Iza Marfisi-Schottman

Isabelle Vinatier
email: isabelle.vinatier@univ-nantes.fr

Elisabetta Bevacqua
email: bevacqua@enib.fr

Mamadou Kébé
email: mamadou.kebe@univ-lemans.fr

Enabling Teachers to Create Authentic Interview Simulations

Keywords: Interview simulator, Technology Enhanced Learning, Virtual Reality, social skills, authoring tool

Social skills are essential and it is often necessary to train in order to react in the best way to certain difficult, stressful situations such as a job interview, dating. The best way of training for these challenging interview situations is to role play with actors, capable of simulating emotions, but this solution is not affordable for most schools and universities. We therefore propose TGRIS, a Teacher-Guided Realistic Interview Simulator that allows students to practice interviews with an emotional virtual agent in Virtual Reality. Most importantly, this tools allows teachers to create custom interview situations by changing the agent's face, emotional state and piloting the agent's verbal and non-verbal reactions during the interview. Finally, we discuss the first experimentations and show how this solution might turn out to be better than live actors.

Practicing Social Skills

Social skills are the core of our society. Learning how to react properly in certain situations is very important in many domains. Such skills are taught in medical, business and communication schools but the need for this type of training is omnipresent in all types of educational programs, even in those where you might not expect it at first.

For example, Education Trainers (ETs) need to practice their social skills in order to conduct productive interviews with novice teachers. Their job consists in helping novice teachers during the two first years of their service. Every month, they observe novice teachers while they teach a class, and conduct interviews with them to help them improve their teaching methods. During these interviews, novice teachers feel vulnerable and are often profoundly destabilized by the ETs' remarks (e.g. crying, rejecting criticism, offensive attitude). For fear of a bad evaluation, they have developed strategies to reject the ETs' recommendations, because accepting them would mean recognizing they are wrong and that they must change their teaching methods. ETs follow a basic institutional training that does not help them cope with these difficulties while leading interviews. A few years ago, fifteen ETs in Nantes (France), toke the initiative to get together and share their experience regarding the way to conduct these interviews. After just a year, the French National Association of Educational Counselors set up an official training session on this topic in collaboration with the CREN research lab. During these training sessions, ETs try to relive past interviews during which they encountered tense moments. They collectively analyze these challenging interview situations in order to understand what went wrong and how they should have reacted in order to improve the communication. These sessions are obviously useful for the ET who lived the situation but they are primarily aimed at helping the other ETs prepare for their future interviews.

As it would be impossible to film the interviews, given the already tense setting, the ETs discretely record their interviews as audio files. They then use written transcription of these recordings to analyze the interviews. These transcriptions lack all the non-verbal communication (i.e. mimicry, gestures, attitudes and postures) and the rhythm with which the sentences are said. Without these elements it is almost impossible to understand the emotions displayed by the novice teacher and the tensions that occurred during the interview. Yet, experiencing these destabilizing interview moments is the key to help ETs deal with these situations.

Analyzing written transcriptions of interviews is a common technique for teaching communication methods, used in many domains. In order to make the simulation more realistic, teachers also use role playing to help their students train. Even though these sessions are very useful, the students do not have the skillsets of actors, and the situations are usually not very realistic. Some schools pay specialized companies to train their students for job interviews but they can only afford one session. Certain assessment companies pay actors to play the role of an angry customer, or an employee who is about to get fired, in order to test the reactions of future managers. However, this costly solution is not affordable for public schools and universities.

Several interview simulation tools have been developed these past years to offer affordable and efficient solutions to this problem. We will analyze these tools and the functionalities they offer in the next section. In the third section, we propose TGRIS, a Teacher-Guided Realistic interview Simulator that allows teachers to create authentic emotional situations. In the fourth section we discuss the first experimentations of our prototype with a group of 15 ETs. After a short conclusion, we present the future work and experimentations.

Tools for Interview Simulations

These past years, several private companies have tried to answer the need for interview training simulators. SIMmersion1 for example, allows learners to train on several job and sale interview scenarios. VTS Editor2 also offers the possibility to create new scenarios by selecting the background, the virtual agents and the tree dialogue that contains all the possible answers for the virtual agent and the learner. However, these interview simulations are far from authentic. Indeed, the learners alternatively watch a virtual agent or a video of a real actor and then choose a predefined answer. This has three major disadvantages for teaching:

-the learners do not work on their oral communication skills (because they click on sentences) -the learners do not work on constructing their own sentences (because the sentences are predefined) -the learners do not train their non-verbal communication such as intonation, posture or facial expressions MACH offer a much more natural interactions [START_REF] Hoque | MACH: My Automated Conversation Coach[END_REF]. This system allows learners to train for job interviews by naturally answering questions of a virtual agent recruiter. This system is capable of detecting certain key words to adapt the virtual agents' interactions. However, the logic of this system only works for simulating interviews where the agent is the motor in the conversation and there is only need to slightly adapt their reactions to what the learner says.

TARDIS project [START_REF] Anderson | The TARDIS Framework: Intelligent Virtual Agents for Social Coaching in Job Interviews[END_REF]) provides a scenario-based application for helping people improve their social skills for job interviews. A virtual agent, playing the role of the recruiter, is displayed on a screen and conducts the interview by following a predetermined scenario. While the dialogue is scripted, the agent's emotional and social behavior is determined run-time according to non-verbal signals performed by the user, such as facial expression, posture, head direction, voice intonation. These signals are used to infer the user's emotional state, mood and attitude.

Virtual Reality (VR) is the latest breakthrough in interview simulations. VR headsets allow to create truly immersive and emotional simulations. Several researchers have proven the effectiveness of such environments for education: [START_REF] Ponder | Immersive VR decision training: telling interactive stories featuring advanced virtual human simulation technologies[END_REF] used VR simulations for teaching rapid decision making in stressful environments, [START_REF] Bell | Simulated Job Interview Skill Training for People with Psychiatric Disability: Feasibility and Tolerability of Virtual Reality Training[END_REF] for helping people with psychiatric disabilities to train for job interviews and [START_REF] Brinkman | A Virtual Reality Dialogue System for the Treatment of Social Phobia[END_REF] for helping people to overcome their social phobia. In order to create authentic simulations that trigger emotions, like in the real world, the virtual agents and the elements of the virtual environment are piloted, in real type, by a teacher or a therapist through a Wizard of Oz interface.

