account this contrast distribution to synthesise a lesion would be to increase the intensity inside a candidate lesion region, $M_s$, such that the mean intensity is increased by a multiplicative factor, i.e.,

$$ \frac{1}{|M_s|} \sum_{v \in M_s} I_v^* = (1+c) \times \frac{1}{|M_s|} \sum_{v \in M_s} I_v \quad (2) $$

for example by increasing all intensities by this multiplicative factor inside the candidate lesion region, i.e., $I_v^* := (1+c) \times I_v, \forall v \in M_s$, where $I$ is the original intensity of normal-appearing tissue, $I^*$ is the updated intensity, and $c$ is a contrast factor sampled from a distribution $\psi$, chosen to follow that of the empirical distribution in Fig. 3.

In our experiments, we modelled $c$ as a truncated normal distribution $\psi(\bar{\mu}, \bar{\sigma}, a, b)$, with the parameters computed from the available lesions in the training set of a given experiment. First, the contrast was calculated between the mean intensity of each lesion and its surrounding tissue. $\bar{\mu}, \bar{\sigma}, a$ were then given by the mean, standard deviation, and 20th percentile over these values, respectively. $b$ was set to 1.0 in our experiments, i.e., the right side of the distribution was effectively not truncated. The left side was truncated at the 20th percentile of real cases to avoid sampling very low or negative contrast values.

**Hyperintensity is more pronounced near lesion centre** Intensity in lesions is typically not spatially uniform. In particular, intensities tend to be higher near the lesion's centre of mass and to decrease
towards its boundary. This tendency is illustrated in Fig. 4 (see supplementary material for details on this analysis).

<figure><img src="image_5.png" /><figcaption>Figure 4: Mean intensity of lesion voxels as a function of the distance from the lesion centroid, based on all lesions in the dataset. Distances are rounded to the nearest 0.5mm, and bounds are ±1.96 × SE, where standard error is calculated across all voxels from all lesions. See supplementary material for further details on how this graph was generated.</figcaption></figure>

This observation, together with the intensity scaling defined in Eq. 2 motivated the following rule to model lesion hyperintensity at each voxel $(i, j, k) \in M_c$:

$$I_{i,j,k}^* = I_{i,j,k} \times (1 + c \times f_{M_c}(|i - i_0|, |j - j_0|, |k - k_0|)). \quad (3)$$

Where:

* $f_{M_c}: \mathcal{R}_+^3 \to \mathcal{R}_+$ is any decreasing function satisfying $\sum_{(i,j,k) \in M_c} f(|i - i_0|, |j - j_0|, |k - k_0|) = 1$,

* $(i_0, j_0, k_0)$ is the coordinate of the lesion's centre of mass.

In practice, we used a 3D Gaussian function whose scale parameters are independently fitted to the lesion's spatial extent in each dimension:

$$I_{i,j,k}^* = I_{i,j,k} \times \left( 1 + A e^{-\left( \frac{(i - i_0)^2}{2\sigma_I^2} + \frac{(j - j_0)^2}{2\sigma_J^2} + \frac{(k - k_0)^2}{2\sigma_K^2} \right)} \right), \quad (4)$$
where,

$$A = \frac{c|M_c|}{\sum_{(i,j,k) \in M_c} e^{-\left(\frac{(i - i_0)^2}{2\sigma_I^2} + \frac{(j - j_0)^2}{2\sigma_J^2} + \frac{(k - k_0)^2}{2\sigma_K^2}\right)}}$$

Parameters $\sigma_I$, $\sigma_J$, and $\sigma_K$ control how quickly the intensity increase decays along each axis. These rates are dynamically adjusted based on both the size and shape of the lesion. The decay of the Gaussian function, determined by $\sigma_I$, $\sigma_J$, and $\sigma_K$, should be related to the length of the lesion. For example, a short lesion requires a sharper decay, i.e., a lower $\sigma$; if not, there would be very little difference across the whole lesion. On the other hand, a long lesion requires a slower decay, i.e., a higher $\sigma$; otherwise, the function would quickly taper to zero and most of the lesion would receive no intensity increase. Similarly, $\sigma$ should be independently determined for each axis, given that the length of the lesion along each axis can vary significantly. For a given lesion with length along axis m given by $l_m$, we sampled $\sigma_m \sim U(l_m/8, l_m)$. To avoid cases where part of the lesion area receives no intensity increase (typically when c is small and $\sigma_m$ is close to $l_m/8$), we applied a minimum intensity increase of 0.015 to ensure at least some small signal is present within the entire candidate lesion mask. Overall, the process described here allows diversity in the hyperintensity profile, ranging from a very sharp decay when $\sigma_m \approx l_m/8$ to virtually no spatial gradient when $\sigma_m \approx l_m$.

It should be noted that the generated intensity profile is not strictly decreasing from the centre of mass as it incorporates variation from the normal-appearing spinal cord in the target image.

**Intensity Homogeneity** As illustrated in Fig. 5, variance of intensity tends to be lower within lesions than within lesion neighbourhoods. The final step in generating our synthetic lesions intensity profile is thus to apply a blur filter to the lesion to increase local homogeneity and to reduce the intensity variance inside the lesion. This is applied with the gaussian_filter function from the Scipy package, with blur radius set to 2 and blur sigma set to 0.67. These values were chosen after visually inspecting how realistic generated examples were.

## 3.2 Lesion Shapes and Locations

The previous sections described the process to generate lesion intensity profile by assuming that a mask $M_c$ for a candidate lesion is available. In this section, we describe how this mask is created. This process takes place after the data preprocessing outlined in Sec. 2.3 and described in detail in Sec. A.1 of the supplementary material. In particular, in this section, we assume that images have 0.5mm isotropic
<figure><img src="image_6.png" /><figcaption>Figure 5: Distributions of standard deviation of intensities within A) lesions and B) neighbourhoods around lesions, with the latter obtained by dilating the lesion mask with a disk structuring element of radius 5 voxels and masking with the spinal cord segmentation mask.</figcaption></figure>

spacing and have been cropped and centred around the spinal cord.

**Lesion Shape and Orientation** Lesions vary in size and shape. In this work, we used a very simple approach with the lesion masks from the training set annotations. In practice, a lesion from the training set was first randomly selected from lesions with volumes between the 10th and 90th percentiles, to avoid extremely small or large lesions. Then, two steps were applied to introduce slight deviations from the original lesion mask. First, a random scaling and rotation operation was applied to the lesion mask with probability $p = 0.5$. The scaling factor was sampled from [0.9, 1.1] and rotation degrees were sampled from ([-5, 5], [-5, 5], [-45, 45]). Second, the mask was either eroded ($p = 0.25$) or dilated ($p = 0.25$) using a ball structuring element with radius 1 voxel. These operations introduced variation in lesion shape and size.

**Lesion Position** Given a target MR volume, the centroid of the candidate lesion was placed at a random point along the z-axis. The axial position of the source lesion was used, though altered by the rotation operation described above. No registration was needed as volumes are roughly aligned axially after preprocessing. Prior probability maps may also be used to choose lesion position, as in LesionMix (Basaran et al., 2024), but in cases with few annotated examples, this may not be appropriate as the full range of lesion positions would not be represented. After placing the source lesion mask in the target
image, any area outside the spinal cord was removed. This was done using the spinal cord mask, after eroding with a 1-voxel radius disk structuring element to reduce the chance of CSF voxels being included in synthetic lesions.

## 3.3 Summary of the Lesion Synthesis Process

**Capturing parameters** – From the set of lesions in the training set (which will change from one experiment to another):

1. Compute the mean and standard deviation of the contrast between the lesions and their surrounding normal-appearing tissue. These parametrise the contrast distribution used for synthesis.

2. Extract the segmentation masks, to be used as the lesion shapes in the synthesised examples.

**Producing a synthetic case** – For a given acquisition containing no lesions:

1. Choose a random position and insert a random segmentation mask from the training set, after applying some augmentation transformations to the mask.

2. Synthesise the appearance of a lesion within the candidate mask by increasing the mean intensity by a multiplicative factor, inducing a spatial gradient in the intensity increase using a Gaussian function, and increasing local homogeneity of the intensity with a blur applied locally.

# 4 Experiments

We evaluated the impact of our synthetic lesion generation framework through a series of controlled experiments. Specifically, we assessed segmentation and detection performance when training with a combination of LesionSCynth and real lesions, and we compared to two synthesis alternatives and training on real data alone. All of these experiments were conducted at four different training set sizes. Finally, we examined several components of the method to understand the contribution of each part. The experimental settings are described in more detail below.
### 4.1 Training Strategies

We trained models using different combinations of real and synthetic lesion data to isolate the contribution of each. All experiments share the same architecture and training hyperparameters, which will be described in Section 4.4.

