S Mazouzi
email: mazouzi@leri.univ-reims.fr

Z Guessoum
email: zahia.guessoum@leri.univ-reims.fr

F Michel
email: fmichel@leri.univ-reims.fr

M Batouche
email: batouche@wissal.dz

A potential field-based multi-agent model for contour detection in range images

In this paper, we propose a reactive potential-based multi-agent system for edge detection in range images. A population of situated agents is launched to explore the image. While moving, each agent smoothes the image along its path and alters points which do not belong to surface on which it moves. On the border between two adjacent surfaces, two groups of agents will be in competition to include border points into their respective surfaces. This competition will preserve contours against erasing. However, noise is erased by successive smoothing operated by agents moving on the same surface. A potential field, created around the altered points, allows the agents, moving in the neighborhood, to concentrate their actions around these points. After several alterations of the same point, the potential field around it is relaxed, allowing, agents which were under its influence, to be released and explore other areas of the image.

Introduction

Due to their complex acquisition methods, and to the surface orientations of the contained objects, range images are considered extremely noisy [START_REF] Shin | Adaptive regularized noise smoothing of dense range image using directional Laplacian operators[END_REF]. Several approaches have been proposed to segment range images [START_REF] Hoover | Experimental Comparison Of Range Image Segmentation Algorithms[END_REF]. Unfortunately, traditional methods, which are based on the examination of the immediate neighborhood of the treated pixel do not provide satisfactory results and, thus do not lead to a reliable interpretation of the image content [START_REF] Freixenet | Yet Another Survey on Image Segmentation: Region and Boundary Information Integration[END_REF][START_REF] Hoover | Experimental Comparison Of Range Image Segmentation Algorithms[END_REF]. The Gaussian or impulsive noise, which characterizes the images produced by a given range sensor, makes the contour detection is such images more or less reliable [START_REF] Page | simultaneous mesh simplification and noise smoothing of range images[END_REF]. Indeed, if the image is highly noisy, strong smoothing can lead to erase the object contours [START_REF] Pulli | Surface Modeling and Display from Range and Color Data[END_REF]. However, if the image is not sufficiently smoothed, the remaining noise makes contour detection ineffective and sullied with errors. To remedy the problem of local vision of image content, inherent to traditional methods, several works proposed agent-based systems for image processing and understanding [START_REF] Rosin | Editorial/Agent based vision[END_REF]. These systems inherit the advantages of the agent-based approach for problem resolution. This approach consists in collective and distributed problem solving. In such a system, a stand-alone agent, for lack of general competence or global data, cannot solve the problem in its entirety. Thus, the agents have to cooperate in order to overcome their individual insufficiency. Contrary to non multi-agent based systems, the dynamical agent interactions in agent societies lead to the emergence of a global solution. Rather, some traditional segmentation algorithms have been reinterpreted using agent technology. For instance, in split and merge algorithm, agents correspond to regions, and reassigning pixels from one region to another can be considered as a cooperative negotiation scheme [START_REF] Rosin | Editorial/Agent based vision[END_REF].

In this paper, we propose a multi-agent system for both image smoothing and contours detection in range images. In contour detection, one of the difficulties is that criteria for edge point differentiation can not be trivially defined and verified. In order to overcome this difficulty, we introduce a competition scheme between antagonistic agent groups, where the system dynamic leads to contour detection. Used images represent scenes containing polyhedral objects. While moving, agents smooth the image at points along their paths. When an agent encounter a point does not belong to its surface, the point is altered in order to better align it to the surface. Isolated points which do not belong to any surface or points gathered in small numbers will disappear after several smoothing iterations which are performed by an agent group moving on the surrounding surface. However, points situated on a border between two adjacent surfaces will be alternatively modified by the two groups of agents which move on the two sides of the border. So, the contour is preserved against erasing. The use of a potential field for agent cooperation [START_REF] Ferber | Les systèmes multi-agents, vers une intelligence collective[END_REF][START_REF] Simonin | Construction of numerical potential fields with reactive agents[END_REF] around altered point allows gathering agents and so, to concentrate treatments on the contour lines and noise regions. The principle of our approach, compared with other approaches, consists in agent competition to modify the points of interest in the image. This competition allows the emergence and the enhancement of contours as well as noise erasing.

The remainder of the paper is organized as follows: Section 2 presents the works which have proposed multi-agent systems for image segmentation. Section 3 gives an overview of the proposed approach and describes the behaviors of our agents. In section 4, we show how the potential field is used to provide an efficient agent spatial coordination mechanism, allowing an indirect cooperation scheme. Sections 5 and 6 show respectively the resulted mechanism of collective contour detection, and the mechanism of noise removal. Section 7 provides some experimental results and comparison results with some published range image segmentation methods. We conclude the paper by summarizing the proposed system and showing the possible extensions of this work.

Related works

Several works have used agent-based systems for image segmentation. J. Liu and Y. Y. Tang [START_REF] Liu | Adaptative image segmentation with distributed behavior-based agents[END_REF] proposed a system for brain MR Image segmentation. Their approach uses four types of agents to label image pixels according to their membership values to the four predefined regions. Agents which succeed in recognizing their referred regions create other agents and place them according to some preferred directions. Theses directions increase the chance that the created agents meet new pixels of the same referred region. V. Rodin et al. [START_REF] Rodin | An immune oriented multi-agent system for biological image processing[END_REF] proposed a multi-agent system for rings detection in images with specific contents. Two types of agents, based on BRIC formalism [START_REF] Ferber | Les systèmes multi-agents, vers une intelligence collective[END_REF], allow following lighten rings and darken rings. Their actions aim to reinforce rings by stressing the contrast in order to allow a reliable future detection of these rings. In [START_REF] Haroun | A Massive Multi-gent System for Brain MRI Segmentation[END_REF], the authors use a massive multi-agent system, to implement an FCM-based region growing algorithm. The fusion of adjacent regions is performed according to the negotiation between agents which hold these regions. Fernandes et al. [START_REF] Fernandes | Self-Regulated Artificial Ant Colonies on Digital Image Habitats[END_REF] use artificial ant colonies for contour point localization in a grey level image. The movements of the ants (agents) are stochastic, weighted by the pheromone deposited beforehand by other ants, having detected non similar close areas. Y. Wen and Y. Q. Chen [START_REF] Chen | An evolutionary system and its application to automatic image segmentation[END_REF] proposed an evolutionary artificial life algorithm for image segmentation. Agents are placed in the image which is considered as an ecosystem. They are organized in tribes and exchange local properties of the image in their neighborhood. The aim of the agent evolution is to minimize the intra variability of any tribe and to maximize the inter variability between the various tribes. S. Mazouzi et al. [START_REF] Mazouzi | A selfadaptive multi-agent system for segmentation and reconstruction of 3D scenes[END_REF] have proposed a multi-agent system for contour detection and edge reconstruction using a population of autonomous agents. The smoothing parameters were automatically adapted according to the organization which is established within the agent population.

Contrary to works listed bellow, which use other agent interaction schemes, the model proposed in this work, introduces a competition scheme between antagonistic agent groups. We show, along the paper, that the agent group competition, allow contour enhancement and emergence. Potential field based spatial coordination, used in this work, enables processing optimization, by self agent gathering around interesting image regions.

The Proposed multi-agent system

For our system, the environment in which agents evolve is a relief image. Each point of this image represents the best tangent plane of the surface at this point according to the least square method. A population, of a greater number of agents, is launched in the image. Used agents have a low granularity and a reactive behavior. They are initialized in arbitrary positions in the image. Each agent is characterized by its current position in the image and by its energy acquired during moving on a planar surface. While evolving an agent memorize its current surface and considers it as its reference surface. According to its energy and to its position, each agent exhibits several behaviors. Figure 1 shows the different behaviors of an agent and conditions for which it topples between these behaviors.