This type of RV interview simulation could be used in many educational field. The group of ETs for example, could greatly benefit from this type of immersive simulation. In the next section, we therefore propose a tool that allows teachers to create their own authentic VR interview simulations.

TGRIS: Teacher-Guided Realistic Interview Simulator

In this section, we propose TGRIS (Teacher-Guided Realistic Interview Simulator). The main objective is to provide a tool that enables teachers to create their own custom interview scenarios to train their students. The goal is not to replace the transcription analysis or the role playing sessions currently used by teachers. TGRIS is an additional means to help students prepare for challenging interview situations they will be faced with and learn the best way to react in such situations.

As shown in Figure 1, the learner sits at a desk and talks directly to the virtual agent. TGRIS actually offer two versions: the virtual agent can either be projected on a screen, in front of the learner or in a VR headset 3 . Even if the VR version is more immersive, we wanted to provide a basic version that does not require costly equipment. The verbal and non-verbal reactions of the virtual agent are triggered by the teacher, in real time, through a Wizard of Oz interface. The name "Wizard of Oz" comes from The Wonderful Wizard of Oz story, in which a man hides behind a curtain and pretends to be a powerful wizard by piloting a huge puppet with levers and amplifying his voice. The term in commonly used in the field of Human Computer Interfaces to refer to an interface that allows a human to simulate the behavior of a theoretical intelligent computer application [START_REF] Ford | Collocational Grammar As a Model for Human-computer Interaction[END_REF].

Figure 1. TGRIS setting

For the virtual agent, we choose GRETA, an agent that has the specificity of providing a very large pallet of multimodal emotions, combining the tone of voice, facial expression and body language [START_REF] Pelachaud | Modelling multimodal expression of emotion in a virtual agent[END_REF]. In addition, the GRETA agents react to the sound of the user's voice by nodding and shifting eye contact, giving the impression they are really listening. Thanks to these features, the virtual agents convey emotions and seem to have their own personality. It is important to note that GRETA's visual aspect is not very realistic. Surprisingly, this is actually an advantage. Indeed, according to Masahiro Mori's Uncanny Valley theory [START_REF] Seyama | The Uncanny Valley: Effect of Realism on the Impression of Artificial Human Faces[END_REF], virtual agents that appear almost, but not exactly, like real human beings, create feelings of eeriness and revulsion.

Like the other VR tools described in the previous section, the virtual agents in TGRIS are piloted by the teacher, via a Wizard of Oz interface. The top part of this interface is composed of a dialogue tree that contains the pre-defined reactions that the agent can say. The teacher also has access to several basic answers such as "yes", "no" and "I don't' understand". They can also write a new text if they cannot find the response they need. In addition, the teacher can launch non-verbal reactions such as crossing arms, raising shoulders or looking down. On the bottom of the interface, the teacher can adapt the emotional response of the agent with an emotion charts (happy, surprises, scared, angry, disgusted and sad) and several scales (e.g. agree or not, interested or not).

TGRIS also records and interview simulation via a Web cam so that the teacher and the learners can play it again during a debriefing session and analyze the way the student and the agent reacted.

3

The first prototype works with HTC Vive Before the simulation starts, the teacher will be able to set up the interview situation they want their students to work on by choosing the face of the agent, its emotional state (e.g. nice, neutral, angry, sad) and the background and ambient sounds of the VR world (for the time being we only have one classroom with the typical sound of a school playground). Most importantly, teachers can import new interview scenarios. These scenarios contain the sequence of answers and responses for the virtual agent. For the time being, teachers can create these scenarios with a free mind mapping software (see Figure 3) and then export them to xml file.

First Experimentations

In order to provide solutions that fit the real needs of teachers and students, TGRIS was created by following the User Centers Design principals [START_REF] Gay | The utility of computer tracking tools for user centered design[END_REF]. As a matter of fact, the project was initiated by a group of ET's and their teacher, who wanted to improve their training methods. It was therefore natural to include them at all the staged of the project. At the beginning of the project, we attended one of their training sessions to understand their current training methods and needs. We also made them test different scenes with a VR headset to see if this would help them simulate an interview situation. Four out of the twelve ET's did not like the idea of talking to a virtual agent but all the others (eight out of twelve) were very eager to use VR for their future training. They were very impressed by the immersion brought by the VR and felt that it could be a good tool to relive interview situations. In order to make the simulations more realistic, they expressly asked to have a VR environment that looked like a middle school classroom with the sound of a school playground in the background.

The TGRIS setting presented above was also co-designed with the ETs' teacher. The possibility to record the interview simulation and play them back during a debriefing session was especially important to her as a large part of her teaching method is based on analyzing interviews. She even mentioned the possibility of letting the ETs pilot the agent in order to mimic novice teachers they had interviewed. During one of the ET's training sessions, we presented four of GRETA's virtual agents to see how the ETs felt about simulating interviews with virtual agents. We purposefully choose four very different emotions and faces: happy Poppy, neutral Prudence, nasty Spike and sad Obadiah (Figure 2). Even with just a photo, the encounter with these agents immediately generated a flow of emotions. Here are a few examples of their reactions for Poppy: "she looks like a teacher" "she is nice" "she is sure of herself" "she is ready to listen", "she seems worried", "she probably thinks she did a great job", "she is a pest". It appears that the use of virtual agents uninhibited the ETs to express their feelings. These spontaneous reactions would have been impossible to obtain if we had used real people [START_REF] Rimé | Emotion Elicits the Social Sharing of Emotion: Theory and Empirical Review[END_REF]. The use of virtual agents could therefore turn out to be better than training with actors.

The ET's also decided which interview scenario they wanted to be able to practice with TGRIS. After listing several challenging interview situations, they unanimously decided that they wanted to train on the introductory phase of the interview, traditionally starter by the question "What do think of your morning class?". Indeed, the beginning of the interview with the novice teachers is a very tense moment and a misplaced remark can radically annihilate any change of constructive dialogue. The ETs collaboratively came up with a list of possible answers that the novice teachers could say and that they didn't really know how the react to. Seven cases of answers are presented in figure 3.

Conclusion and Work in Progress

In this paper, we propose TGRIS, a Virtual Reality interview simulation tool that allows teachers to create authentic emotional simulations to train their students during their class. The teacher can set up various interview situations by choosing the looks and the emotional state of the virtual agent and the virtual environment in which the interview will take place. During the simulation, the student sees the agent on a screen or through a VR headset if the school is equipped with one. The student simply talks to the agent and the teacher pilots the verbal and non-verbal reactions of the agent, in real time. TGRIS was designed in close collaboration with end-users: a group of twelve ETs and their teacher validated the choices regarding the VR environment and the virtual agents. The ETs also supplied the dialogue scenarios for interview simulations.