#### 4.1.1 LesionSCynth

In our base training setup, each epoch included all real volumes containing ground-truth (GT) lesions, along with an equal number of synthetic examples. These synthetic examples were created by inserting lesions into real volumes without GT lesions, similar to the training process from Walsh and Tardy (2023). The number of synthetic lesions inserted per volume was a random whole number between 0 and 8, inspired by the finding by Basaran et al. (2024) that using a uniform distribution for target lesion load achieved the best performance.

It is unclear a priori whether real or synthetic lesions should be seen relatively more frequently during training. On the one hand, we want the segmentation model to learn the characteristics of real lesions, but on the other hand, if few real lesions are available, inserting a higher proportion of synthetic lesions may help reduce overfitting. Thus, while our base method used 50% real and 50% synthetic examples per epoch, we also examined scenarios with 25%/75% and 75%/25% real and synthetic examples (the number of iterations was consistent with the base 50/50 experiments). The results of these extra experiments are presented in Sec. 5.4

#### 4.1.2 Synthetic Lesion Baselines

To contextualise our method, we compared it to two state-of-the-art lesion synthesis methods, CarveMix and LesionMix. For both synthesis baselines, we followed the same training framework as for our method, i.e., the only difference with the training method described in Sec. 4.1.1 is that the synthetic examples were created with an alternative method.

**CarveMix** The original implementation of CarveMix involved generating a fixed number of synthetic examples offline before training, and so we re-implemented this as a TorchIO transform that can be used on-the-fly during training. Moreover, CarveMix was originally proposed as a general data augmentation technique, i.e., to mix any pair of images in the training set. Therefore, our use of CarveMix to only insert real lesions into an image with no lesions deviates from the original proposed usage. However, we
aim to isolate the impact of the lesion synthesis part and so prefer to align with the training framework
of our proposed method.

The intensity profiles varied substantially among the images in our training set. Therefore, a local hyperintensity in one image may be a hypointensity when that region is copied into another image. Standardising both images to have mean 0 and standard deviation 1, as suggested by X. Zhang et al. (2023), helped to reduce the impact of this, but did not fully eliminate this problem. Examples of lesions generated with CarveMix are given in the supplementary material.

**LesionMix** The original LesionMix contains two branches, one for *populating* an image with a new lesion and another for *removing* an existing lesion from an image using inpainting. Since, as before with CarveMix, we wish to assess only the effectiveness of the synthetic lesions, we use only this part of LesionMix, which we refer to hereafter as LesionMix$_{pop}$.

Given that the code for LesionMix is not publicly available, we implemented a version of LesionMix$_{pop}$
as a TorchIO transform. First, before training, all lesions were extracted from the standardised training
images in patches of size 48 × 48 × b, where b is the length of the bounding box of the lesion along the
z-axis. During training, lesions were randomly inserted into volumes without GT lesions such that the
total lesion load reaches a target load. This target was sampled from a uniform distribution between the
5th and 95th percentiles of the lesion load in the training samples having real lesions, as Basaran et al.
(2024) found that this uniform distribution yielded the best performance in their experiments.

As in the original paper, several augmentations were applied to the original lesions before being inserted
into a new volume. In particular, random flips with p = 0.5 for each axis, random scaling between 50%
and 180% with p = 0.5, elastic deformation with maximum displacement of 4 voxels and p = 0.5, and
gamma intensity transformation. Although Basaran et al. (2024) applied noise with σ = 1, this level of
noise dominated the lesions in our case, so we reduced this to σ = 0.1. We applied random rotation
around the z-axis with degrees ≤ 89 with p = 0.5 as in the original paper, but we limited rotation around
the other axes to [-5, 5] degrees because our patches are narrow in the x-y plane.

We matched the choice of inserted lesion position with our method, i.e., the position is randomly varied
along the z-axis, and any area of the inserted lesion that lies outside the spinal cord mask was removed.
### 4.1.3 Real-Only Baselines

To understand the contributions of synthetic data, we also examined models trained exclusively on real data under various sampling strategies.

When comparing to a real-image-only approach, two important questions arise: 1) could any observed benefit of our method be simply because of the introduction of a larger variability in normal anatomy and imaging characteristics, and 2) is the benefit of the method due simply to a higher frequency of lesions observed during training, i.e., because we reduce class imbalance.

**Real - Balanced** To address the first question above, we take the same training framework as for our method, where the only difference is that no synthetic lesions are inserted. In other words, for each training epoch, the model will see all examples with real annotated lesions and an equal number of real volumes with no lesions. We assess if there is an impact on the proportion of lesion/no lesion by also running experiments with 25%/75% and 75%/25% lesion/no lesion examples, respectively. The number of iterations and epochs were kept consistent with the base experiments.

**Real - Lesions Only** To address the second question above, i.e., is there a benefit from our method simply because of the higher frequency of lesions during training, we train a model which sees only examples with real lesions during training. To maintain consistency in the number of iterations and epochs, we sample four patches from each volume for each epoch rather than two patches per volume for the other experiments.

## 4.2 Training Set Size

To examine the impact of training set size on our method and the baselines, we conducted all experiments at four different training set scales. The number of volumes with real lesions used for training at each scale was 17, 36, 72, and 145. The volumes at scale 17 were a subset of those at scale 36, and so on. For all scales, the number of available real volumes with no GT lesions was approximately 70. These volumes were randomly sampled during each epoch to match the number of volumes with real lesions at that scale. At the highest scale (i.e., 145), this sampling procedure leads to oversampling the volumes with no lesions at every epoch. At each scale, the validation set contained volumes with real lesions and was approximately one-third the size of the training set. The test sets remained the same across all training set scales. For experiments where we vary the ratios of real to synthetic lesion volumes or
lesion to no lesion volumes, we kept the number of epochs and iterations consistent with the balanced 50%/50% setting. For example, at scale 17 with a 25%/75% real/synthetic ratio, at each epoch, we randomly sampled 8-9 volumes with real lesions and 25-26 volumes with no lesions, and synthetic lesions were inserted into these latter volumes.

## 4.3 Method Component Analysis

We conducted several experiments to determine the impact of certain design choices in our method and experimental setup, and the results of these are presented in Sec. 5.4. First, as has been already described, we conducted experiments with different proportions of synthetic to real examples while training with LesionSCynth. Second, we examined the impact of three parts of the intensity synthesis, namely 1) simply increasing the intensity by a multiplicative factor, 2) inducing a spatial gradient to the intensity increase using a Gaussian function, and 3) applying a local blur after introducing the Gaussian spatial gradient. Third, we explored the effect of generating diverse synthetic examples on-the-fly compared to a small fixed set of synthetic examples. In the experiments described thus far in the paper, our method used a set of approximately 70 volumes with no GT lesions into which synthetic lesions were inserted on-the-fly during training. Moreover, these volumes were sampled randomly *per epoch* to match the number of volumes with real lesions at that training set scale. We tested a scenario where a fixed subsample of these volumes is selected randomly *before training* and a fixed set of synthetic lesions are inserted into these, thereby reducing the variability of both lesion appearance and normal-appearing anatomy observed during training. We conducted this experiment at the two lower training set scales. At scale 17, we use 17 real volumes with real lesions and a fixed set of 17 volumes with inserted lesions, and at scale 36, we use 36 in each group.

## 4.4 Segmentation Model

All training procedures described above were implemented using a consistent segmentation model, described below.

**Architecture** The model architecture was based on a fully 3D U-Net from nnU-Net (Isensee et al., 2021), a state-of-the-art medical image segmentation framework. We used a residual encoder, shown to outperform the base nnU-Net in many tasks in the recent update (Isensee et al., 2024). We limited the number of levels in the U-Net to five (i.e., four strided convolution operations) after observing no benefit to extra levels in preliminary experiments. We further applied dropout with $p = 0.2$. Although
this is usually not applied in nnU-Net, the current study uses small training set sizes and so we applied dropout to help limit the risk of overfitting. Finally, we used a combined dice and cross-entropy loss, the default proposed by nnU-Net.