Searching for a reference surface

After its creation, an agent randomly moves in the image and searches for a first homogeneous region which will be its current reference surface during the future exploration. The seed of an agent reference surface is a set of neighbor points situated on a planar surface. With this intention, the agent examines the neighborhood around its position and counts the number N 0 of points having roughly the same tangent plane. The agent acquires an initial energy E 0 proportional to the planarity degree of its reference surface seed. It is defined as follow:

i N i E q E × = ∑ = 0 1 0 δ (1)
δ E and q i represent respectively the energy gain at each step and the quality of the plane estimation factor, regarding the least square method, at the point i.

Surface exploration

Without the influence of the potential field, an agent randomly moves on its surface of reference. Along its path, and in order to increase the homogeneity of its surface, the agent smoothes the points on its path by using an average filter applied to the tangent planes at the traversed points. The average plane equation of the reference surface is continuously readjusted according to traversed points. Along the path on its reference surface an agent accumulates energy. Energy supply at each step is δ E .q, where q is the quality of the estimated plane at the current point. The accumulated energy E upper bounded by E max , represents the adaptation degree of the agent to its surface of reference. It determines the agent capability to alter the points which do not belong to its surface of reference. The accumulated energy determines also the force intensity applied to an agent by the potential field (see section 4). The agent direction is stochastic but influenced by the attractive force of the potential field which induce the agent to move towards the non aligned points which were reached beforehand by other agents.

Contour or noise point alteration

When an agent meets a point not belonging to its reference surface, it modifies the encountered point so that this point will be roughly aligned to the surface of reference by computing the average plane at this point. After the execution of this task, the agent loses a part, λδ E , of its energy. The constantλ, (λ>>1) represents the loss to gain ratio of energy. For our experimentations the factor λ was chosen so that an agent can alter only one point, so λ = E max /δ E .

Agent adaptation to a novel surface

An agent loses the whole of its energy when it moves towards another surface. It becomes unable to modify points on its path. At this stage, a process of readaptation is started within the agent. This process consists in agent adaptation to the current surface on which it is situated and considers it as its new surface of reference. This mechanism is necessary to ensure alteration equilibrium of a boundary independently of the surface areas. Indeed, with two adjacent surfaces having significantly different sizes; agents moving on the biggest surface will invade the second one. So, the border between the two surfaces will moves towards the interior of the surface having the smallest size, and this latter will disappear after a high number of iterations. (Fig. 2).

Agent cooperation via potential field

An artificial potential field inspired from the electrostatic potential fields, is created around altered points. Contrary to other works where the potential field is created according to known positions of objects, the field which we use results from the interaction of the agents with the objects of the environment. At any point having coordinates (x,y), the intensity of the field Ψ(x,y) created by a set of N previously altered points (x 0,i ,y 0,i ), {i=1..N} is calculated as follows:

+ = ∈ - + - - × = ∑ R k y y x x q k y x Ψ N i i i i , ) ( ) ( ) 1 ( ) , ( 1 2 , 0 2 , 0 (2)
Where k is the electrostatic force constant, and q i the plane estimation quality at point (x 0,i ,y 0,i ).

An agent situated at the position (x,y) having an energy E, equivalent to the load in the electrostatic field, undergoes a force calculated by the gradient of the potential field as follow:

, , 0 ), , ( inf + ∈      > Ψ ∇ × - = R E else E E if y x E F l Infl r v r (3)
E infl is an energy threshold expressing the agent sensitivity to potential field. An agent does not undergo any force if its energy is lower than this threshold. Indeed, this will allow the agents having lost all their energy to be released from attractive forces, and so searching for a new surface on which they will be readapted. The stochastic direction of an agent is influenced by the attractive force of the potential field.

A mechanism of relaxation of the field is introduced in order to allow agents to be released and explore other regions of the image. At a given point, the field intensity decreases after each alteration of this point. The relaxation dynamic equation is defined as follow: 1 ), , ( ) , (

) ( ) 1 ( < × = + ξ ξ y x Ψ y x Ψ t t (4) ) , ( ) 0 ( y x Ψ
corresponds to the created field after the first alteration. The constant ξ denotes the decrease rate of the field intensity. After several alterations, the field generated by the same point becomes insignificant. At the dynamic limit, the potential field is full-relaxed in the whole image. This represents the final state of the dynamic, after which the system is stopped.

Contour emergence

The goal of each agent consists in smoothing the image by aligning points which do not belong to its associated surface. These points can be, unfortunately, really contour points. Nevertheless, at the border between two adjacent surfaces, agents will be in competition situation. Indeed, agents moving on one of the two surfaces align the points of the border in order to include them in their associate surface. However, agents moving on the second surface make similar, but include points in their own surface. Thus, the points of a border are altered by one group of agents and restored by the other. A task of object contour thinning is also performed. The points of external edge sides are continuously aligned to the surface on which the agents operate. The points in the middle of the band, which represents a thick edge, will be preserved due to the competition of the two groups of agents operating on the two sides of the edge (Fig. 3). At the dynamic convergence, the contour points between two adjacent surfaces will be seen rocking continuously between the two surfaces. It results an emergent structure produced by the competition of the two groups of agents in order to include the points of contour in their respective surfaces.

Noise removal

Agents exploring the image smooth the noise areas on their path and lose their energy when crossing the contours. However, and contrary to true object surfaces, any agent having spent its energy to smooth noise points will not have sufficient area, in the traversed noise region to be readapted. So, it will leave this region and will be self readapted in the surface surrounding the noise region. According to the detail level of image content, a threshold ∆u s determines the minimal distance traversed by an agent to have space to be self readapted to a given surface.

u True region

Noise zone Figure 4 shows image function variation of both a true object surface and a noise region. The length ∆u 1 which represents the size of a true object region, is higher than the threshold ∆u s . So, the agents which move in this surface will have sufficient space to be readapted, and will smooth the image by including points to the surface while leaving it. However, agents which move into noise region (Fig. 4), traverse a distance ∆u 2 lower than the threshold ∆u s . In this case, agents will not have sufficient space to be readapted to this region. They leave the area without altering its contours. In other words, true surfaces of objects have sufficient area to allow agents to be readapted and then smooth borders by including points into these surfaces. So, the surfaces are preserved to disappear by consecutive smoothing. However, noise regions which are characterized by weak areas, do not allow agents to be readapted. Borders of these areas are continuously smoothed from outside by including their points in the surrounding regions. After several iterations theses regions will disappear.

I(u) ∆u2 ∆u1 (a) (b) (c) (d) (f) (e) (g) (h) (i) (j) (k)

Experimental results

The proposed approach was tested on real images from ABW sensors. These images were used in segmentation comparison projects [START_REF] Hoover | Experimental Comparison Of Range Image Segmentation Algorithms[END_REF]. Each image represents a scene containing polyhedral objects in visual occlusion. Initially, a spatial smoothing of the image, by an average filter is performed. In a second stage, an image of relief is calculated. In this novel image, each point is represented by the best tangent plane to the surface at this point according to the least square method. After several tests using a subset of real range images, parameter values were chosen as follows: energy gain δ E =1, the upper bound energy E max = 100 and the noise region length threshold ∆u s = 7. This latter value does not allow agents to be adapted if their path length in a novel crossed region is lower than this threshold. This value corresponds in fact, to the smallest size of a true surface in the image. Any area whose dimensions are lower than this value will be considered as a noise region and will be completely erased at the end of treatments. Values of parameters E infl and ξ , which control the potential field dynamic, are respectively 20 and 0.01. These values are empirically determined according to both image size, nature of the noise, as well as the level of detail of objects which are contained in the treated images. Figure 5 shows an example of the dynamic evolution of the system. A 360x360 range image was used (Fig. 5.a). It was illuminated by a simple ray tracing algorithm using the orientation of the normal vector to the surface to calculate the corresponding grey level value. A population of 1000 agents was used. Figure 5.b shows the detected contour using direct computation of normal vector variation. Due to the high level of noise present in the image, the obtained result is unsatisfactory and not exploitable. We have presented this result to allow comparison between the direct use of a detection operator and the use of the same operator by the proposed multi-agent system. Figures 5.c and 5.d show the state of the agents and the set of altered points after 20 iterations. At this stage, no agent is under the influence of the potential field, although some points were altered and thus generated potential fields around them. Figure 5.e and 5.f show the first influence of the field at 200 iterations. At this stage the attracted agents have cumulated an energy E higher than the threshold E Infl . After 800 iterations, clusters of agents were formed (Fig. 5.g , 5.h) around regions of interest (contours and noise regions) under the effect of the potential field. Figure 5.i shows the state of the system after potential field relaxation in the whole of the image. The final detected contours obtained at 8000 iterations are shown in figure 5.j. At this stage the agents move according to stochastic directions free from any influence. Figure 5.k shows the new state of object surfaces and contours. The noise was highly smoothed and the contours were enhanced and thinned.