The fact that the agent is piloted by the teachers gives the impression that the agent is truly taking part in the conversation. It also allows teachers to trigger the right sequence of reactions that lead to a "difficult" interviews depending on the students' experience and their teaching objectives. However, the fact the agent's reactions are triggers by a human, via a Wizard of Oz interface, can also lead to slow reactions from the agent and interactions that do not have the right rhyme. The interface must offer a large variety of responses yet be simple enough so that the teacher can trigger the right response as fast as possible. This is the main challenge we are working on at present. A first prototype of TGRIS will be tested with colleagues in Mai and we have planned on testing TGRIS during the next ETs training session, in June 2018.

Figure 2 .

 2 Figure 2. four GRETA agents: Poppy, Prudence, Spike and Obadiah

Figure 3 .

 3 Figure 3. scenarios for the introductory phase of an interview between Educational Trainers (ET) and novice teachers (played by a GRETA virtual agent)

Marfisi, I., Vinatier, I., Bevacqua, E. & Kébé, M. (2018). Enabling Teachers to Create Authentic Interview Simulations. In Proceedings of EdMedia: World Conference on EducationalMedia and Technology (pp. 1506-1511). Amsterdam, Netherlands: Association for the Advancement of Computing in Education (AACE), 25-29 June 2018.

http://simmersion.com

https://www.seriousfactory.com/virtual-training-suite/


F Cochachin

E Boutillon

Senior Member, IEEE D Declercq

Optimization of Sign-Preserving Noise-Aided Min-Sum Decoders with Density Evolution

The novelty of this paper is to propose a new LDPC decoder called Sign-Preserving Noise-Aided Min-Sum (SP-NA-MS) decoder that improves the decoding performance compared to classical Offset Min-Sum (OMS) decoder when messages are quantized, with only 3 or 4 bits. The particularity of the SP-NA-MS decoder is that the variable-to-check messages are never set to 0, and always carry the sign information. Moreover, the decoder incorporates random perturbation due to deliberate noise injection. The parameters of the SP-NA-MS decoders are optimized in the asymptotic limit of the code length thanks to the Density Evolution (DE) method. The finite-length simulations confirm the conclusions of the DE analysis and gain of up to 0.3 dB in SNR can be obtained compared to regular OMS with same quantization level.

I. INTRODUCTION

Low-Density Parity-Check (LDPC) codes are widely used in communications standards like DVB-S2, DVB-S2X, IEEE 802.3 [START_REF]IEEE Standard for Ethernet[END_REF], etc. LDPC codes can be efficiently decoded by Message-Passing (MP) algorithms that use a Tanner graph [START_REF] Tanner | A Recursive Approach to Low Complexity Codes[END_REF] representation of the LDPC codes. The Belief-Propagation (BP) decoder has excellent decoding performance in the waterfall region but at a cost of a high computational complexity. The Min-Sum (MS) and Offset Min-Sum (OMS) decoders [START_REF] Chen | Density Evolution for Two Improved BP-Based Decoding Algorithms of LDPC Codes[END_REF], [START_REF] Chen | Reduced-Complexity Decoding of LDPC Codes[END_REF] are simplified version of the BP that are much less complex but at a cost of a slight decoding performance degradation. Reducing the bit-size representation of messages is a technique that further reduces the complexity of the decoder, again, at a cost of performance loss. In the past fifteen years, the quantization of MP decoders has been extensively studied over the Binary-Input Additive White Gaussian Noise (BI-AWGN) channel [START_REF] Chen | Reduced-Complexity Decoding of LDPC Codes[END_REF]- [START_REF] Zhao | On Implementation of Min-Sum Algorithm and Its Modifications for Decoding Low-Density Parity-Check (LDPC) Codes[END_REF]. From these works, it is usually advised that 6 bits of quantization gives almost floating point performance. It can also be observed that, to the best authors knowledge, all paper on finite precision use the "no-decision value", i.e., a Log-Likelihood Ratio (LLR) equal to 0 (without defined sign, thus) in their messages representation. This is also true for the recent work on Non-surjective Finite Alphabet Iterative Decoders (NS-FAIDs) [START_REF] Nguyen-Ly | Analysis and Design of Cost-Effective, High-Throughput LDPC Decoders[END_REF] which provides a unified framework for several MS-based decoders like Normalized MS (NMS) decoder, OMS decoder, Partially OMS decoder. In [START_REF] Cochachin | Density Evolution Thresholds for Noise-Against-Noise Min-Sum Decoders[END_REF], the authors have shown that 3 or 4 bits quantized decoder can benefit from the introduction of particular randomness applied in the amplitude of messages during the decoding process. Thanks to the Density Evolution (DE) method [START_REF] Richardson | The Capacity of Low-Density Parity-Check Codes Under Message-Passing Decoding[END_REF], optimized parameters of noise injection could be determined in the asymptotic mode. Those type of decoders are called Noise-Against-Noise MS (NAN-MS) decoders. In this paper, we propose a new type of decoder for low complexity hardware implementation (i.e. 3 or 4 bits only for finite length representation of messages) that always preserve the sign of the messages. In other words, we forbid the 0 value in the message alphabet during the iterative decoding, i.e. a message cannot be erased. In order to optimize this new decoder, we use the optimization method proposed in [START_REF] Cochachin | Density Evolution Thresholds for Noise-Against-Noise Min-Sum Decoders[END_REF], i.e. we introduce a certain level of randomness in the optimization process. The result can be either a decoder that keeps some randomness, named Sign-Preserving Noise-Aided Min-Sum (SP-NA-MS) decoder, or a deterministic decoder that combines MS and OMS behaviors, named Sign-Preserving decoder. DE allows us to show that a 4-bits SP-NA-MS decoder can have the same DE threshold than a classical 5-bit OMS decoder. Our DE analysis is corroborated by finite length Monte Carlo simulations of various regular LDPC codes. Those results open new possibilities for massive parallel implementation of LDPC decoders where in average, 100 to 1000 bits are decoded per clock cycle, allowing 100 Gbit/s up to 1 Tbit/s decoders required in optical fiber applications. Due to paper size limitation, in this paper we present only the results for regular LDPC codes, but the proposed decoder can be used to decode irregular LDPC codes. The outline of the paper is as follows. Section II introduces the basic notions of quantized classical decoders and LDPC codes. In Section III, we explain how to preserve the sign of the exchanged messages. In Section IV, we discuss the probabilistic error model used to inject noise to the quantized decoders, and briefly explain how to optimize the model parameters with DE. In section V, we present the results of the asymptotic analysis of SP-NA-MS decoders for regular LDPC codes. Section VI shows finite length performance validation of the gains obtained with the proposed SP-NA-MS decoders, and section VII concludes the paper. For quantized decoders the message alphabet A C is defined as A C = {-N q , ..., -1, 0, +1, ..., +N q } consists of N s = 2N q + 1 states, with N q = 2 (q-1) -1 and where q is the number of quantization bits. Let us denote A L the decoder input alphabet, and denote ∈ N the number of iterations. Let us also denote m