**Training** Patch size was set to 48 × 48 × 320 and two patches were randomly sampled from each preprocessed volume at each epoch. The batch size was set to eight. The total number of epochs was set such that the validation loss for most experiments had converged at that point. The number of iterations required until convergence was longer in experiments with more training data, and so the number of epochs was set to 2000 for scale=17, 1500 for scale=36, 1250 for scale=72, and 1000 for scale=145. The number of iterations per epoch was kept consistent across experiments for the same training data scale and was based on observing two patches per volume with real lesions and two patches from an equal number of volumes with no lesions or with synthetic lesions inserted. For example, the number of iterations per epoch at scale=17 was ⌈(17×2×2)/8⌋ = 9, where 8 is the batch size.

During training we applied the following data augmentations, similar to nnU-Net, but here using the TorchIO library (Pérez-García et al., 2021): gamma intensity transform, flipping, blurring, simulating a bias field, downsampling, noise, and an affine transformation including rotation and scaling. Given the long and narrow nature of our patches, rotation was applied only around the z-axis, with a maximum of 30 degrees.

We assessed two hyperparameter settings. The first included the default optimiser, scheduler and normalisation from nnU-Net, i.e., SGD, polynomial decay of the learning rate, and InstanceNorm. The second used the AdamW optimiser with a weight decay factor of 0.01, no learning rate scheduler, and GroupNorm with 16 groups. We speculated that if there were certain filter channels in the network associated primarily to recognising lesions and there were no lesions in a given patch, InstanceNorm may destroy this information, whereas GroupNorm allows some extra degrees of freedom so that this problem could be reduced. We ran 5-fold cross validation with these two hyperparameter settings at two scales, 17 and 36, training with our method, and also the *Real - Lesions Only* and *Real - Balanced* baselines. The AdamW+GroupNorm setting achieved the highest FROC scores on the validation sets in all of the above cases, so we used this setting for the remaining experiments. The full results on the test sets for these two hyperparameter settings are available in the supplementary material.

During training, we saved checkpoints for two epochs, the epoch with the best loss on the validation set and also the final epoch. When evaluating each experiment, we calculated the FROC metric on the validation set for both checkpoints and selected the one which achieved the maximal performance.
**4.5 Evaluation**

We used the evaluation protocol proposed by the MS-Multi-Spine Challenge on MS spinal cord lesion
detection, which is taking place at MICCAI 2025¹. The challenge uses the FROC metric, which puts more
emphasis on lesion detection rather than segmentation, as this is currently more important in clinical
practice. In particular, given a prediction mask where each lesion has a predicted score or probability, the
sensitivity is calculated at five levels of False Positive lesions Per Image (FPPI), namely 0.25, 0.5, 1, 2,
and 3, where a predicted lesion is considered a true positive if the intersection over union (IoU) with a
GT lesion is above 0.2. The FROC score is then the average of these five sensitivity values. Evaluating
methods in such a way gives a fairer comparison and a more complete picture than evaluating at a single
threshold.

To calculate the FROC score from the output of a segmentation model, i.e., where each voxel is associated
with an output score, a typical approach is to first binarise the mask at some threshold, compute the
connected components, and then aggregate (e.g., mean or max) the voxel scores to have one score for
each connected component. We tested two values for the initial binarisation threshold, 0.01 and 0.5,
and two aggregation approaches, mean and max. In early experiments, max aggregation nearly always
yielded superior FROC scores, so we used only max aggregation for the results reported in the paper. The
optimal initial binarisation threshold, however, depended on the model, so we evaluated at both 0.01 and
0.5 for all experiments, and chose the threshold which yielded the highest performance on the validation
set. For each of the five runs of each experiment, we therefore had four possible sets of predictions –
two choices of saved checkpoint from the training run (see Sec. 4.4) and two choices of binarisation
threshold.

In general, this procedure to choose which checkpoint and binarisation threshold to use tended to yield
improved results. However, for experiments with a small validation set, individual images have a larger
impact on the optimal choice for the validation set, and so this might diverge from the optimal configu-
ration for the test set. Therefore, alongside the FROC score on the test set using the ‘best’ configuration
for the validation set, we also report the maximum possible FROC on the test set out of the four pos-
sibilities (two checkpoints and two binarisation thresholds), which we refer to as FROC<sub>max</sub>. This allows
us to separate the effect of whether the training process allows to learn a better separation of lesion and
non-lesion from the effect of choosing the ‘best’ configuration based on the validation set.

We also report the lesion sensitivity and precision at a standard binarisation threshold of 0.5, as well as
lesion sensitivity, precision, F1 and Dice score at the threshold which yields an average of one false positive

<footnote n="1">¹https://portal.fli-iam.irisa.fr/ms-multi-spine/</footnote>
per image. To separate segmentation performance from detection performance, we report Dice$_{IoU>0}$,
i.e., Dice score calculated on the subset of GT lesions and predicted lesions that have a non-zero overlap
with each other.

In Sec. 5.5, we compare the best models in the current study to open-source lesion segmentation models
from SCT and to the results reported in a clinical evaluation study (Lodé et al., 2025). For this part
of the evaluation, we used the same data and evaluation metrics as Lodé et al. (2025): a GT lesion is
detected if there is a non-zero overlap with the prediction, i.e., at least one voxel is captured, and a
predicted lesion is a false positive if it does not overlap with any GT lesion. This diverges from the other
definition used in this study, which is based on a GT lesion requiring IoU > 0.2 with a predicted lesion
to be considered a true positive.

Finally, we carried out two types of statistical tests in the study. First, when comparing two sets of FROC
results, where we had five FROC values arising from the five cross-validation runs, we conducted a two-
sided pairwise t-test. Second, when comparing metrics calculated at the image level (e.g., sensitivity,
precision, etc.), we calculated the mean result for each volume across the five runs, and then conducted
a two-sided pairwise wilcoxon signed-rank test. Many volumes had values of 1 or 0 for these image-level
metrics, and so a parametric t-test was not appropriate in this case.

# 5 Results

We first consider the high-level results of all methods in a low-data scenario, i.e., at the lowest scale
of training set size in Sec. 5.1, before going into more detail in comparing LesionSCynth vs. using real
images only in Sec. 5.2, and vs. other synthesis methods in Sec. 5.3. Finally, we present the results of
ablation studies and other investigations in Sec. 5.4, and compare to other spinal cord lesion segmentation
models in Sec. 5.5.

## 5.1 Overall Performance in Low-Data Setting

Table 1 presents the results of all methods when trained at the lowest training set scale, i.e., with 17
volumes with real lesions. Our method led to a better FROC score in this low-data setting than all
other baselines. In fact, using synthetic lesions generated by CarveMix or LesionMix$_{pop}$ actually led to
a lower performance than simply training with real data. Training only on synthetic lesions from our
method and excluding the 17 volumes with real lesions led to a much lower performance. This suggests
<caption>Table 1: Performance when training at the lowest scale, i.e., 17 volumes with real lesions in the training set. Mean ± standard deviation were taken over five runs.</caption>

<table><thead><tr><th>Method</th><th>FROC Score</th><th>FROC<sub>max</sub></th></tr></thead><tbody><tr><td>Real - Balanced</td><td>0.365* ± 0.051</td><td>0.365* ± 0.052</td></tr><tr><td>Real - Lesions Only</td><td>0.439 ± 0.091</td><td>0.455 ± 0.061</td></tr><tr><td>CarveMix (X. Zhang et al., 2023)</td><td>0.405 ± 0.029</td><td>0.408* ± 0.025</td></tr><tr><td>LesionMix<sub>pop</sub> (Basaran et al., 2024)</td><td>0.404 ± 0.022</td><td>0.432* ± 0.039</td></tr><tr><td>LesionSCynth (Synthetic Only)</td><td>0.224* ± 0.076</td><td>0.249* ± 0.081</td></tr><tr><td>LesionSCynth (50%/50% Real/Synthetic)</td><td><strong>0.460</strong> ± 0.066</td><td><strong>0.523</strong> ± 0.036</td></tr></tbody></table>

that the characteristics of generated lesions are still relatively distinct from real lesions, and the benefit only comes when real and synthetic lesions are combined to broaden the learned distribution of lesion characteristics. Finally, although some differences with our method were not statistically significant, notably when compared to *Real - Lesions Only*, it should be noted that this may simply be a question of statistical power, given that only five observations were used for the statistical test. Indeed, looking at statistical significance using metrics calculated at the image level in Sec. 5.2, most differences were statistically significant.