In order to evaluate the performance of our system, we carried out a comparative study by using the framework proposed in [START_REF] Hoover | Experimental Comparison Of Range Image Segmentation Algorithms[END_REF]. This framework is conceived especially for performance evaluation of algorithms for range image segmentation. Our results were compared with those produced by three algorithms, which are [START_REF] Hoover | Experimental Comparison Of Range Image Segmentation Algorithms[END_REF]: USF algorithm from University of South Florida, UB algorithm from University of Bern, Switzerland and UE algorithm from University of Edinburgh, Scotland.

The comparison results obtained after reproducing segmentation results of the considered algorithms, on 19 images with variable complexity, allow us to compare the ratios of correct detection of the various algorithms, according to the error tolerance threshold T. Table 1, shows the various values of the average ratio of correct detection, according to the tolerance threshold T. Figure 6 shows a comparison graphic allowing locating the performance of the considered systems according to the correct detection ratio.

Conclusion and perspectives

In this paper we have proposed a potential fieldbased multi-agent system for contour detection and noise smoothing in range images. A great number of agents were used. The agents have a low granularity and stochastically move in the image. Noise regions are erased by successive smoothing performed by a group of agents moving on surfaces surrounding these regions. However, the competition of two agent groups evolving of the two sides of a contour preserves this contour against erasing. In order to get the system to speed up a cooperation mechanism between agents via a potential field was introduced. The potential field is created around points which are altered by agents. The potential field around a given area influences the agents which are in the neighborhood to move towards the points which are to be aligned and situated in areas requiring a concentration of agents. The relaxation mechanism of the potential field allows the agents to be released and explore other areas of the image for searching new regions which must be treated. The proposed system can be extended to be used to other types of images. For that it is necessary to define homogeneity criteria of image regions, and to define the various used parameters which are best appropriate to the types of treated images.

Figure 1 .

 1 Figure 1. Agent behaviors. States: S 1 : reference surface searching, S 2 : surface exploration, S 3 : point alteration. Conditions: C 1 : reference surface not found, C 2 : NOT C 1 , C 3 : current point belongs to reference surface, C 4 : NOT C 3 , C 5 : positive energy and current point belongs to reference surface, C 6 : positive energy and current point does not belongs to reference surface, C 7 : null energy.

Figure 2 .

 2 Figure 2. a) Range image with three surfaces s 1 ,s 2 and s 3 . b) Contour detection using a group of 500 agents (without readaptation), the smallest surface, s 3 starts to narrow.

Figure 3 .

 3 Figure 3. Contour thinning by agent competition. a) resulted contours at 800 iterations, b) resulted contours at 8000 iterations.

Figure 4 .

 4 Figure 4. True object surface and noise region lengths.

Figure 5 .

 5 Figure 5. Dynamic evolution, contour detection and noise smoothing results.

Table 1 . Average correct detection values according to the tolerance error threshold T. Figure 6. Correct detection comparison

 1


Influence of Temporal Parameters of DCE-MRI on the Quantification of Heterogeneity in Tumor Vascularization

Keywords: median age: 68 years Radiomics, Texture analysis, oncology, DCE-MRI, Sarcoma, Sequence optimization ABBREVIATIONS AIF: Arterial input function AUC: Area under curve AUROC: Area under the receiver operating characteristics curve CI95%: 95% confidence interval Coefficient of variation DCE-MRI: Dynamic contrast-enhanced MRI Quantitative Imaging Biomarkers Alliance rm: Repeated measures

Background: Evaluating heterogeneity in tumor vascularization through texture analysis could improve predictions of patients' outcome and response evaluation. Purpose: To investigate the influence of temporal parameters on texture features extracted from DCE-MRI parametric maps. Study type: Prospective cross-sectional study Subjects: 25 adults with soft-tissue sarcoma (STS),

INTRODUCTION

The extensive quantification of tumor heterogeneity on medical imaging is a growing field of research in oncology referred to as radiomics. The underlying hypothesis of radiomics is that the imaging phenotype of a tumor could reflect its intrinsic molecular identities and aggressiveness [START_REF] Connor | Cancer heterogeneity and imaging[END_REF][START_REF] Limkin | Promises and challenges for the implementation of computational medical imaging (radiomics) in oncology[END_REF]. Texture analyses consist in the mathematical processing of images in order to extract numeric indices that objectively measure the heterogeneity, named texture features. The most commonly encountered ones in the medical literature are 1 st order features, which are based on frequency histograms without spatial information, and 2 nd order features, which quantify the 2D and/or 3D rearrangements of voxels of different gray-levels. Predictive radiomics approaches based on texture features, machine learning algorithms and the potential combination with clinical characteristics and other -omics data (i.e. genomics, transcriptomics, proteomics and metabolomics) could help better stratify the therapeutic strategy for cancer patients and evaluate treatment responses [START_REF] Limkin | Promises and challenges for the implementation of computational medical imaging (radiomics) in oncology[END_REF].