II. BASIC NOTIONS

( ) v→c ∈ A L (resp. m ( ) c→v ∈ A L ) the message sent from VN v to CN c (resp. CN c to VN v) in the th iteration.
The LLR can be computed at the channel output as

LLR(y n ) = log Pr(y n | x n = 0) Pr(y n | x n = 1) = 2y n σ 2 . (1)
We assume in this paper that A C = A L , hence, LLR(y n ) has to be quantized and saturated. Let us denote the quantizer by Q : R → A L , defined as

Q (y) = S ( α × y + 0.5 , N q ) , (2)
where . depicts the floor function and S(x, N q ) is the saturation function clipping the value of x in the interval [-N q , N q ], i.e. S(x, N q ) = min(max(x, -N q ), +N q ). The parameter α is called channel gain factor and is used to enlarge or decrease the standard deviation of quantized values at the decoder input, α can be seen as an extra degree of freedom in the quantized decoder definition that can be analyzed and optimized on the BI-AWGN channel. With those notations, we define the quantized version of the LLR that initialize the MP decoder by the vector

I = (I 1 , ..., I N ) ∈ A N C , with I n = Q (LLR(y n )) ∀n = 1, . . . , N. (3)
A MP decoder exchanges messages between VNs and CNs along edges using a Tanner graph. Let us briefly recall the VN update (VNU) and CN update (CNU) equations for classical MS-based decoders. The update rule at a CNU is given by

m ( ) cm→vn =   v∈V(cm)\{vn} sign m ( ) v→cm   min v∈V(cm)\{vn} m ( ) v→cm . (4)
The update rule at a VNU is expressed as

m ( +1) vn→cm = Λ   I n + c∈V(vn)\{cm} m ( ) c→vn   , (5)
Table I: Binary representation of the quantized values.

Classical Decoder SP-NA-MS Decoder

m ∈ AC q = 3 bits m ∈ AS q = 3 bits (sign(m), |m|) -3 101 -3 111 (-1,3) -2 110 -2 110 (-1,2) -1 111 -1 101 (-1,1) - 100 -0 100 (-1,0) 0 000 +0 000 (+1,0) +1 001 +1 001 (+1,1) +2 010 +2 010 (+1,2) +3 011 +3 011 (+1,3)
where Λ(x) = sign(x)×S(max(|x|-λ v , 0)), N q ) 1 . We define the classical OMS with offset value λ v = 0, where the special case of λ v = 0 corresponds to the classical MS.

III. SIGN-PRESERVING NOISE-AIDED MIN-SUM DECODERS

In the classical MS-based decoders, the value of the v-to-c message can be zero, see [START_REF] Ping | Decoding Low Density Parity Check Codes with Finite Quantization Bits[END_REF]. In that case, the erased message, i.e. m ( +1) vn→cm = 0, does not carry any information and does not participate in the convergence of the decoder. In this paper, we propose a new type of decoder, with a modified VNU using a sign preserving factor, which never propagates erased messages.

A. Quantization used for SP-NA-MS Decoders

Using the sign-and-magnitude representation one can obtain a message alphabet which is symmetric around zero and which is composed of 2 q states. Hence the message alphabet for SP-NA-MS decoders denoted by A S is defined as A S = {-N q , ..., -1, -0, +0, +1, ..., +N q }2 . The sign of a message m ∈ A S indicates the estimated bit value associated with the VN to or from which m is being passed while the magnitude |m| of m represents its reliability. In this paper, it is assumed that A L = A S . An example of the binary representation of A C and A S for q = 3 is shown in Table I, one can see that -0 is represented by 100 2 , +0 is represented by 000 2 , etc. The quantization process defined in (2) is replaced by

Q * (y) = (sign(y), S ( α × |y| -1, N q )) , (6)
where . depicts the ceiling function. The quantized LLR is thus defined as

I n = Q * (LLR(y n )) ∈ A S for n = 1, . . . , N .
Let us define the update rules for Sign-Preserving decoders.

B. Sign-Preserving Min-Sum Decoders

One can note from (4) that the CNU, by construction, generates outgoing messages that always belong to A S . In the case of the VNU, (5) should be modified to ensure that the outgoing message will always belong to A S . To preserve always the sign of the messages, let us denote by µ ( ) vn→cm the sign-preserving factor of the message m ( +1) vn→cm , defined as

µ ( ) vn→cm = ξ × sign(I n ) + c∈V(vn)\{cm} sign m ( ) c→vn , (7)
where ξ = 1 + ((d v + 1) mod 2) where d v is the degree of the VN v. Note that the other values of ξ give worse decoding performance. From [START_REF] Nguyen-Ly | Analysis and Design of Cost-Effective, High-Throughput LDPC Decoders[END_REF], one can note that, by construction, µ

( ) vn→cm is the sum of d v (resp. d v +1) values in {-1, +1} if d v is odd (resp. if d v is even). Thus, µ ( )
vn→cm is always an odd number. The update rule of the Sign-Preserving Offset Min-Sum (SP-OMS) VNU is changed from [START_REF] Ping | Decoding Low Density Parity Check Codes with Finite Quantization Bits[END_REF] to

m ( +1) vn→cm = Λ *   µ ( ) vn→cm 2 + I n + c∈V(vn)\{cm} m ( ) c→vn   , (8)
where Λ * (x) = (sign(x), S (max( |x|λ v , 0), N q )). Note that Λ * (.) is applied on a non-null value since by construction, the fractional part of (µ

( ) vn→cm )/2 is 0.5.
We define a Sign-Preserving Min-Sum (SP-MS) with λ v = 0.