## 5.2 Comparison with Real-Only Baselines

Fig. 6 presents the performance at different training set scales for our method vs. baselines trained on real data only. As seen in the previous section, our method outperformed these baselines by a considerable margin at the lowest scale. However, this gap narrowed as the number of real volumes available for training increased. When 145 volumes with real lesions were available, then an equivalent performance was given by a baseline trained only on real data. Importantly, in all cases, our method did not deteriorate performance compared to training on real data only, and improved results when only a small number of annotated volumes were available.

As might be expected, the average performance increased in most cases when adding more training data. There were, however, two exceptions to this, including for LesionSCynth, where the FROC dropped by 0.016 between scales 17 and 36. Possible explanations for this are discussed in Sec. 6.

Fig. 7 explores the relationship between performance and the proportion of volumes per epoch containing lesions when training only on real volumes. The point at 100% corresponds therefore to the *Real - Lesions Only* baseline in Fig. 6 and 50% corresponds to the *Real - Balanced* baseline. The most striking pattern

<footnote>*Statistically significant difference vs. LesionSCynth (50%/50%) at 0.05 significance level.</footnote>
<figure><img src="image_7.png" /><figcaption>Figure 6: Performance at different training set scales for our method vs. baselines using only real data. The best FROC score on the test folds is reported, with the mean and standard error (SE) calculated over five runs. Error bars are ±1.96 × SE. Note that each of the methods was trained with the same amount of data, but the points are offset along the x-axis for clarity. Training set scales are 17, 36, 72, 145 real volumes with lesions, with an equivalent number of volumes with no lesions or with synthetic lesions, depending on the method used.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 7: When using only real volumes during training, what is the effect of the proportion of volumes per epoch that contain lesions? The dashed lines represent the performance of our LesionSCynth method trained with real & synthetic lesions.</figcaption></figure>
observed here is at training set scale 17, where performance increased significantly when using more
volumes with lesions per epoch and fewer volumes with no lesions, with FROC increasing from 0.335
at 25% to 0.455 when only volumes with lesions were used for training. This pattern was not repeated
at the other scales, and indeed no consistent pattern was discernible among the three larger training
set sizes. When comparing each scale to the corresponding dashed line representing our method, we
observed a clear increase in performance at scale 17 between the real baselines and our method. We
note a more modest, but consistent, gap between the baselines and our method at scale 36, with FROC
of 0.487 at 100% vs. our method at 0.507. At the two highest training set scales, however, our method
fell in a similar range to the baselines.

Moving from the multi-threshold evaluation given by FROC to an evaluation at individual thresholds
on the predicted scores, Table 2 presents lesion-wise metrics alongside the Dice score for our method
and the baselines on real data only. When evaluated at a point with an average of one false positive
per image, our method consistently achieved the best lesion sensitivity and Dice$_{IoU>0}$ at all training set
scales. However, the gap between our method and the next best result decreased as the training set
scale increases, similarly to the previous observations on the FROC score. All experiments had relatively
low Dice and lesion F1 scores, particularly if compared to brain lesion segmentation. However, Sec. 5.5
will put these results into a broader context and will show that these models are still clinically relevant.

Finally, Fig. 8 shows the segmentations for three lesion examples in the dataset where training with LesionSCynth improves performance compared to real-only baselines. *Real - Lesions Only* model did segment at least part of these three lesions using a threshold of 0.5 on the output scores. However, the outputs for this model also contained many false positives, so applying a threshold to give one false positive per image on average led to the true positive predictions being removed. For LesionSCynth, however, the true positive segmentations remained and a false positive in Fig. 8-2A was removed when applying the threshold which yields FPPI=1 (2B). Finally, none of these lesions were detected by the model trained only on real examples with 75% lesion examples and 25% non-lesion examples per epoch. The model segmented small parts of the lesions at thresh=10⁻⁵, but also segmented many false positives at this level, including even areas outside the spinal cord.

5.3 Comparison with Synthetic Lesion Baselines

Similar to the trends observed when comparing to real-only baselines, we can see from Fig. 9 that our
method outperformed the state-of-the-art synthesis baselines by a large margin at small training set
sizes, but this gap reduced as the training set size increased. Specifically, our method achieved the
Table 2: Evaluation at specific thresholds on the softmax outputs (mean ± std. dev. over five runs). Lesion sensitivity and precision are given when **binarising at a standard threshold of 0.5** on the softmax outputs. Results are also reported for the threshold which yields **1 false positive per image (FPPI) on average**: lesion sensitivity, precision and F1 score are given, alongside standard Dice score and also Dice evaluated only on GT and predicted lesions for which there is a non-zero overlap. **Real - LO**: Baseline trained on real volumes with lesions only; **Real - Bal**: Baseline trained on real volumes, balanced per epoch between volumes with real lesions and volumes with no lesions; **LSC**: LesionSCynth - trained on a mix of volumes with real lesions and volumes with synthetic lesions.

<table><thead><tr><th rowspan="2">Scale</th><th rowspan="2">Method</th><th colspan="2">Eval at thresh=0.5</th><th colspan="6">Eval at FPPI@1</th></tr><tr><th>Sensitivity</th><th>Precision</th><th>Sensitivity</th><th>Precision</th><th>F1</th><th>Dice</th><th>Dice<sub>IoU>0</sub></th></tr></thead><tbody><tr><td rowspan="3">17</td><td>Real - LO</td><td>.55 ± .05**</td><td>.24 ± .07**</td><td>.42 ± .07**</td><td>.45 ± .03**</td><td>.36 ± .02**</td><td>.31 ± .02**</td><td>.51 ± .01**</td></tr><tr><td>Real - Bal</td><td>.49 ± .08**</td><td>.28 ± .07**</td><td>.39 ± .05**</td><td>.56 ± .05**</td><td>.41 ± .04**</td><td>.30 ± .03**</td><td>.51 ± .02**</td></tr><tr><td>LSC (Ours)</td><td><strong>.66</strong> ± .02</td><td><strong>.29</strong> ± .04</td><td><strong>.52</strong> ± .05</td><td><strong>.58</strong> ± .01</td><td><strong>.45</strong> ± .05</td><td><strong>.37</strong> ± .03</td><td><strong>.55</strong> ± .02</td></tr><tr><td rowspan="3">36</td><td>Real - LO</td><td>.63 ± .04**</td><td>.27 ± .03**</td><td>.47 ± .06**</td><td>.54 ± .04</td><td>.42 ± .06**</td><td>.34 ± .03**</td><td>.54 ± .03</td></tr><tr><td>Real - Bal</td><td>.60 ± .06**</td><td>.30 ± .05**</td><td>.50 ± .05**</td><td><strong>.60</strong> ± .04</td><td><strong>.48</strong> ± .05**</td><td>.36 ± .02</td><td>.55 ± .03</td></tr><tr><td>LSC (Ours)</td><td><strong>.66</strong> ± .02</td><td><strong>.34</strong> ± .02</td><td><strong>.52</strong> ± .03</td><td>.55 ± .02</td><td>.45 ± .03</td><td><strong>.37</strong> ± .02</td><td><strong>.56</strong> ± .02</td></tr><tr><td rowspan="3">72</td><td>Real - LO</td><td>.66 ± .04*</td><td>.34 ± .04**</td><td>.53 ± .04</td><td>.53 ± .04*</td><td>.44 ± .05</td><td><strong>.40</strong> ± .02</td><td><strong>.58</strong> ± .02</td></tr><tr><td>Real - Bal</td><td>.64 ± .04**</td><td><strong>.35</strong> ± .06</td><td>.53 ± .04</td><td><strong>.56</strong> ± .01</td><td><strong>.46</strong> ± .03</td><td>.37 ± .02</td><td>.55 ± .02**</td></tr><tr><td>LSC (Ours)</td><td><strong>.68</strong> ± .05</td><td>.31 ± .05</td><td><strong>.54</strong> ± .03</td><td>.55 ± .03</td><td><strong>.46</strong> ± .04</td><td>.39 ± .03</td><td><strong>.58</strong> ± .004</td></tr><tr><td rowspan="3">145</td><td>Real - LO</td><td>.67 ± .05**</td><td><strong>.33</strong> ± .04</td><td>.53 ± .02**</td><td>.52 ± .03</td><td>.42 ± .03*</td><td>.39 ± .02</td><td>.58 ± .02</td></tr><tr><td>Real - Bal</td><td>.68 ± .04**</td><td>.32 ± .06</td><td><strong>.59</strong> ± .03</td><td><strong>.57</strong> ± .02</td><td><strong>.49</strong> ± .02</td><td><strong>.41</strong> ± .03</td><td>.58 ± .01</td></tr><tr><td>LSC (Ours)</td><td><strong>.71</strong> ± .02</td><td>.31 ± .02</td><td><strong>.59</strong> ± .01</td><td>.56 ± .02</td><td>.48 ± .02</td><td>.40 ± .03</td><td><strong>.59</strong> ± .01</td></tr></tbody></table>