Radiomics approaches can be applied to every imaging modality including dynamic contrast-enhanced MRI (DCE-MRI). DCE-MRI aims at providing a non-invasive macroscopic assessment of tumor perfusion and neo-angiogenesis -a key prooncogenetic process -through the rapid acquisition of a time series of T1-weighted imaging [START_REF] Jackson | Imaging tumor vascular heterogeneity and angiogenesis using dynamic contrast-enhanced magnetic resonance imaging[END_REF]. DCE-MRI parameters have been used to discriminate benign from malignant tumors or to monitor treatment efficacy especially anti-angiogenic regimens -the area under the time intensity curve (AUC) and the influx volume transfer constant (K trans ) being the most studied) (4) . However, these studies were based on average values of the DCE-MRI parameters that do not reflect the complexity of tumors. Indeed, homogeneous poorly vascularized tumors could have the same mean AUC and K trans values as heterogeneous tumors with both hypervascularized and large avascular necrotic areas. Consequently, quantifying the spatial heterogeneity in vascularization of the whole tumor volume from DCE-MRI data may be more informative and realistic. In that sense, radiomics approaches on DCE-MRI have recently shown encouraging results, alone or with other MRI sequences, in order to improve the detection of prostate cancer, to distinguish benign and malignant adnexal masses, to identify relevant molecular subtypes of breast cancers, to detect lymph node metastases in breast cancers, or to predict response to neoadjuvant treatment for rectum, breast and nasopharyngeal cancers [START_REF] Ginsburg | Radiomic features for prostate cancer detection on MRI differ between the transition and peripheral zones: Preliminary findings from a multi-institutional study[END_REF][START_REF] Nie | Rectal Cancer: Assessment of Neoadjuvant Chemoradiation Outcome based on Radiomics of Multiparametric MRI[END_REF][START_REF] Braman | Intratumoral and peritumoral radiomics for the pretreatment prediction of pathological complete response to neoadjuvant chemotherapy based on breast DCE-MRI[END_REF][START_REF] Bowen | Tumor radiomic heterogeneity: Multiparametric functional imaging to characterize variability and predict response following cervical cancer radiation therapy[END_REF][START_REF] Liu | Preoperative prediction of sentinel lymph node metastasis in breast cancer by radiomic signatures from dynamic contrast-enhanced MRI[END_REF][START_REF] Thomassin-Naggara | Quantifying tumor vascular heterogeneity with DCE-MRI in complex adnexal masses: A preliminary study[END_REF][START_REF] Fan | DCE-MRI texture analysis with tumor subregion partitioning for predicting Ki-67 status of estrogen receptor-positive breast cancers[END_REF][START_REF] Rose | Quantifying spatial heterogeneity in dynamic contrast-enhanced MRI parameter maps[END_REF] . Softtissue sarcomas (STS) are malignant mesenchymal tumors with important inter and intra-tumoral heterogeneity known to be associated with high grade [START_REF] Zhao | Can MR imaging be used to predict tumor grade in soft-tissue sarcoma?[END_REF]. Previous studies have shown that DCE-MRI could be useful to predict response to chemotherapy in high-grade STS [START_REF] Soldatos | Multiparametric Assessment of Treatment Response in High-Grade Soft-Tissue Sarcomas with Anatomic and Functional MR Imaging Sequences[END_REF][START_REF] Meyer | Phase I trial of preoperative chemoradiation plus sorafenib for high-risk extremity soft tissue sarcomas with dynamic contrast-enhanced MRI correlates[END_REF][START_REF] Crombé | High-grade soft-tissue sarcoma: optimizing injection improves MRI evaluation of tumor response[END_REF][START_REF] Huang | Evaluation of Soft Tissue Sarcoma Response to Preoperative Chemoradiotherapy Using Dynamic Contrast-Enhanced Magnetic Resonance Imaging[END_REF], as well as radiomics approaches [START_REF] Crombé | High-grade soft-tissue sarcoma: optimizing injection improves MRI evaluation of tumor response[END_REF][START_REF] Tian | Response assessment to neoadjuvant therapy in soft tissue sarcomas: using CT texture analysis in comparison to tumor size, density, and perfusion[END_REF][START_REF] Hayano | Texture Analysis of Non-Contrast-Enhanced Computed Tomography for Assessing Angiogenesis and Survival of Soft Tissue Sarcoma[END_REF]. Thus, it can be hypothesized that combining radiomics and DCE-MRI could enhance the early prediction of tumor response to treatment.

Robust radiomics models require the inclusion of a large number of patients, divided into training, validation and external test cohorts, before being implemented into clinical practice. Pooling data from different centers is necessary but it runs the risk of introducing bias to the values of texture features. Indeed, each step of the radiomics process can introduce variability independently from the intrinsic heterogeneity of the tumor, for instance: MRI field strength, manufacturers, coils, acquisition parameters, segmentation, voxel-size resampling, normalization techniques or grey-level discretization [START_REF] Buch | Quantitative variations in texture analysis features dependent on MRI scanning parameters: A phantom model[END_REF][START_REF] Mayerhoefer | Effects of MRI acquisition parameter variations and protocol heterogeneity on the results of texture analysis and pattern discrimination: an application-oriented study[END_REF][START_REF] Collewet | Influence of MRI acquisition protocols and image intensity normalization methods on texture classification[END_REF][START_REF] Ford | Quantitative Radiomics: Impact of Pulse Sequence Parameter Selection on MRI-Based Textural Features of the Brain[END_REF]. Previous studies have demonstrated that temporal parameters (i.e. scan duration and temporal resolution) could significantly modify the ability to discriminate benign from malignant prostate or breast lesions [START_REF] Othman | Optimized Fast Dynamic Contrast-Enhanced Magnetic Resonance Imaging of the Prostate: Effect of Sampling Duration on Pharmacokinetic Parameters[END_REF][START_REF] Othman | Effect of Temporal Resolution on Diagnostic Performance of Dynamic Contrast-Enhanced Magnetic Resonance Imaging of the Prostate[END_REF][START_REF] Hao | Influence of scan duration on the estimation of pharmacokinetic parameters for breast lesions: a study based on CAIPIRINHA-Dixon-TWIST-VIBE technique[END_REF], but they were based on average values of DCE-MRI indices or morphology of the time-intensity curves. Only one study has focused on the stability of texture features extracted from computed tomography perfusion maps identifying an influence of temporal resolution [START_REF] Bogowicz | Stability of radiomic features in CT perfusion maps[END_REF]. Hence, data regarding the influence of temporal parameters on texture features extracted from DCE-MRI parametric maps are lacking. Thus, our aims were to investigate the influence of temporal parameters: (i) on the values of widely used texture features extracted from DCE-MRI parametric maps of STS, (ii) on the dispersion of these parameters, and (iii) on the performance of predictive models for chemotherapy responses.

MATERIALS AND METHODS

Patient population

In this prospective single-center study, the institutional review board waived the requirements of informed patient consent. From November 2017 to June 2018, 30 consecutive adult patients were included as they presented at our sarcoma reference center for the management of a histologically-proven high-grade (according to the French Federation Nationale des Centres de Lutte contre le Cancer [FNCLCC]

grading system) STS of the trunk wall or extremities of more than 4cm, and required a contrast-enhanced MRI for diagnostic and/or therapeutic management. Age, gender, histological type, tumor depth relative to superficial fascia, tumor location, longest diameter, specific treatments and short-term patients' outcome were retrieved from medical records. We defined a good responder as: (i) <10% of stainable viable tumor cells on surgical specimen after neo-adjuvant chemotherapy for locally-advanced nonmetastatic STS [START_REF] Cousin | Clinical, radiological and genetic features, associated with the histopathologic response to neoadjuvant chemotherapy (NAC) and outcomes in locally advanced soft tissue sarcoma (STS) patients (pts)[END_REF], and (ii) a partial or complete response 6 months after performing DCE-MRI according to RECIST 1.1 criteria for metastatic or inoperable patients, without changing treatment -this last empirical definition being proposed regarding the usual median progression-free survivals of metastatic STS patients [START_REF] Ray-Coquard | Treatment patterns and survival in an exhaustive French cohort of pazopanib-eligible patients with metastatic soft tissue sarcoma (STS)[END_REF].

Data acquisition

Patients underwent MRI scans in the same 1.5T MR-system (MAGNETOM Aera;

Siemens Healthineers, Erlangen, Germany) with adapted coils depending on tumor locations and sizes, i.e. 15 channels transmit/receiver coil for knee and extremities Breath hold Examination) sequence [START_REF] Michaely | CAIPIRINHA-Dixon-TWIST (CDT)volume-interpolated breath-hold examination (VIBE): a new technique for fast timeresolved dynamic 3-dimensional imaging of the abdomen with high spatial resolution[END_REF]. The T1-mapping used a similar spoiled gradient-echo sequence with variable flip angles (2° and 15°) and with echo and repetition times of 1.41ms and 3.79ms, respectively. In brief, the principle of TWIST is to divide the k-space in a central region, which encodes information about contrast, and a peripheral region, which encodes information about shapes, edges and details and is undersampled [START_REF] Michaely | CAIPIRINHA-Dixon-TWIST (CDT)volume-interpolated breath-hold examination (VIBE): a new technique for fast timeresolved dynamic 3-dimensional imaging of the abdomen with high spatial resolution[END_REF]. The suppression of the fat signal was performed using a Dixon-based water-fat separation (echo times were 2.39ms for in-phase and 4.77ms

for opposite-phase conditions). A repetition time of 6.89ms and a flip angle of 25° were used. The sampling was accelerated with a parallel acquisition technique with an undersampling factor of 2. The value of the TWIST view-sharing parameters A (i.e.

the percentage sizes of the central portion of the k-space) and B (i.e. the percentage sizes of the peripheral portion of the k-space) were 15% and 20%, respectively. The temporal resolution resulted in dt=2s, except for the first TWIST phase (6.9s for the full k-space sampling). Five phases were acquired before the intra-venous powerinjection of 0.1mmol/kg of gadoteric acid (Dotarem, Guerbet, Villepinte, France) at a rate of 2mL/s followed by a 20mL flush of 0.9% of NaCl solution thanks to a MRIcompatible automatic injector (Sonic Shot 7, Nemoto Kyorindo, Tokyo, Japan). The total scan duration was 5min and included 144 phases (full-dataset).