C. Sign-Preserving Noise-Aided Min-Sum Decoders

The noisy version of the SP-MS decoder, i.e., the SP-NA-MS decoder is defined by introduction some randomness during the VNU processing following the same principle as for the NAN-MS decoder of [START_REF] Cochachin | Density Evolution Thresholds for Noise-Against-Noise Min-Sum Decoders[END_REF]. The SP-NA-MS decoder is implemented perturbing unsaturated v-to-c messages m( +1) vn→cm . In [START_REF] Cochachin | Density Evolution Thresholds for Noise-Against-Noise Min-Sum Decoders[END_REF], the saturation function S in the function Λ * is not used to compute m( +1) vn→cm , i.e. we use Λ * (x) = (sign(x), |x| ). The update rule for a noisy-VNU is given by

m( +1) vn→cm = Υ m( +1) vn→cm , (9)
where Υ is a noise model which is defined in the next section. Note that the Υ performs also the saturation operation.

IV. PROBABILISTIC ERROR MODEL AND NOISY DENSITY EVOLUTION FOR SP-NA-MS DECODERS

In this section, we first introduce the constraints on the noise models, then we present the noise model that we use to perturb m. Finally, we briefly explain how to optimize the model parameters with noisy DE.

A. Probabilistic Error Model for SP-NA-MS Decoders DE analysis can be performed only using memoryless noise models which must satisfy the following condition of symmetry [START_REF] Cochachin | Density Evolution Thresholds for Noise-Against-Noise Min-Sum Decoders[END_REF] Pr(Υ(β

1 ) = β 2 ) = Pr(Υ(-β 1 ) = -β 2 ), ∀β 1 , β 2 ,
these noise models allow the VNUs to be symmetric, allowing to use the all-zero codeword assumption necessary in DE [START_REF] Richardson | The Capacity of Low-Density Parity-Check Codes Under Message-Passing Decoding[END_REF]. Moreover, since the addition of noise is independent of the sign of the message, we will suppose in the sequel without loss of generality that the message m is always positive. Let us denote A N the alphabet of m, with probabilities, denoted ϕ = (ϕ s , ϕ a , ϕ 0 ). ϕ s denotes the CPDF Pr( m = +N q -1 | m = +N q ), ϕ a denotes the CPDF Pr( m = β -1 | m = β), ∀β ∈ {+2, ..., +(N q -1)}, and finally ϕ 0 denotes the CPDF Pr( m = +0 | m = +1). The saturation function is performed by setting Pr( m = +N q | m > +N q ) = 1. Table II give the resulting CPDF.

A N = {-N q × d v -d v /2 ), ..., -0, +0, ..., +N q ×d v + d v /2 }.
m = m -1 0 ϕ0 ϕa ϕs 0 m = m 1 1 -ϕ0 1 -ϕa 1 -ϕs 0 m = Nq 0 0 0 0 1 m +5 +4 +3 +2 +1 +0 m +3 +2 +1 +0 ϕ s ϕ a ϕ 0 1 1 -ϕ s 1 -ϕ a 1 -ϕ 0
The rationale behind Υ is to implement a probabilistic offset with the purpose of always keeping the sign of the messages. Let us discuss the case of ϕ s = ϕ a = ϕ 0 . It can see that SP-MS and SP-OMS decoders are implemented with ϕ = (0, 0, 0) and ϕ = (1, 1, 1), respectively. For other values of ϕ, the offset is only applied from time to time during the decoding iterations, implementing a probabilistic weighted combination of a SP-MS decoder and a SP-OMS decoder. With ϕ s and ϕ 0 , the extreme values of A S are studied. m = ±1 is a special case because it will be changed to m = ±0 with probability ϕ 0 . Since m = ±0 propagates the sign but with a reliability of zero, therefore, ϕ 0 has to be analyzed differently than ϕ a . Additionally, in quantized decoders, all values greater than N q are saturated to N q . As a result, many more configurations of the VNU states lead to m( ) vn→cm = N q compared to other values, and ϕ s should also be analyzed differently than ϕ a . Fig. 1 depicts Υ for (q = 3, N q = 3).

B. Noisy Density Evolution for SP-NA-MS Decoders

The goal of DE is to recursively compute the probability mass function (PMF) of the exchanged messages in the Tanner graph along the iterations. DE allows us to predict if an ensemble of LDPC codes, parametrized by its degree distribution, decoded with a given MP decoder, converges to zero error probability in the limit of infinite block length. For the BI-AWGN channel, the maximum value of σ or the minimum SNR at which the DE converges to a zero error probability is called the DE threshold δ, as in [START_REF] Cochachin | Density Evolution Thresholds for Noise-Against-Noise Min-Sum Decoders[END_REF] δ db = 10 log 10 1 2 R σ * 2 where σ * = δ, and R is the rate of the code. In this paper the details of the noisy-DE equations are not presented, we refer to [START_REF] Varshney | Performance of LDPC Codes Under Noisy Message-Passing Decoding[END_REF], [START_REF] Ngassa | Density evolution and functional threshold for the noisy min-sum decoder[END_REF] for more details. The noisy-DE threshold δ is a function of the code family, parametrized by its degree distribution (d v , d c ), of the number of precision bits q, of the value of the channel gain factor α, and of the values of the transition probabilities of the noise model (ϕ s , ϕ a , ϕ 0 ). For a fixed q and a fixed (d v , d c ), δ is used to jointly optimize (ϕ s , ϕ a , ϕ 0 ) and α:

(ϕ * s , ϕ * a , ϕ * 0 , α * ) = arg max (ϕs,ϕa,ϕ0,α) δ (d v , d c , q, α, (ϕ s , ϕ a , ϕ 0 )) . (10)

V. ASYMPTOTIC ANALYSIS FOR REGULAR LDPC CODES

In this section, we consider the ensemble of (d v , d c )-regular LDPC codes with code rate R ∈ {1/2, 3/4} for d v ∈ {3, 4}, R = 0.8413 for the IEEE 802.3 ETHERNET code [START_REF]IEEE Standard for Ethernet[END_REF], and quantized decoders with q ∈ {3, 4}. The optimization of the transition probabilities of the noise model Υ and the channel gain factor is made using a greedy algorithm which computes a local maximum DE threshold. For noiseless classical decoders, the optimization ( 10) is reduced to the optimum channel gain factor α * which is computed performing a grid-search.