<footnote>**: 0.01; *: 0.05 – statistically significant difference, comparing to LesionSCynth at the same scale.</footnote>
<figure><img src="image_9.png" /><figcaption>Figure 8: Examples where adding synthetic lesions during training improves sensitivity. The first row (A) in each plot is the result from a simple threshold of 0.5 on the output softmax scores, whereas the second row (B) involves first thresholding at 0.01, computing connected components, and applying a second threshold which achieves an average of 1 false positive per image. See the description of FROC for more details on this process (Sec. 4.5).</figcaption></figure>

highest FROC scores at scales 17, 36, and 72. However, the FROC score for LesionMix$_{pop}$ increased impressively from 0.492 at scale 72 to 0.578 at scale 145, achieving the highest result at this scale, and indeed the highest result across all experiments and methods in this study. This trend is not surprising as when there are few volumes with real lesions available, synthesis methods based on directly copying existing lesions may overfit to the specific intensity patterns of this small set. In contrast, our parametric synthesis method can help the model to generalise to a wider distribution. On the other hand, given a large and diverse set of lesions in the training set, it can be more beneficial to use these as they can be more realistic than those synthesised by a parametric method. We note that CarveMix had the worst performance across all scales, indicating that it is not well adapted to the spinal cord lesion setting.

## 5.4 Method Component Analysis

**Synthetic Lesion Ratio** Fig. 10 examines the impact of different ratios of synthetic vs. real lesion examples used per epoch. We note that there is a significant overlap in the confidence intervals for most of the observations, due in part to the fact that we have only five observations to calculate the standard error. However, even if the comparisons may not be statistically significant, the results still
<figure><img src="image_10.png" /><figcaption>Figure 9: Performance at different training set scales for our method vs. two lesion synthesis baselines, CarveMix and LesionMix$_{pop}$. The best FROC score on the test folds is reported, with the mean and standard error (SE) calculated over five runs. Error bars are ±1.96 × SE. Note that each of the methods was trained with the same amount of data, but the points are offset along the x-axis for clarity. Training set scales are 17, 36, 72, and 145 real volumes with lesions, with an equivalent number of volumes with no lesions per epoch, into which synthetic lesions have been inserted using the respective synthesis method.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Figure 10: Effect of the proportion of synthetic lesions per epoch when training our method. For example, training with 25% synthetic examples means that for each epoch, there is a 3 : 1 ratio between real volumes with real lesions and volumes with inserted synthetic lesions.</figcaption></figure>

provide valuable insights. For example, the highest FROC score ($FROC_{max} = 0.554$) was observed at training scale 17 when 25% of volumes per epoch contained synthetic lesions and 75% were real. Indeed, this also outperformed all baselines trained on real volumes only. The standard error for this result is relatively large, influenced in particular by one outlier with a low value among the five runs. The FROC values for the five runs were 0.469, 0.558, 0.562, 0.577, and 0.603. Conversely, the worst performance across scales occurred when 75% of volumes per epoch contained synthetic lesions and 25% were real.

**Ablation – Lesion Generation** Table 3 presents the results of ablation experiments on key parts of the synthesis process at the training set scale of 17 volumes with real lesions. In fact, there was very little change in the results between these three experiments, indicating that although the extra steps of introducing a spatial gradient and a local blur may increase how realistic the synthesised lesions are, these steps did not help the segmentation model to generalise further. Indeed, it seems sufficient to simply increase the intensity inside a candidate lesion area by a well chosen multiplicative factor.

**On-the-fly vs. Fixed Synthetic Examples** Table 4 presents the results of using a fixed set of synthetic examples generated offline rather than generating more diverse examples on-the-fly during training. We can see that at scale 17, the standard setting with more diversity achieved a higher FROC
<table><caption>Table 3: Results without selected parts of synthesis method, at training set scale 17.</caption><thead><tr><th>Gaussian Spatial Gradient</th><th>Blur</th><th>FROC<sub>max</sub></th></tr></thead><tbody><tr><td></td><td></td><td>0.525 ± 0.057</td></tr><tr><td>✓</td><td></td><td>0.532 ± 0.040</td></tr><tr><td>✓</td><td>✓</td><td>0.523 ± 0.036</td></tr></tbody></table>

<table><caption>Table 4: Results when using a smaller fixed set of examples synthesised offline vs. the default setting of creating more diverse synthetic examples on-the-fly while training our method. The differences were not statistically significant at the 0.05 significance level.</caption><thead><tr><th>Training set scale</th><th>Setting</th><th>FROC<sub>max</sub></th></tr></thead><tbody><tr><td rowspan="2">17</td><td>Synthesise on-the-fly (default)</td><td><strong>0.523</strong> ± 0.036</td></tr><tr><td>Fixed synthetic images</td><td>0.507 ± 0.070</td></tr><tr><td rowspan="2">36</td><td>Synthesise on-the-fly (default)</td><td>0.502 ± 0.062</td></tr><tr><td>Fixed synthetic images</td><td><strong>0.511</strong> ± 0.051</td></tr></tbody></table>

with a difference of 0.022, whereas at scale 36 it is the opposite, where the setting with a fixed set of synthetic examples had a slightly higher performance with a difference of 0.009. In both cases, the differences were not statistically significant.

## 5.5 Comparison to other lesion segmentation tools

Finally, we place the models trained in this study in a broader context by comparing to existing open-source models from SCT and to a model which helped to improve the lesion sensitivity of radiologists in a clinical evaluation study (Lodé et al., 2025). The results are shown in Table 5. Note that the definitions of lesion sensitivity and precision here are different than those used in the previous sections – see Sec. 4.5 for details.

From the models in the current study, we see again that LesionMix<sub>pop</sub> trained at the highest training set scale achieved the best performance, with a mean lesion sensitivity of 0.83 and lesion precision of 0.59. We note that this is a lower sensitivity and higher precision than the model in the clinical evaluation study (sens=0.89, prec=0.54), but adjusting the threshold on the softmax outputs may allow us to get closer to these values. This demonstrates that, even though the metric values in the previous sections seem low, for example compared a typical Dice score for brain lesion segmentation, models at this level of performance can still be impactful in a clinical setting, given the difficulty of the task.
<table><caption>Table 5: The best models from the previous analysis, evaluated with the metric definitions used by Lodé et al. (2025), after binarising the softmax outputs at a threshold of 0.5. A GT lesion is a true positive here if there is a non-zero overlap with a prediction. Results are presented as mean ± std. dev. over five runs.</caption><thead><tr><th>Method</th><th>Scale</th><th>Sensitivity</th><th>Precision</th></tr></thead><tbody><tr><td>LesionSCynth (25%/75% synth/real)</td><td>17</td><td>0.79 ± 0.05</td><td>0.53 ± 0.06</td></tr><tr><td>LesionSCynth (50%/50% synth/real)</td><td>145</td><td>0.81 ± 0.04</td><td>0.56 ± 0.06</td></tr><tr><td>Real - Balanced</td><td>145</td><td>0.79 ± 0.08</td><td>0.56 ± 0.07</td></tr><tr><td>LesionMix<sub>pop</sub></td><td>145</td><td>0.83 ± 0.02</td><td><strong>0.59 ± 0.02</strong></td></tr><tr><td>sct_deepsegLesion (v6.5)</td><td></td><td>0.41</td><td>0.55</td></tr><tr><td>sct_deepsegLesion_ms (v6.5)</td><td></td><td>0.79</td><td>0.42</td></tr><tr><td>Lodé et al. (2025)</td><td></td><td><strong>0.89</strong></td><td>0.54</td></tr></tbody></table>

From Table 5, we can also see that the newer lesion segmentation model from SCT (sct_deepsegLesion_ms) achieved a much higher sensitivity than the previous version, with a sensitivity in a similar range to the models trained in this study. However, the precision was lower than the models from this study, which ranged from a precision of 0.53 to 0.59.