Data reconstruction

Data reconstruction and post-processing were achieved with Olea Sphere®, v3.0 SP14 Software (Olea Medical, La Ciotat, France) by a senior radiologist with 7 years of experience in MRI blinded to clinical data. First, motion artifacts were systematically corrected with a rigid body co-registration method. For each patient, the full-dataset was downsampled and truncated to obtain the datasets to assess the effect of scan duration and temporal resolution. In any case, the 5 first phases were kept in the datasets to ensure a similar baseline for all maps. In total, 7 DCE-MRI datasets per patient were generated to evaluate temporal resolution, namely: dt=2s (raw data), 4s, 6s, 8s, 10s, 12s, 20s, with a scan duration of 5min. Three DCE-MRI datasets were generated to evaluate the influence of scan duration, namely: T=3min, 4min, 5min, all with a temporal resolution of dt=6s. Figure 1 shows how the datasets were built.

The next step consisted in the calculation of the parametric maps using the permeability plug-in of Olea Sphere®. First, the senior radiologist manually chose the largest feeding artery within the field-of-view of the raw DCE-MRI dataset, with the exclusion of the first and the last slices to avoid artifacts. A fixed voxel was manually placed in this artery and the arterial input function (AIF) was measured as the average of 4 directly adjacent voxels within this artery that demonstrated an arterial enhancement and the less noise. The same artery and the same voxels were used for the other reconstructed datasets. Hence, even if the baseline of the AIF was preserved, the AIF was also downsampled and truncated (Fig. 1). Second, the AIF signal intensity time-course was converted into blood R1 time-course, with the hematocrit = 0.45 and the gadoteric acid relaxivity at 1.5T = 3.6 L/mmol.s -1 . We chose to focus on the most widely used parameters: the area under the time-intensity curve (AUC), at 90s (units: mmol/L/s) and the pharmacokinetic parameter K trans (influx volume transfer constant from plasma to extra-vascular, extracellular space, which represents the capillary permeability, units: min -1 ). K trans maps were calculated using the Extended Tofts model [START_REF] Tofts | Estimating kinetic parameters from dynamic contrast-enhanced T(1)-weighted MRI of a diffusable tracer: standardized quantities and symbols[END_REF]. Of note, AUC was not evaluated for scan duration because we focused on the first 90 seconds of the time-intensity curve.

Five out of the 30 MRI examinations were excluded due to Dixon fat-water swap artifacts (n=3) and motion artifacts (that were too large to be well corrected with the motion correction, n=2) biasing the quantitative assessment.

Data analysis

Texture analysis. For each patient, the entire tumor volume was manually segmented by the same senior radiologist using OleaSphere®, slice-by-slice, on the last phase of Texture analysis consisted in the 3D extraction of 32 quantitative features, provided in Table 1, from histogram analysis (: first order statistics, FOS), grey-level cooccurrence matrix (GLCM), grey-level run-length matrix (GLRM) and grey-level size zone matrix (GLSZM) [START_REF] Haralick | Textural features of image classification[END_REF][START_REF] Galloway | Texture analysis using gray level run lengths[END_REF][START_REF] Thibault | Texture Indexes and Gray Level Size Zone Matrix Application to Cell Nuclei Classification[END_REF]. Before, K trans and AUC values were discretized in 256 bins. The spatial offset was fixed to a displacement of 4 pixels and an angle of 45° (details regarding the definitions and calculations of the texture features are given in Supplementary Data 1). No technique for resampling or standardization was applied because the voxel size was initially the same for all patients and texture analysis was performed on scaled parametric maps and not on raw MRI data.

For each patient 'p' (i Î {1;2;…;Np} where Np is the total number of included patients), for each feature 'Fi' (i Î {1;2;…;32}) and for each DCE-MRI map 'X (X Î {K trans ;AUC}), we extracted 7 paired values of Fp,i,X regarding sampling and 3 paired values of Fp,i,X regarding scan duration (Fp,i,X(dt) and Fp,iX(T), respectively).

Coefficient of variation (CV).

We calculated the mean CV and its standard deviation (SD) on each feature Fi in order to assess the influence of sampling (: CV-dt, with AUC or K trans ), and scan duration (: CV-T, with K trans ) on the dispersion of the texture features, as follows:

CV-dt= For texture features with a statistical influence of temporal resolution, a linear model was applied for correlation analysis. A Bonferroni correction was applied for multiple comparisons and a p-value of 0.01 was considered significant.

Finally, we investigated the influence of temporal parameters on the performance of a model aiming at predicting the treatment response based on texture features from K trans and AUC maps. Twenty patients were analyzable for this part of the study; the 5 others were either operated directly after the MRI without chemotherapy or were not sufficiently followed-up. Texture features that were associated with the response at univariate level according to Student t-tests (or Mann-Whitney tests) with a p-value <0.05 were entered in a multivariate binary logistic regression using a backward stepwise selection method based on the probability of the Wald statistics. The area under the receiver operating characteristics curve (AUROC) of the models were calculated according to scan durations and temporal resolutions and compared according to the Delong methods [START_REF] Delong | Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach[END_REF].

RESULTS

Patients (Table 2)

Twenty-five patients were finally included (9/25 (36%) women, median age 68 years old, range: 31-94). The most frequent histotype was undifferentiated pleomorphic sarcoma. The median size was 81mm (range: 42-180) and the median tumor volume was 0.357L (range: 0.023 -1.048). Three texture features were influenced by temporal parameters in the 3 settings:

Influence of temporal parameters on DCE-MRI texture features

GLRLM_GL_Variance, GLSZM_Large_area_emphasis, and

GLSZM_Zone_variance. Six texture features were not, no matter the setting:

GLCM_Correlation, GLRLM_Gray_level_non-uniformity, GLRLM_Run_entropy, GLRLM_Run_variance, GLSZM_Small_area_emphasis and GLSZM_Zone_entropy.

A summary of post-hoc tests is given in Table 4. Regarding the influence of temporal resolution on AUC maps, the highest number of texture features that statistically differed was observed in post-hoc comparisons between dt=20s and dt=2s (10/32, 31.3%) and dt=20s and dt=4s (9/32, 28.1%). On K trans maps, the highest differences were seen between dt=20s and dt=2s (10/32, 59.4%), followed by dt=20s versus dt=6s (6/32, 18.8%). Regarding the influence of truncating on K trans maps, 23/32 (71.9%) and 17/32 (53.1%) texture features were significantly different between T=5min and T=4min, and between T=5min and T=3min, respectively.

Significant linear correlations were found between sampling on AUC and GLSZM_Size_zone_non-uniformity (p=0.0018, r 2 =0.879) and GLSZM_Zone_variance (p=0.0043, r 2 =0.830). Similarly, there were significant linear correlations between sampling on K trans and 4 texture features: GLSZM_nonuniformity (p<0.0001, r 2 =0.978), GLSZM_Large area emphasis (p=0.0009, r 2 =0.909), GLSZM_Size_zone_non-uniformity (p=0.0002, r 2 =0.954), GLSZM_Zone_variance (p=0.0002, r 2 =0.950) (Fig. 2). Variations in scan duration did not reveal any linear correlations. Details for linear regressions are given in Supplementary Data 2. Figure 3 shows an example of variation of parametric maps and corresponding histograms with changes in scan duration and temporal resolution.

Effect of temporal parameters on the dispersion of DCE-MRI texture features

Figure 4 and Table 5 Supplementary Data 3 provides all the values of CV with SD.