The DE thresholds of the noiseless classical MS and OMS decoders are given in Table III. It can be seen that the OMS is almost always superior to the MS for the considered cases, which was expected, except for the regular d v = 3 LDPC codes with low precision q = 3.

Table III: DE thresholds of classical MS and OMS decoders.

(dv, dc)-regular LDPC code, BI-AWGN channel In Table IV, we indicate the noisy DE thresholds obtained with [START_REF] Varshney | Performance of LDPC Codes Under Noisy Message-Passing Decoding[END_REF], we also show the DE gains obtained comparing the best thresholds indicated in bold in Table III and the noisy thresholds of SP-NA-MS decoders. Moreover, we list the best noisy DE thresholds of NAN-MS decoders presented in [START_REF] Cochachin | Density Evolution Thresholds for Noise-Against-Noise Min-Sum Decoders[END_REF]. Several conclusions can be derived from this analysis. 1) First, the DE thresholds of the SP-NA-MS decoders are almost always better than the DE thresholds of the noiseless classical decoders. The DE gains for the SP-NA-MS decoders are quite important for q = 3, the largest gain obtained is around 0.3399 dB for (d v = 4, d c = 8). While the DE gains are smaller for the largest precision q = 4. We can observe a loss of around 0.0102 dB for (d v = 6, d c = 32) and q = 4.

(dv = 3, dc = 6) (dv = 3, dc = 12) (dv = 6, dc = 32) q λv α * δ db α * δ db α * δ db 3 bits 0 0.
From this analysis, we can conclude that the preservation of the sign of messages and the noise injection are more and more beneficial as the decoders are implemented in low precision.

2) Second, when comparing the noisy thresholds of SP-NA-MS and NAN-MS decoders, one can observe that the SP-NA-MS decoders achieve better DE thresholds for almost all (d v , d c )-regular LDPC codes tested, the only exception appears for the regular (d v = 6, d c = 32) LDPC code and q = 4. The largest gain obtained, when comparing the SP-NA-MS thresholds and NAN-MS thresholds, is around 0.1803 dB for the regular (d v = 6, d c = 32) LDPC code and q = 3.

3) A third remark comes from the interpretation of the optimum ϕ * obtained through the DE analysis. We have ϕ * 0 = 0 for regular d v = 3 LDPC codes, this makes sense because d v = 3 is small enough to transform m = ±1 into m = ±0, which gives to m( ) vn→cm a reliability of zero and which could not help to extrinsic messages become more and more reliable at each new decoding iteration. For regular d v > 3 LDPC codes, we have almost always ϕ * 0 = 1, hence, one can conclude that for regular d v > 3 LDPC codes, the transformation from m = ±1 to m = ±0, does not affect the decoding process. Note that in [START_REF] Cochachin | Density Evolution Thresholds for Noise-Against-Noise Min-Sum Decoders[END_REF], the transformation from m = ±1 to m = 0 should not be allowed since m = 0 ∈ A C erase the bit value.

VI. FINITE LENGTH PERFORMANCE

In order to corroborate the asymptotic results obtained in the previous section, the frame error rate (FER) performance of quantized decoders over the BI-AWGN channel is presented.

For this purpose, we designed four (d v , d c )-regular QC-LDPC codes with length N = 1296, R ∈ {1/2, 3/4} for d v ∈ {3, 4}, and circulant size L = 54 for R = 1/2 and L = 27 for R = 3/4, using the PEG algorithm from [START_REF] Venkiah | Design of Cages with a Randomized Progressive Edge Growth Algorithm[END_REF]. The classical OMS decoder performance for q = 5 is also shown as benchmark.

A maximum of 100 iterations has been set for d v = 3 and d v = 4 LDPC decoders. Fig. 2 shows the FER performance comparisons between the classical MS, classical OMS, and SP-NA-MS decoders, for the two considered precisions q = 3 and q = 4, and for the regular (i.e. at FER = 10 -2 ) an SNR gain for the SP-NA-MS decoders which corresponds to the threshold differences: around 0.27 dB for (q = 3, d v = 3, R = 1/2), 0.06 dB for (q = 4, d v = 3, R = 1/2), 0.32 dB for (q = 3, d v = 4, R = 1/2), and the same performance for (q = 4, d v = 4, R = 1/2). We have made the same analysis for QC-LDPC codes with rate R = 3/4, i.e. (d v = 3, d c = 12) and (d v = 4, d c = 16), and obtained that the SNR gains correspond to the DE gains. Simulation results for the IEEE 802.3 ETHERNET code are provided on Fig. 4 with a maximum of 30 iterations. Again, the SNR gains in the waterfall correspond to what was predicted with the DE analysis, with a 0.19 dB gain for q = 3 and the same performance for q = 4.

(d v = 3, d c = 6) QC- LDPC code.

VII. CONCLUSION

In this paper we have proposed to use a sign-preserving factor which helps the message passing decoders to keep the sign information of extrinsic messages during the VNU processing. We have also proposed a noise model to introduce randomness in the message passing decoders. Both the signpreserving factor and the noise model help to improve the error correction performance of quantized iterative decoders. Density Evolution was used to obtain the optimum noise parameters and the optimum channel gain factor. The DE thresholds results have shown that the preservation of the sign of messages and the effect of the injected noise is

Figure 1 :

 1 Figure 1: The mapping used for the noise model Υ.

4 )

 4 Finally, all SP-NA-MS decoders can be implemented as deterministic decoders since the values of the transition probabilities are close or equal to 0 or 1. The optimum noise parameters ϕ * are close to (ϕ * s , ϕ * a , ϕ * 0 ) = (1, 1, 0) for the regular d v = 3 LDPC codes. While in the case of the regulard v > 3 LDPC codes, ϕ * are close to (ϕ * s , ϕ * a , ϕ * 0 ) = (1, 1,1) which correspond to a deterministic SP-OMS decoder.