# 6 Discussion

## 6.1 Comparison with Real-Only Baselines

As observed in Sec. 5.2, when few annotated volumes with lesions are available for training, introducing synthetic lesions with our method can significantly outperform training with real data only. A surprising and promising result was observed in Sec. 5.4 in the experiments with different ratios of synthetic to real examples at each epoch. Here, training with 25% synthetic lesion examples and 75% real examples per epoch at the lowest training set scale achieved an average FROC of 0.554, which is higher than all the other experiments with our method and higher than all baselines trained on real data only, regardless of the training set size. The standard error for this experiment is relatively large over the five runs, with the lowest FROC at 0.469 and the other four runs having a FROC between 0.558 and 0.603. This indicates that the particular volumes in the training set can have a large impact on the score when few volumes with real lesions are available. Nonetheless, this observation shows that, with a small training set and our method of lesion synthesis, it is possible to achieve the same, or possibly better, performance as having a much larger dataset for training.
A surprising result in Sec. 5.2 was that, when training on real samples only, adding volumes with no lesions to the training set leads to a significant drop when we train with 17 real volumes with lesions, but improves performance when the training set contains 145 real volumes with lesions. We speculate that at scale 17, the higher diversity of volumes without lesions relative to those with lesions leads the model to learn a wider distribution for this group, which leads to a reduced sensitivity at inference. Finally, *Real - Lesions Only* is not superior in all aspects to *Real - Balanced* at scale 17, as we saw in Table 2 that the latter achieves a higher lesion precision and thus higher F1 score.

In Sec. 5.2, we observed two cases where performance does not increase when we increase the training set size, including a drop from scale 17 to 36 when training with LesionSCynth. Given that the standard error bars overlap significantly across the results for the three training set scales, it is possible that this pattern is due to chance, and that if the same experiments were repeated many times with different random seeds, we might see a more intuitive pattern of increasing performance as we increase the training set size. We do observe the same pattern of higher performance at scale 17 vs. 36 in Fig. 10, with different proportions of real vs. synthetic lesion MR volumes, but again the range indicated by the standard error is relatively high there. Another explanation of the pattern might be that the particular samples in the training set at scale 17 are 'better' in some way than the set at scale 36, e.g., more similar lesion characteristics to those in the held-out test fold, or there is some label noise introduced at scale 36 in the form of missing lesions in the GT mask. However, the same volumes with lesions are used for all three methods in Fig. 6, and for the other two cases, performance does increase from scale 17 to 36. Therefore, it is more likely here that the combination of synthetic lesions with the particular real lesions at scale 17 achieves a better generalisation to the lesions in the held-out test set. However, given the large observed standard errors, it is not possible to make a concrete conclusion on these observations.

## 6.2 Comparison with Other Lesion Synthesis Methods

The results in Sec. 5.3 demonstrated that our method generally outperforms state-of-the-art lesion synthesis methods which are based on copying real lesions from one volume to another. The improvement of our method over the baselines decreases as we scale up the training dataset, and at the highest training set scale, a previous synthesis method, $LesionMix_{pop}$, achieves the highest performance. CarveMix, however, remains consistently lower than both methods across all training set scales. At higher training set scales, therefore, it would seem that $LesionMix_{pop}$ is a better choice. Moreover, as the training set size increases, GANs and diffusion models become a more viable option for synthesis.

One advantage of a parametric method such as ours over methods which copy existing lesions into other
volumes is that the parameters could be adapted for domain adaptation or generalisation to other MR
sequences. This could be done even without training on real lesion examples in the other MR sequences
by instead drawing on prior knowledge. For example, previous studies have shown that lesions in STIR
acquisitions tend to have higher contrast (Philpott & Brotchie, 2011), so we could increase the mean
of the contrast distribution (μ = 0.17 from Sec. 3.1), using a small validation set with STIR lesions
to determine a reasonable value. For T1-w acquisitions where lesions appear hypointense, we could
similarly adjust the contrast calculation so that μ = 0.17 would mean that synthetic lesions have 17%
lower intensity than their neighbourhoods, on average.

We note that there are several parts of the original LesionMix that are not applied in this study, notably the
other branch which also randomly removes existing lesions through inpainting as an extra augmentation
technique and also the use of a prior probability map to choose new lesion positions. These elements are
excluded here as we chose to isolate the impact of synthesis of lesion appearance, and those techniques
are agnostic of the synthesis method used and so could also be added to our method to potentially
improve performance.

**6.3 Method Component Analysis**

Although our three-part approach to synthesising lesions allows us to create more realistic-looking lesions, one can ask whether synthetic lesions need to be completely realistic to benefit the trained segmentation model. Indeed, our ablation study presented in Sec. 5.4 indicates that simply increasing the intensity by a multiplicative factor to create a lesion may be enough to guide the model to learn a wider representation of lesion characteristics. Inducing a spatial gradient in the intensity and increasing local homogeneity of intensity did not further increase performance when training at the lowest training set scale.

One of the proposed advantages of the method is from the introduced diversity, both in the characteristics
of the lesions given that the parameters for each lesion are drawn from random distributions, and also in
the tissue surrounding lesions, given that lesions are inserted in random positions into a random selection
of volumes originally containing no lesions. However, as we observed in Sec. 5.4, there is a limit to the
benefit from diversity. Indeed, inserting a fixed set of synthetic lesions into a fixed subset of volumes
achieves similar performance to randomly sampling among 70 volumes with no lesions at each epoch, and
synthesising new lesions on-the-fly. However, we can imagine situations where more no-lesion volumes
might still be beneficial, if these contain types of acquisitions otherwise under-represented, e.g., different
scanners, resolutions, or even different MRI sequences.
6.4 Outlook

In Sec. 5.5, we observed that LesionSCynth, trained on 17 volumes with real lesions and 70 volumes with no lesions outperformed a state-of-the-art model from the SCT. This difference in performance is likely due in large part to the similar distribution between our training and testing data. The acquisitions in the test set from Lodé et al. (2025) were extracted from OFSEP, as were a large part of the acquisitions in the training set for the current study (note, however, that there is no overlap between the subjects from these two sets). Therefore, both sets contain typical sagittal T2-w acquired in clinical practice in France, as well as similar distributions of resolution and even acquisitions from the same scanners. Moreover, both sets of manual annotations were reviewed and validated by the same senior neurologist (AK), so there may be more annotation shift between the SCT training set and the clinical evaluation study than for our training set. However, it is very promising that, given an in-distribution dataset with fewer than 20 volumes with real lesions, plus a larger set of volumes with no lesions, it is possible to achieve similar or better performance than training on a large out-of-distribution dataset containing over 1000 T2-w acquisitions.

Although the metric values may seem low when compared to brain lesion segmentation, spinal cord lesion segmentation is a more difficult task and suffers higher inter-rater variability (Lodé et al., 2025; Walsh et al., 2023). The best models from the current study achieved similar results to the model used by Lodé et al. (2025), albeit with a lower sensitivity and higher precision. Lodé et al. (2025) found that the outputs of the model in that study helped to improve the mean sensitivity of 20 radiologists and neurologists by five percentage points, and also led to an improvement in mean precision among raters with less than 10 years' experience. Given that the models in the current study achieved similar performance, they may also be beneficial in a clinical setting.

Finally, LesionSCynth could also be used as a domain adaptation or generalisation technique. Given a set of manually annotated acquisitions from one scanner or one MR sequence and a set of acquisitions from another scanner or sequence of healthy controls or people with MS who do not have spinal cord lesions, the LesionSCynth parameters could be adapted to synthesise lesions in the new domain, which could increase the applicability of the trained segmentation model. Moreover, such a technique could also be used in an active learning scenario, where a small set of manual annotations are used to train an initial model, whose outputs are then given to experts to manually correct.
## 6.5 Limitations

Our method is based on empirical observations on 1) the contrast of lesions compared to neighbouring normal-appearing tissue, 2) the spatial variation of intensity within lesions, and 3) the variance of intensities within lesions. We apply independent operations to emulate these observations and therefore the method implicitly assumes independence of these aspects, which is not necessarily the case. It is likely, for example, that lesions with a higher level of spatial variation also have a higher overall intensity variance, and it is possible that lesions with higher contrast have higher variance. Further research would be required to analyse these relationships and adapt the method, if required. However, ablation experiments indicated that extra steps inducing spatial variation or reducing overall variance do not necessarily bring more benefit than simply increasing the intensity within a lesion candidate by a multiplicative factor, even if they do help to make more realistic lesions, so it is not clear that future work in this direction would bring further benefit.

The approach we took of inserting synthetic lesions into volumes without lesions assumes that these volumes are available, even in scenarios with few data annotations. We believe this a fair assumption to make, given that there are already open-source spinal cord datasets with acquisitions of healthy subjects (Cohen-Adad et al., 2021), and in clinical databases, radiologist reports associated with the acquisitions could be used to identify acquisitions containing no lesions.