Effect of temporal parameters on a prediction based on DCE-MRI texture features

Twenty patients were treated with chemotherapy and were analyzable for this sub-part of the study. There were 5/20 (25%) good responses (4 good histological responses and 1 partial response after 6 months without changing treatment). Table 6 shows the results of univariate analyses and performances of the models quantified by AUROC.

After univariate analyses, the selected variables entered in the binary logistic regression were not systematically the same when temporal resolution and scan duration changed, even if some were frequently encountered:

AUC_GLRLM_Run_entropy (in 8 models), Ktrans_GLSZM_Small_area_emphasis (in 3 models). AUROC ranged from 0.77 (CI95%=(0.54-1.00)) with a scan duration of 5min and a temporal resolution of 6s, to 0.90 (CI95%=(0.74-1.00)) with a scan duration of 4min and a temporal resolution of 6min. Details of the univariate analyses for each model and comparisons between AUROC can be found in Supplementary Data 4 and Supplementary Data 5, respectively.

DISCUSSION

In this study, we examined the influence of temporal parameters on a large set of widely used and easily available statistical texture features extracted from whole tumor volumes segmented on K trans and AUC parametric maps. We found that a large number of them were significantly dependent on the scan duration and temporal resolution. Moreover, merely half of them remained poorly variable with changes in temporal parameters. This led to non-negligible variations in the AUROCs of the models for a response prediction to chemotherapy, even though the comparisons did not provide statistical differences.

A major challenge for radiomics approaches is to ensure a good quality of the quantitative data on which they rely. Besides reproducibility, repeatability, nonredundancy and validity, quality here means controlling the bias due to slight variations in the imaging acquisition parameters [START_REF] Limkin | Promises and challenges for the implementation of computational medical imaging (radiomics) in oncology[END_REF]. Standardizing the imaging protocols between radiological centers is unavoidable. However, thousands of MRI examinations (and DCE-MRI sequences) have already been acquired and the temptation to pool data from different MR-systems in order to begin to build and test predictive models for key oncological questions is understandable. Our study focused on STS as a tumor model to examine the influence of temporal parameters. Highgrade STS are characterized by complex architectures and changes during treatments, making them particularly appropriate for radiomics. In particular, Vallières et al.

stressed the influence of the post-processing parameters of imaging on a prediction model of occurrence of lung metastases in STS patients [START_REF] Vallières | A radiomics model from joint FDG-PET and MRI texture features for the prediction of lung metastases in softtissue sarcomas of the extremities[END_REF].

Our results are in agreement with previous studies that investigated the influence of temporal parameters on dynamic acquisitions. Othman et al. showed that shorter scan duration was responsible for overestimation of pharmacokinetic parameters and lead to incorrect classifications of benign prostate lesions as malignant [START_REF] Othman | Optimized Fast Dynamic Contrast-Enhanced Magnetic Resonance Imaging of the Prostate: Effect of Sampling Duration on Pharmacokinetic Parameters[END_REF]. A similar influence on prediction models was found with breast lesions [START_REF] Hao | Influence of scan duration on the estimation of pharmacokinetic parameters for breast lesions: a study based on CAIPIRINHA-Dixon-TWIST-VIBE technique[END_REF]. This could be explained by the Tofts model itself because it assumes an immediate equilibrium between the compartments though it requires up to 2min in case of breast imaging [START_REF] Kuhl | Dynamic breast MR imaging: are signal intensity time course data useful for differential diagnosis of enhancing lesions?[END_REF]. Poor temporal resolutions can also lead to incorrect assessments of pharmacokinetic parameters according to pre-clinical and clinical studies regarding prostate lesions -even if it did not significantly modify the ability of these parameters to discriminate benign and malignant tumors [START_REF] Othman | Effect of Temporal Resolution on Diagnostic Performance of Dynamic Contrast-Enhanced Magnetic Resonance Imaging of the Prostate[END_REF]. Heisen et al. showed that the K trans variations could go up to 25% of its initial value with varying temporal resolutions [START_REF] Heisen | The influence of temporal resolution in determining pharmacokinetic parameters from DCE-MRI data[END_REF]. In the single study that focused on the acquisition parameters at risk of influencing perfusion maps, Bogowicz et al. found that the percentage of unstable texture features ranged from 56 to 98% with different artery contouring, and from 58 to 75% with different temporal resolution, which is higher than in our study [START_REF] Bogowicz | Stability of radiomic features in CT perfusion maps[END_REF]. This highest variability in their study may be explained by the difference in histological types, in imaging modality (CT vs. MRI), in the texture features that were calculated and in the perfusion maps that were studied (blood flow, mean time transit and blood volume vs. AUC and K trans in our studies).

Regarding STS, our results also highlight potential cut-offs for temporal resolution and scan duration beyond which statistical differences in texture features from DCE-MRI maps may occur. Indeed, even if temporal resolution had an influence on several texture features, post-hoc tests with correction for multiple comparisons showed that data with temporal resolution below 8s could be pooled, as well as data with temporal resolution above 8s. On the contrary, we found that data obtained with a scan duration of 5min should not be pooled with those with a scan duration of 3 or 4min.

After All the categories of texture features seemed equally influenced by temporal resolution, but the dispersion was more marked with FOS, then GLCM, GLRLM and finally GLSZM. The high sensitivity of FOS could be due to their lack of spatial information. Indeed, all the voxels are pooled without considering the fact that adjacent voxels may react similarly and proportionally to changes in temporal parameters, which is the case of GLCM, GLSZM and GLRLM.

Regarding the influence of temporal parameters on the performance of a model for response prediction based on AUC and K trans of STS, we identified 6 relevant features that were selected across the different models, namely:

Interestingly, GLRLM_Run_entropy and GLRLM_Small_area_emphasis were not significantly influenced by temporal resolution and showed low CVs. Thus, these texture features could be good candidates for multi-center studies based on DCE-MRI sequences of STS. However, these results do not mean that ultra-fast DCE-MRI acquisitions are unnecessary. The aim of DCE-MRI is to represent and estimate at best the vascular characteristics of tumors. Hypervascularized tumors require excellent temporal resolutions. If some researchers want to increase the statistical power of their radiomics study by putting together DCE-MRIs with different temporal parameters, then it should be carefully done because it could introduce a significant bias in their results.

We did not investigate the test-retest reproducibility of DCE-MRI-based texture features because it was hardly justifiable to inject a contrast agent twice in cancer patients. However, further radiomics studies performed on perfusion phantoms could help analyzing this crucial aspect. It should be noted that we designed our study to limit bias that could have been introduced in the quantification of heterogeneity: we utilized the same 1.5T MR-system, the same DCE-MRI sequences with the same acquisition parameters following QIBA® recommendations, the same contrast agent, the same imaging filters, the same software for post-processing and the same feature extraction parameters. Nevertheless, we had to adjust the coils because of variations in tumor sizes and locations, which may have introduced some bias. Moreover, truncating and downsampling the AIFs probably contributed to the variations in texture features from DCE-MRI parametric maps, even if we kept the same voxels in the same artery of interest. Indeed, the AIF is crucial in pharmacokinetic modeling [START_REF] Tofts | Estimating kinetic parameters from dynamic contrast-enhanced T(1)-weighted MRI of a diffusable tracer: standardized quantities and symbols[END_REF]. For instance, a recent study showed that K trans could range from 0.25/min to more 2/min in prostate cancers in a same series of DCE-MRI acquisitions depending on the method to determine the AIF from different cancer centers, which led to variations in times to peak and peak amplitudes [START_REF] Huang | The Impact of Arterial Input Function Determination Variations on Prostate Dynamic Contrast-Enhanced Magnetic Resonance Imaging Pharmacokinetic Modeling: A Multicenter Data Analysis Challenge[END_REF]. Herein, poor temporal resolutions could lead to missing the real AIF peak though the K trans estimation strongly relies on it, as well as to superposition of the AIF and the tumor enhancement curve during the first part of the acquisition.