Fig. 3 ( 3 , 6 )

 336 draws the same curves for the regular (d v = 4, d c = 8) QC-LDPC code. A first conclusion is that the finite length FER performance are in accordance with the gains predicted by the DE analysis. We observe in the waterfall E b /N 0 (dB) -regular LDPC, N = 1296 Classic OMS (5-bit), α = 2.625 Classic MS (3-bit), α =0.9375 Classic MS (4-bit), α =2 Classic OMS (3-bit), α =1.0625 Classic OMS (4-bit), α =1.875 3-bit, SP-NA-MS, α = 0.96 4-bit, SP-NA-MS, α = 1.79

Figure 2 :( 4 , 8 )

 248 Figure 2: FER performance for (3, 6)-regular LDPC code.

Figure 3 :

 3 Figure 3: FER performance for (4, 8)-regular LDPC code.

( 6 ,

 6 32)-regular LDPC, N = 2048 Classic OMS (5-bit), α = 1.45 Classic MS (3-bit), α =0.455 Classic MS (4-bit), α =1.035 Classic OMS (3-bit), α =0.84 Classic OMS (4-bit), α =1.28 3-bit, SP-NA-MS, α = 0.74 4-bit, SP-NA-MS, α = 1.18

Figure 4 :

 4 Figure 4: FER performance for the ETHERNET code.

  VN in the Tanner graph corresponds to a column of H and a CN corresponds to a row of H, with an edge connecting CN c m to VN v n exists if and only if h mn = 0. Let us assume that v is any VN and c is any CN. Let us also denote V(v) the set of neighbors of a VN v, and denote V(c) the set of neighbors of a CN c. The degree of a node is the number of its neighbors in G. A code is said to have a regular columnweight d v = |V(v)| if all VNs v have the same degree d v .

	Similarly, if all CNs c have the same degree d c = |V(c)|, a code is said to have a regular row-weight d c . Let x = (x 1 , ..., x N ) ∈ {0, 1} N denote a codeword which satisfies Hx T = 0. In this paper, x is mapped by the BPSK
	modulation and transmitted over the BI-AWGN channel with
	noise variance σ 2 . The channel output y = (y 1 , ..., y N ) is
	modeled by y n = (1 -2x n ) + z n for n = 1, . . . , N , where z n is a sequence of independent and identically distributed (i.i.d.)
	Gaussian random variables with zero mean and variance σ 2 .
	OF CLASSICAL QUANTIZED
	DECODERS AND LDPC CODES
	An LDPC code is a linear block code defined by a sparse
	parity-check matrix H = [h mn ] of M rows by N columns,
	with M < N . The usual graphical representation of an LDPC
	code is made by a Tanner graph which is a bipartite graph
	G composed of two types of nodes, the variable nodes (VNs)
	v n , n = 1...N and the check nodes (CNs) c m , m = 1...M . A

Table II :

 II Conditional probability density function of Υ.

	m\ m	+0	+1	+1 < . < +Nq	+Nq	. > +Nq

The function Υ is defined as Υ : A N → ÃS , where ÃS = A S , with the random process that transforms m ∈ A N into m ∈ ÃS defined by the conditional probability density function (CPDF) Pr(Υ( m) = m). Υ is parametrized by three different transition

Table IV :

 IV Noisy DE thresholds of SP-NA-MS decoders

	SP-NA-MS decoders, (dv, dc)-regular LDPC code, BI-AWGN channel	NAN-MS
	(dv, dc)	q	α *	ϕ * s	ϕ * a	ϕ * 0	δdb	DE gain	δdb -NIV
	(3, 6)	3 4	0.96 1.79	0.987 1.000	0.712 0.000 1.000 0.000	1.4994 1.2688	0.2894 0.0793	1.5711 1.2877
	(3, 12)	3 4	0.72 1.34	1.000 1.000	0.725 0.000 0.938 0.000	2.5421 2.3596	0.1895 0.0888	2.5989 2.3777
	(4, 8)	3 4	1.01 1.54	0.900 1.000	1.000 1.000 1.000 1.000	1.9820 1.7306	0.3399 0.0203	2.1056 1.7411
	(4, 16)	3 4	0.75 1.30	1.000 1.000	0.962 0.712 1.000 1.000	2.7448 2.4941	0.3184 0.0351	2.8121 2.5077
	(6, 32)	3 4	0.74 1.18	1.000 1.000	1.000 1.000 1.000 1.000	3.3963 3.1787	0.1965 -0.0102	3.5766 3.1685

Note that in the literature λv is often applied at the CN. Applying the offset at the VN or at the CN is equivalent only when the saturation function is not used since min i=1,...,n (|x i | -λv) = min i=1,...,n (|x i |) -λv.

The alphabet A S can be easily implemented in hardware because each value of A S has its corresponding binary representation.

ACKNOWLEDGEMENT

This work has been funded by the french ANR under grant number ANR-15-CE25-0006-01 (NAND project).


V Daanen

J Gastaldo

J Y Giraud

P Fourneret

J L Descotes

M Bolla

D Collomb

Jocelyne Troccaz
email: jocelyne.troccaz@imag.fr

MRI/TRUS data fusion for brachytherapy

Background: Prostate brachytherapy consists in placing radioactive seeds for tumour destruction under transrectal ultrasound imaging (TRUS) control. It requires prostate delineation from the images for dose planning. Because ultrasound imaging is patient and operator-dependant, we have proposed to fuse MRI data to TRUS data to make image processing more reliable. Technical accuracy of this approach has already been evaluated. Methods: We present work in progress concerning the evaluation of the approach from the dosimetry viewpoint. The objective is to determine which impact this system may have on the treatment of the patient. Dose planning is performed from initial TRUS prostate contours and evaluated on contours modified by data fusion. Results: For the 8 patients included, we demonstrate that TRUS prostate volume is most often underestimated and that dose is overestimated in a correlated way. However, dose constraints are still verified for those 8 patients. Conclusions: This confirms our initial hypothesis.