## 7 Conclusion

This study introduced LesionSCynth, a parametric lesion synthesis method that improves MS lesion segmentation in spinal cord MRI, particularly when annotated data are limited. Our experiments showed that models trained with synthetic examples and a small number of real lesions can match or exceed the performance of models trained on much larger real-only datasets. LesionSCynth outperforms existing synthesis methods at smaller data scales and offers flexibility for domain adaptation through adjustable parameters. Despite its simplicity, the method provides substantial gains in model performance, making it a practical tool for enhancing spinal cord lesion detection and reducing annotation effort.
# Data and Code Availability

Most of the data used in this study is from the French MS Registry (OFSEP), and requests can be made directly to OFSEP in the form of a project proposal.<fnref n="1" />

Code for the project is available on GitHub.<fnref n="2" />

# Author Contributions

R.W.: conceptualisation, methodology, software, validation, formal analysis, investigation, and writing (original draft, review & editing). P.K., D.K.: conceptualisation, methodology, writing (review & editing). A.K.: data curation, writing (review & editing). S.W.: conceptualisation, methodology, supervision, and writing (review & editing). F.G., B.C.: conceptualisation, methodology, supervision, and writing (original draft, review & editing)

# Funding

R.W. was supported by the French doctoral programme in artificial intelligence, managed by the French National Research Agency (ANR) (ANR-20-THIA-0018), and travel grants from FranceSEP, GdR IASIS, and Rennes Métropole. This research was supported in part by NIH R01 LM013608. This work was supported in part by ANR through the France 2030 programme (ANR-21-RHUS-0014). Data collection was supported by ANR through the France 2030 programme (ANR-10-COHO-002 OFSEP).

# Declaration of Competing Interests

The authors have no competing interests to declare.

# Acknowledgements

Experiments presented in this paper were carried out using the Grid'5000 testbed, supported by a scientific interest group hosted by Inria and including CNRS, RENATER and several universities as well as other organisations (see https://www.grid5000.fr).

<footnote n="1">¹https://www.ofsep.org/en/data-access</footnote>

<footnote n="2">²https://www.github.com/rickymwalsh/LesionSCynth</footnote>
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# A Supplementary Material

## A.1 Preprocessing

### A.1.1 Spinal Cord Segmentation

A key part of preprocessing is to obtain a segmentation mask of the spinal cord. This is later used in 1) cropping the image to remove redundant information, 2) calculating the contrast between a lesion and its neighbouring spinal cord voxels, and 3) ensuring inserted synthetic lesions are only within the spinal cord. Spinal cord segmentations were obtained using the trained deep learning models from the Spinal
Cord Toolbox (SCT) (De Leener et al., 2017).

The T2-w model was used for both the upper and lower volumes. However, this model often fails to segment the conus medullaris (lower end) well and frequently descends below the terminal end of the spinal cord or segments parts of the CSF. The available SCT lumbar T2-w model, on the other hand, performs well in the conus region but often does not capture the spinal cord at the top of the lower acquisitions. Therefore, we merge both segmentations for lower volumes to capture the best of both models. Specifically, we compute the midpoint of the lumbar model's segmentation along the superior-inferior axis and construct the final mask by taking the lumbar model's segmentation below this point and the T2-w model's segmentation above it. In future implementations, ...The more recent update of the contrast-agnostic model from SCT (v6.4 and above) seems to perform well on both our upper and lower acquisitions from preliminary investigations, and so this model could be used in future to segment the spinal cord, replacing the current two-step approach.

We applied several postprocessing steps to the spinal cord masks to reduce the possibility of false positive segmentations outside of the spinal cord. First, we applied a morphological closing operation using a cube-shaped structuring element with a width of 3 voxels. This helped close small gaps in the segmentation which can occur occasionally, particularly along the S-I axis. Next, we removed all but the largest 3D connected component in the segmentation, and we applied a 2D binary opening to each sagittal slice, with a square structuring element of width 3 voxels. This helped to remove isolated parts of the segmentation which could cause unusual results when synthesising lesions. Finally, we observed several upper acquisitions where the spinal cord segmentation did not capture a small part of the bottom of the volume (e.g., 2-3 vertebrae). To address this, we extrapolated the segmentation into this region, given that the spinal cord shape tended to be approximately linear in this small section.

### A.1.2 Orientation and Spacing

We converted all images and segmentation masks to LAS+ orientation and re-sampled to 0.5mm isotropic spacing. Although the default setting of nnU-Net for anistropic data is to retain anistropic spacing, we found in previous experiments that isotropic spacing can lead to better results, which is also observed in a recent nnU-Net update (Isensee et al., 2024). Finally, the choice of 0.5mm is slightly lower than our median in-plane spacing of 0.58mm, but retains consistency with previous works on spinal cord lesion segmentation (Gros et al., 2019; Walsh et al., 2023, 2024).
### A.1.3 Spinal Cord Centreline

We computed the spinal cord centreline by taking the centre of mass of each axial slice. Where there were no voxels segmented in a given slice, we interpolated linearly from the nearest adjacent slices with segmented voxels. We extrapolated the centreline above and below by 10 slices to ensure that we captured the full cord as well as a small buffer zone. Finally we applied smoothing to the centreline, taking the vectors of x and y coordinates in each axial slice and applying a 1-D uniform filter with a window size of nine slices.

### A.1.4 Crop and Shift

Finally, we cropped and shifted the image around the spinal cord centreline, an approach proposed by (Gros et al., 2019) and recently used by (Walsh et al., 2024). Concretely, for each axial slice, we cropped to a square patch of 48 x 48 voxels around the centreline point. The 2D slices were then stacked along the z-axis, leading to a 'straightened' spinal cord without introducing interpolation. Although shifting the image around the centreline does not necessarily lead to improved segmentation performance, doing so allowed us to reduce the training time by a factor of three compared to simply cropping around the bounding box of the whole spinal cord. Moreover, it simplifies the positioning and orientation of synthetic lesions as all volumes are approximately aligned.

## A.2 Lesion Contrast & Intensity Variation

**Contrast vs. Neighbourhood** We chose to compare the lesion intensity to the intensity in its neighbourhood, rather than comparing to background or an average over the spinal cord, because a hyperintense lesion is only detectable in the image if it appears as hyperintense with respect to surrounding local tissue, not relative to the image as a whole. Furthermore, the intensities of different tissues can vary over the image. For example, to unambiguously detect a small lesion in the region of visible grey matter in the spinal cord, the intensity must be higher than for a lesion in a more homogeneous, lower intensity region of the spinal cord. Moreover, field inhomogeneities can introduce bias and affect the calculation of average background or spinal cord intensity.

**Effect of Neighbourhood Size** Fig. 11 compares the different contrast distributions obtained when changing the area taken around each lesion, i.e., the radius of the structuring element used when dilating each slice. Although the contrast increases slightly on average as we increase the area around the lesion,
the distributions remain largely similar. For the purposes of this study, we used a 5-voxel radius for the
dilation structuring element.

<figure><img src="image_12.png" /><figcaption>Figure 11: Distributions of lesions vs. their neighbourhoods, for different sizes of the dilation element used to obtain the neighbourhood masks, i.e., a disk structuring element with radius of A) 3 voxels, B) 5 voxels, or C) 7 voxels.</figcaption></figure>

**Low Contrast Lesions** As we can see from Fig. 11, there are several lesions with negative contrast or low contrast compared to their neighbourhoods. Low contrast lesions typically occur when: 1) the neighbourhood takes into account voxels with CSF partial volume effects (or normal tissue with high intensity, e.g., grey matter), 2) the lesion (or part of the lesion) is not clearly discernible in the sagittal T2-w acquisition but is evident in other acquisitions for the same subject, such as STIR or axial acquisitions, or 3) the manual segmentation misses some hyperintensity or includes some lower intensity voxels. Fig. 12 presents several examples of these.
<figure><img src="image_13.png" /><figcaption>Figure 12: Examples of lesions in the ground truth annotations with low average contrast with surrounding tissue. A) Not all of the segmented area contains hyperintensity in the T2-w image (average contrast = -0.06), though the hyperintensity is discernible in the STIR acquisition. B) The lesion occurs next to hyperintense grey matter (average contrast = -0.005). C) The lesion occurs in the region of visible grey matter (average contrast = 0.002).</figcaption></figure>
**Spatial Variation of Intensity** The following is a more detailed explanation of the background analysis and processing used to arrive at Fig. 4 in the main paper, which plots the average intensity vs. the distance from the lesion centroid, and shows that lesion intensity tends to be higher at the centre of the lesion.