Our study has several limits. First, the population was small and made of heterogeneous histological types, though all were high-grade. Some tumors enhanced rather homogeneously and progressively (for instance myxoid/round cell liposarcomas) while others showed more heterogeneous enhancements, with the timeintensity curves of some components displaying a strong wash-in, followed by a peak and a wash-out (for instance, undifferentiated pleomorphic sarcomas). Temporal However, given that some areas in STS can show a wash-out, it is also possible that the pharmacokinetics that quantify the decreasing part of the time-intensity curve are also influenced by temporal parameters. Third, alternative methods for downsampling could have been applied by recombining k-space data instead of removing some phases [START_REF] Heisen | The influence of temporal resolution in determining pharmacokinetic parameters from DCE-MRI data[END_REF]. In a clinical setting, there is a compromise between temporal resolution, signal-to-noise ratio and spatial resolution. A decrease in temporal resolution will benefit signal-to-noise-ratio (by averaging twice if there is a down-sampling by a factor 2, for instance). Fourth, our multivariate models for the outcome sub-study can be questioned since only 20 patients were included with 2 definitions of good treatment responses depending on the patient's operability. We used a classical statistical approach without validation cohort to build the predictive models. More advanced selection methods could have been used (for instance: least absolute shrinkage and selection operator, ElasticNet, supervised principal component analysis), as well as supervised machine-learning classifiers (for instance: random forest, k-nearest neighbors, support vector machines) or deep learning [START_REF] Erickson | Machine Learning for Medical Imaging[END_REF].

Consequently, we did not test if the influence of temporal parameters was still present with these other statistical methods. The aim of this part of the study was to illustrate the influence of temporal parameters on a prediction and not to validate a radiomics model for response prediction. However, we hope that further prospective studies will take into account this research aiming at improving the quality of radiomics methods in order to build clean and robust models to answer key oncological questions.

To conclude, our study screened several aspects of the influence of temporal parameters on texture features extracted from DCE-MRI parametric maps of STS. We showed that both scan duration and temporal resolution introduced a non-negligible variability in the quantification of heterogeneity that could lead to a decreased performance of prediction models for response to chemotherapy. In addition to all the other acquisition and post-processing parameters, standardizing the scan duration and temporal resolution of DCE-MRI must be considered in prospective multi-centric trials to build reliable radiomics approaches.

  and 18 channels transmit/receiver body coil for trunk wall and thighs. Patients were examined in supine position. The protocol followed the Quantitative Imaging Biomarkers Alliance recommendations (QIBA®) and consisted in a T1-mapping followed by the DCE-MRI acquisition with the same field-of-view (350 x 320 mm) and spatial resolution (1.1 x 1.1 x 4 mm 3 ), in order to optimize the conversion of the signal in Gadolinium chelates concentration. We used a CAIPIRINHA (Controlled Aliasing in Parallel Imaging Results in Higher Acceleration) Dixon TWIST (Timeresolved angiography With Stochastic Trajectories) VIBE (Volume Interpolated

  the DCE-MRI acquisition (because the tumor demonstrated the best contrast with surrounding tissues compared with the other phases) and with the help of the conventional sequences acquired during the same MRI examination, i.e.: axial turbo spin echo (TSE) T2-weighted imaging (refocusing angle = 150°, repetition time = 6860ms, echo time = 120ms, slice thickness = 4mm, field-of-view = 250 x 250mm), coronal or sagittal TSE short time inversion recovery T2-weighted imaging (refocusing angle = 150°, repetition time = 4150ms, echo time = 69ms, inversion time = 150ms, slice thickness = 4mm, field-of-view = 350 x 350mm), axial TSE T1weighted imaging (refocusing angle = 150°, repetition time = 420ms, echo time = 10ms, slice thickness = 4mm, field-of-view = 250 x 250mm), pre-and post-contrast agent injection axial Fat-Sat TSE T1-weighted imaging (refocusing angle = 180°, repetition time = 581ms, echo time = 10ms, slice thickness = 4mm, field-of-view = 250 x 250mm). The voxels located at the extreme edge of the tumor were excluded to avoid partial volume effect. The volume of interest (VOI) was then propagated on all the parametric maps (K trans and AUC for the 7 samplings, K trans for the 3 truncations).

  parameters were certainly more influential in the second case. Nevertheless, until now, the inclusion of STS patients in clinical trials relies on tumor grade and not on histotypes. Second, we did not investigate other semi-quantitative and pharmacokinetic DCE-MRI parameters (such as Time-to-peak, Wash-in, Wash-out, K ep [efflux rate constant from the extra-cellular, extra-vascular space to the plasma compartment], K el [contrast agent elimination rate constant], Ve [extra-cellular, extravascular space volume], Vp [plasmatic volume]), or other perfusion models than extended Tofts. We decided to focus on the most studied parameters in the literature.

FIGURE 1 :

 1 FIGURE 1: Reconstruction of data acquisition. (a) Retrospective downsamplingand truncating were performed to obtain post-processed data with a temporal resolution of 2s (: dt2), 4s (: dt4), 6s (: dt6s)… and 20s (: dt20), and with a scan duration of 4min (: T4'00 -with a temporal resolution of 6s) and 3min (: T3'00 -with a temporal resolution of 6s). Of note, the baseline was not re-sampled. (b) The same voxels in the same artery were used to determine the artery input function (AIF) that was used in the extended Tofts model. However, AIFs were also truncated and downsampled leading to variations in time to reach the peak (from 36s to 54s) and in maximum signal intensity of the peak (from 319 to 396.8) in this example of highgrade synovial sarcoma of the popliteal region. (c) Next, parametric maps of K trans (: influx volume transfer constant) and (d) AUC (: area under the time intensity curves at 90s after arrival of the contrast agent bolus in the acquisition volume) were generated as functions of 'dt' and 'T'.

FIGURE 2 :

 2 FIGURE 2: Linear correlations between texture features from DCE-MRI parametric maps and temporal resolution. Only significant correlations for AUC (a) and K trans (b) after corrections to allow multiple comparisons are shown with their p-value. Sampling is given in seconds. Texture features have arbitrary units.Abbreviations: GL: grey level; GLSLZM: grey level size zone matrix.

FIGURE 3 :

 3 FIGURE 3: Illustrated case of the influence of temporal parameters on DCE-MRI parametric maps and texture features of sarcoma. A 63 years old male with a high-grade, deep and superficial, myxofibrosarcoma of the left thigh underwent his baseline MRI examination including conventional sequences (a) and DCE-MRI acquisition. (b) The whole tumor volume was manually segmented, slice-by-slice, on the last phase of the DCE-MRI acquisition, i.e. 300s after Gadolinium chelates intravenous injection. (c) The AUC (: area under the time intensity curve at 90s after arrival of the contrast agent bolus in the acquisition volume, units: mmol/L/s, on the right) and K trans (influx volume transfer constant, units: /s, on the left) parametric maps were reconstructed with the different scan durations and temporal resolutions. After the whole tumor volume segmentation, frequency histograms were reconstructed for (d) AUC depending on the different temporal resolution, (e) Ktrans depending on the different temporal resolution, and (f) Ktrans according to the

FIGURE 1 FIGURE 2 .

 12 FIGURE 1

FIGURE 4 .

 4 FIGURE 4.

Table 3

 3

	provides the results of the rm-ANOVA (or rm-Friedman test). Regarding the
	effect of temporal resolution, 12/32 (37.5%) AUC-based texture features were
	significantly influenced: 5/7 FOS features, 1/9 GLCM features, 2/9 GLRLM features
	and 4/7 GLSZM features (range of p-value=0.0395 to <0.0001). Fourteen out of 32
	(43.8%) K trans -based texture features were significantly influenced by temporal
	resolution: 1/7 FOS features, 5/9 GLCM features, 4/9 GLRLM features and 4/7
	GLSZM features (range of p-value=0.0331 to 0.0007).

Regarding the effect of scan duration, 23/32 (71.9%) K trans -based texture features were significantly influenced: 7/7 FOS features, 8/9 GLCM features, 6/9 GLRLM features and 2/7 GLSZM features (range of p-value=0.0321 to <0.0001).

  summarize the analysis of dispersion of texture features according to the 3 configurations (i.e. AUC-sampling, Ktrans-sampling, Ktrans-

	Five texture features extracted from K trans maps were highly variable with changes in
	scan	duration:	FOS_Average,	FOS_Energy,	FOS_Inter-quartile_range,
	FOS_Standard_deviation and GLSZM_Zone_entropy (range of CV-T=0.54-0.96).

truncating). Most texture features extracted from AUC maps remained poorly to mildly variable with changes in sampling. Only GLCM_Cluster_prominence was categorized as highly variable (CV-dt=0.50), while 11 out of 32 (34.4%) texture features extracted from K trans were highly to extremely variable (range of CV-dt=0.50-1.11).

  correction of multiple tests, some radiomics features extracted from AUC and

	K trans maps demonstrated linear relationships with sampling. All belonged to the
	GLSZM		category.	GLSZM_Size_zone_non_uniformity	and
	GLSZM_Grey_level_non_uniformity increased with downsampling, suggesting more
	heterogeneity in intensity values and in size zone volumes of the same grey level
	voxels	with	low	temporal	resolutions	(high	dt).	Conversely,
	GLSZM_Large_area_emphasis and GLSZM_Zone_variance tended to decrease,
	suggesting that poor temporal resolution (high dt) led to smaller size zones. No linear
	correlation was found with truncating, probably because we only generated 3 time
	points. Poor temporal resolution (high dt) can be responsible for less accurate
	estimations, especially when the tumor -or areas in the tumor -demonstrates a rapid
	and strong enhancement (wash-in and peak on time-intensity curves). Consequently,
	hypervascularized intra-tumoral areas with high K trans and AUC values could be
	missed, resulting in areas with lower values of K trans and AUC.

TABLE 3 .

 3 Assessment of the influence of temporal resolution (sampling) and scan duration (truncating) on texture parameters extracted from DCE-MRI parametric maps (K trans and AUC).

	Texture features	AUC -Sampling F-value p-value	K trans -Sampling F-value p-value	K trans -Truncating F-value p-value
	First-order Feature
	Average	18.54	0.0050**	5.12	0.5290	14.60	0.0022**
	Energy	25.55	0.0003***	2.13	0.9072	15.00	0.0018**
	Entropy	7.15	0.3069	16.46	0.0115*	19.19	0.0002***
	Inter-quartile range	8.607	0.1969	5.61	0.4688	15.05	0.0018**
	Kurtosis	50.89	<0.0001***	6.35	0.0958	15.49	0.0168*
	Skewness	41.57	<0.0001***	10.88	0.0921	8.80	0.0321*
	Standard deviation	26.12	0.0002***	1.77	0.9395	14.50	0.0023**
	GLCM
	Cluster prominence	17.07	0.0090**	11.46	0.0751	16.20	0.0010**
	Cluster shade	5.07	0.5354	12.15	0.0587	12.55	0.0057**
	Cluster tendency	10.30	0.1127	9.96	0.1262	23.85	<0.0001***
	Contrast	9.27	0.1589	13.7	0.0331*	17.85	0.0005***
	Correlation	2.78	0.8358	5.59	0.4709	4.25	0.2357
	Inverse difference moment	6.58	0.3617	13.70	0.0331*	17.85	0.0005***
	Joint average	1.94	0.9253	13.96	0.0301*	18.75	0.0003***
	Joint energy	6.45	0.3750	13.83	0.0316*	18.40	0.0004***
	Joint entropy	6.87	0.3327	16.64	0.0233*	19.55	0.0002***
	GLRLM
	GL non-uniformity	0.96	0.9869	5.83	0.4427	1.05	0.7892
	GL variance	20.74	0.0020**	17.7	0.0070*	29.30	<0.0001***
	High GL run emphasis	5.74	0.4525	19.16	0.0039**	29.30	<0.0001***
	Low GL run emphasis	3.27	0.7746	19.16	0.0039**	29.30	<0.0001***
	Long run emphasis	11.00	0.0884	17.05	0.0091**	31.50	<0.0001***
	Run entropy	0.32	0.8632 §	1.40	0.2556 §	0.9251	0.4056 §
	Run length non-uniformity	7.32	0.2918	11.46	0.0753	14.85	0.0019**
	Run variance	10.47	0.1062	11.36	0.0778	5.95	0.1141
	Short run emphasis	13.23	0.0395*	1.56	0.2133	22.95	<0.0001***
	GLSZM
	GL non-uniformity	9.69	0.1384	15.31	0.0180*	10.94	0.012
	GL variance	25.72	0.0003***	11.89	0.0645	10.18	0.0171
	Large area emphasis	19.29	0.0037**	21.41	0.0015**	15.30	0.0016**
	Small area emphasis	9.16	0.1649	4.91	0.5555	4.40	0.2214
	Size zone non-uniformity	16.11	0.0132*	16.87	0.0098*	5.87	0.118
	Zone entropy	3.08	0.2190 §	4.746	0.5768	1.01	0.3797 §
	Zone variance	20.26	0.0025**	23.46	0.0007***	15.30	0.0016**
	NOTE. Data are F-values and p-values for the repeated measures (rm-) ANOVA ( : §) or non
	parametric equivalent rm-Friedman test.
	Abbreviations: GL : grey-level; GLCM : grey-level occurrence matrix; GLRLM: grey-level
	run length matrix; GLSZM: grey level size zone matrix
	*: p≤0.05; **: p<0.005, ***: p<0.001

TABLE 6 .

 6 Area under the ROC curves of models for response prediction to chemotherapy based on texture features extracted from AUC and K trans maps with varying temporal resolution (sampling) and scan duration (truncating)

	Temporal	Univariate analysis		Model
	parameters	Significant features	p-value	AUROC (CI95%)	p-value
	u Sampling
	dt2	K trans _GLRLM_Run entropy	0.021	0.85 (0.68-1.00)	0.021
		AUC_GLRLM_Run entropy	0.050
	dt4	AUC_GLRLM_Run entropy	0.050	0.84 (0.62-1.00)	0.026
		K trans _FOS_Inter-quartile range	0.026
		K trans _FOS_Standard deviation	0.013
		K trans _GLRLM_Long run emphasis	0.021
		K trans _GLRLM_Run entropy	0.032
	dt6	AUC_GLRLM_Run entropy	0.050	0.77 (0.54-1.00)	0.074
	dt8	AUC_GLCM_Correlation	0.032	0.83 (0.61-1.00)
	dt10	K trans _GLRLM_Long run emphasis	0.032	0.83 (0.63-1.00)	0.032
	dt12	AUC_GLCM_Correlation	0.040	0.83 (0.58-1.00)	0.032
		AUC_GLRLM_Run entropy	0.032
		K trans _GLSZM_Small area emphasis	0.050
	dt20	AUC_GLRLM_Run entropy	0.049	0.81 (0.58-1.00)	0.121
	u Truncating
	T3'00	AUC_GLRLM_Run entropy	0.050	0.88 (0.71-1.00)	0.021
		K trans _GLSZM_Small area emphasis	0.021
	T4'00	AUC_GLRLM_Run entropy	0.050	0.90 (0.74-1.00)	0.018
		K trans _GLSZM_Small area emphasis	0.016
	T5'00	AUC_GLRLM_Run entropy	0.050	0.77 (0.54-1.00)	0.074

NOTE. Abbreviations: AUROC: area under the receiver operating characteristics curve; CI95%: 95% confidence interval; GL: grey level; GLCM: grey level co-occurrence matrix; GLRLM: grey level run length matrix; GLSZM: grey level size zone matrix; 'dtx' corresponds to a sampling of 'x' seconds; 'Ty' corresponds to a scan duration of 'y' minutes.