When summarising intensity of lesion voxels across the whole dataset, especially when looking at it through the lens of spatial variation, it is important to consider the contribution of the normal tissue in the lesion region to intensity. In particular, if a lesion occurs in the region of CSF at the outer edges of the spinal cord, then partial volume effects may cause the lesion intensity to be higher in that region. Indeed, if we take the voxels of all lesions in the dataset and average them in the axial plane, we get the pattern shown in Fig. 13. The main observable pattern here is a ring of higher intensity around a darker centre, and the size and intensity pattern are comparable to the ring of CSF around the spinal cord for normal-appearing tissue. This is true in particular along the R-L axis, where resolution is limited, and so partial volume effects are more likely between CSF and lesions.

Analysis of the relationship between intensity and relative position within a lesion may be dominated by this higher outer intensity caused by the CSF, and indeed we observed such an effect in an initial analysis of intensity and spatial variation. To eliminate this ‘bias’ from the analysis, we computed the average normalised intensity in the axial plane across many non-lesion patches, and then subtracted this from the corresponding voxels in the normalised lesions. We outline a justification below for this procedure to analyse the spatial variation of lesion intensity.

Given a small patch, $P$, containing normal-appearing tissue, we assume that the image intensity at a given point $x \in P$ is a function $g_P(x)$ with the intensity determined principally by the underlying tissue. $g_P(x)$ also depends on the particular patch (and the acquisition) but we assume that this function $g_P(x)$ is drawn from the same distribution for all patches.

We assume that the intensity in a patch containing a lesion is given by

$$g_P^*(x) = g_P(x) \times (1 + f_P(x))$$

where $f_P(x)$ is zero everywhere outside of a lesion and inside the lesion determines the hyperintensity profile, but we make no further assumption on $f$ at this point. We aim to isolate the effect of this $f_P(x)$ on observed intensities, given that simply taking the raw average across lesion patches is dominated by the higher intensities of CSF (which would be captured by $g_P(x)$).

Standardising a ‘normal’ patch and a ‘lesion’ patch to mean 0 and standard deviation 1 gives the following:

$$z_P(x) = \frac{g_P(x) - \mathbb{E}_{x \in P}(g_P(x))}{s_{x \in P}(g_P(x))}$$
<figure><img src="image_14.png" /></figure>

Figure 13: Average intensity of voxels overlaid on the axial plane. This was done after preprocessing, i.e., all volumes were shifted around the spinal cord centreline so that they align roughly in the axial plane. A) ten random patches of 48 × 48 × 48 voxels containing normal-appearing tissue were extracted from all volumes in the dataset, the patches were each standardised to µ = 0, σ = 1 and the average was taken along the z-axis. B) all lesions were extracted from the dataset in patches of 48 × 48 × b where b is the length of the lesion in the z-axis, the patches were each standardised to µ = 0, σ = 1 and the average was taken along the z-axis, excluding any non-lesion voxels. The non-zero voxels at the edge of the image here were caused by an imprecise centreline during preprocessing, but only a small number of lesions were affected.
$$z_P^*(x) = \frac{g_P(x) - \mathbb{E}_{x \in P}(g_P(x)) + g_P(x)f_P(x) - \mathbb{E}_{x \in P}(g_P(x)f_P(x))}{s_{x \in P}(g_P(x)f_P(x))}$$

where $s^2$ denotes the sample variance.

We assume that $s_{x \in P}(g_P(x)) \approx s_{x \in P}(g_P(x)f_P(x))$ given that 1) $f$ is non-zero for only a subset of points, and 2) the high intensity of CSF and low intensity of normal-appearing tissue will dominate in the calculation of variance.

We can then take the mean of the z-scores for normal-appearing tissue over a large number of patches to estimate the expected 'normal' intensity in the axial plane (shown in Fig. 13A), denoted as $\mathbb{E}_P(z_P(x))$, and subtracting this from the normalised lesion intensities yields

$$z_P^*(x) - \mathbb{E}_P(z_P(x)) \approx z_P(x) - \mathbb{E}_P(z_P(x)) + \frac{g_P(x)f_P(x) - \mathbb{E}_{x \in P}(g_P(x)f_P(x))}{s_{x \in P}(g_P(x)f_P(x))}$$

Taking the expectation over many lesion patches, $\mathbb{E}_{x,P^*}[z_P(x) - \mathbb{E}_P(z_P(x))] = 0$, and so we're left with the normalised $g_P(x)f_P(x)$ term.

To analyse the spatial variation of lesion intensity, we can take voxels at a given distance from the lesion centroid and take the average (transformed) intensity over all such voxels from all lesions in the dataset, and then plot this average intensity vs. the distance from the centroid, as in Fig. 4. Originally, when using $\mathbb{E}_{P^*}(z_P^*(x))$ as the intensity quantity on the y-axis, we observed that lesion intensity increased with increasing distance from the centroid, though this is likely because of the underlying tissue intensity variation.

If $f(x)$ were constant, i.e., $f(x) = c, \forall x$, then we would expect that using $\mathbb{E}_{P^*}[z_P^*(x) - \mathbb{E}_P(z_P(x))]$ as the quantity on the y-axis of this intensity-distance plot would yield a similar pattern, albeit scaled, to using $\mathbb{E}_{P^*}(z_P^*(x))$. Furthermore, if $f(x)$ tended to increase intensities further from the lesion centroid, then this would amplify the underlying effect of $g_P(x)$, and so we should again see a similar pattern to that originally observed, i.e., increasing intensity with increasing distance.

Therefore, given that plotting $\mathbb{E}_{P^*}[z_P^*(x) - \mathbb{E}_P(z_P(x))]$ in Fig. 4 shows that the transformed intensity is highest at the lesion centroid and then decreases, this suggests that this spatial pattern is largely driven by $f(x)$, i.e., that the intensity increase within lesions tends to be higher at the centroid and decrease towards the edges.
<caption>Table 6: Comparison between AdamW setting and nnU-Net SGD at training set scale 17. Mean and standard deviation are taken over five runs.</caption>

Statistically significant difference between SGD and AdamW setting at: *0.05 significance, **0.01 significance.

<table><thead><tr><th>Method</th><th>Setting</th><th>FROC<sub>max</sub></th></tr></thead><tbody><tr><td rowspan="2">Real - Balanced</td><td>SGD + InstanceNorm</td><td><strong>0.372</strong> ± 0.024</td></tr><tr><td>AdamW + GroupNorm</td><td>0.365 ± 0.052</td></tr><tr><td rowspan="2">Real - Lesions Only</td><td>SGD + InstanceNorm</td><td>0.368 ± 0.067</td></tr><tr><td>AdamW + GroupNorm</td><td><strong>0.455</strong> * ± 0.061</td></tr><tr><td rowspan="2">LesionSCynth (Ours)</td><td>SGD + InstanceNorm</td><td>0.425 ± 0.013</td></tr><tr><td>AdamW + GroupNorm</td><td><strong>0.523</strong> ** ± 0.036</td></tr></tbody></table>

## A.3 Synthetic Lesion Examples

Fig. 14 presents random examples of real lesions and synthetic lesions generated by LesionSCynth, LesionMix, and CarveMix. Comparing the three synthesis methods, we see that our method generates examples closer in appearance to the real lesions. In particular, both LesionMix and CarveMix sometimes generate lesions which are hypointense relative to the image, even after normalising all images to mean 0 and standard deviation 1. Moreover, CarveMix sometimes includes areas around the real lesions, which can introduce further unrealistic elements. For example, in several examples, parts of CSF in the source image are included at the edge of the inserted area (e.g., last row, fourth from last column).

## A.4 Additional Results

We report the results on the full test set for two different optimiser settings at the lowest training set scale (17) in Table 6. For these experiments, using the AdamW optimiser with no learning rate scheduler and GroupNorm as the normalisation used in the network outperforms or equals the default setting of nnU-Net of SGD optimiser with polynomial learning rate scheduler and InstanceNorm. As mentioned in Sec. 4.4, since the AdamW/GroupNorm setting performed better than SGD/InstanceNorm on the validation folds across all three experiments, we used this configuration for all other experiments reported in the paper.
<figure><img src="image_15.png" /><figcaption>Figure 14: A random selection of real lesions and synthetic lesions from our method and the other two synthesis methods studied in this paper.</figcaption></figure>