Introduction

Prostate cancer is one of the most common malignancy among men. An estimated 543000 cases and 204000 deaths were attributed to prostate cancer in 2000 [START_REF] Parkin | Global cancer statistics in the year 2000[END_REF]. Its detection is based on digital rectal examination (DRE) and Prostate Specific Antigen (PSA) rating and is confirmed through the anatomo-pathologic analysis of biopsies. Several treatments may be proposed to the patient suffering from localized prostate cancer (T1c-T2b N0 M0, UICC 2002). One of them is prostate brachytherapy which consists in placing permanent radioactive seeds, most often I 125 , inside the prostate thanks to needles passing through the perineum. Most often treatment planning and needle placement rely on the intensive use of transrectal ultrasound imaging (TRUS). Parallel transverse images are acquired with constant inter-slice distance thanks to the use of a stepper. Needle insertion through the perinea is made easier thanks to a grid rigidly connected to the TRUS probe (see figure 1). Prostate volume study is a critical step for treatment planning; it allows selecting precisely the number of seeds to be inserted and their position in the gland in order to obtain a predefined dose distribution (see section 3). Traditionally, this volume definition is manually performed by the clinician from TRUS images (either pre-operatively or intra-operatively). But it is well known that ultrasonic image quality is highly variable from patient to patient and that organ delineation varies from user to user and for a same user, from session to session. In this context, Magnetic Resonance Imaging (MRI) has a great potential. In very few centres, radioactive seeds are implanted inside an open interventional MR machine [START_REF] D'amico | Real-time magnetic resonance image guided interstitial brachytherapy in the treatment of select patients with clinically localized prostate cancer[END_REF][START_REF] Hata | MRI-guided prostate biopsy using surgical navigation software: device validation and feasability[END_REF]. Robots may also be used in conjunction to MRI imaging for improved accuracy and increased possible trajectories [START_REF] Fichtinger | System for robotically assisted prostate biopsy and therapy using intraoperative CT guidance[END_REF]. Often such robots or systems are jointly designed for biopsy and brachytherapy since both gestures basically involve needle insertion into the prostate under TRUS control.

In this project, we chose to bring the MR virtually in the Operating Room (OR) by TRUS/MRI data fusion in order to help the clinician for treatment planning without requiring the presence of both the patient and the implantation team in the MRI room. A similar idea was used by [START_REF] Kaplan | Real-Time MRI-Ultrasound Image Guided Stereotactic Prostate Biopsy[END_REF] in the context of TRUS-guided prostate biopsies. However, where [START_REF] Kaplan | Real-Time MRI-Ultrasound Image Guided Stereotactic Prostate Biopsy[END_REF] uses rigid registration of 6 anatomical landmarks, the present work makes use of a combined rigid and elastic surface registration.

Having demonstrated the accuracy of data fusion (see [START_REF] Reynier | MRI/TRUS data fusion for prostate brachytherapy[END_REF]), a study has been undertaken for evaluating the impact of MRI/TRUS data fusion on dose distribution. This on-going work is described in the paper. Section 2 presents the method and summarizes preliminary results. Section 3 introduces dose constraints to be satisfied. Section 4 describes the evaluation protocol. Results are given in section 5 and discussed in section 6.

MRI/US data fusion: principles and previous results

The developed system is based on combined rigid and elastic surface registration. Preoperatively, a MRI acquisition of the patient prostate is performed; three orthogonal T2 TSE volumes are obtained using an endorectal coil and the prostate contours are segmented jointly on the three volumes. This gives a set of points S MRI defined in a single referential R MRI . Intraoperatively, TRUS axial slices are collected and manually segmented by the urologist as in the conventional procedure and this results in a sparser intra-operative 3D prostate model S TRUS defined in a referential R TRUS ; as mentioned above, the axial contours are necessary for dose simulation and planning. Pseudo-sagital slices may also be acquired and segmented and then merged to the data resulting from the axial acquisition (cf. figure 2). The objective of registration is to determine the transform between R TRUS and R MRI allowing the optimal superimposition of S TRUS and S MRI . Registration determines prostate motion between the two acquisitions as well as prostate deformations. A pre-registration consisting in superimposing the centres of gravity of S TRUS and S MRI initializes the unknown transform. From this initial estimate, rotation and translation parameters between data sets as well as local deformations or distortions are determined. The method is derived from the octree-spline elastic registration described in [START_REF] Szeliski | Matching 3-D anatomical surfaces with non-rigid deformations using octree-splines[END_REF]. It makes use of an adaptive, hierarchical and regularized free-form deformation of one volume to the other coordinate system. The optimization stage is based on the Levenberg-Marquadt minimization procedure. The result is a 3-D function f transforming any ultrasound data point in R TRUS to the corresponding MRI point in R MRI .

Fig. 2. MRI/TRUS fusion for brachytherapy: (left) two of the axial and pseudo-sagital TRUS images (middle) 3D TRUS reconstruction (right) composite image produced after MRI/TRUS elastic registration: for each axial TRUS image the corresponding MRI data are computed -the green cursor enable motion in the modalities.

After MRI/TRUS surface-based elastic registration, for each initial TRUS image, a new composite image divided in 4 quadrants (2 TRUS quadrants and 2 MRI ones) is computed (see figure 2). The pixel intensity I at coordinates (u,v) of the composite image associated to the n th TRUS image is obtained as follows:

-I (u, v, n) = TRUS (u, v, n) in the TRUS quadrant where TRUS (u, v, n) is the pixel intensity at coordinates (u, v) in the n th TRUS image -I (u, v, n) = MRI (x, y, z) where (x, y, z) = f (u, v, n) in the MRI quadrants; since x, y and z have real values MRI (x, y, z) is obtained by interpolating neighbour intensity values in the MRI volume.

The user can interactively modify the composite image by moving the cross cursor dividing this image; this enables exploring the prostate jointly in the MRI and TRUS data. This may result in modifying locally the TRUS segmentations of the axial slices when MRI data make prostate delineation easier. In the following prostate contours obtained after MRI/TRUS data fusion are named "MRI+US contours" whilst original contours are named "US contours". More generally, all data or measurements obtained after MRI/TRUS fusion are named "MRI+US xxx" where measurements from US contours are named "US xxx".

[6] presents a technical evaluation of the system on phantom and patient data. Both rigid and elastic registrations were evaluated; elastic registration which demonstrated higher accuracy is briefly reported below (see table 1). It was measured both in terms of residual distance between matched surfaces and using TRE (Target Registration Error) evaluated from the urethra which does not participate to matched data. Residual surface distance was measured for 11 patients; TRE was evaluated for only 4 of them who were equipped with an endourethral probe making the urethra fully visible on TRUS and MRI modalities. 1: Accuracy evaluation of elastic registration (see [START_REF] Reynier | MRI/TRUS data fusion for prostate brachytherapy[END_REF] for more details).

Another aspect of the evaluation concerned prostate volume measurements from TRUS images with and without data fusion. Because the number of seeds depends on the prostate volume, modification in the latter may have a significant clinical impact. This preliminary study showed that apex and base US slices where often added to the segmented data when MRI information was fused to US data. For the 11 patients involved in the trial, the MRI+US gland volume was higher than the US volume; for elastic registration this volume increase was in average 15.86(±13.57)% of the US volume. Underestimating the prostate volume could result in delivering less radiation than expected to the target. Based on those preliminary observations, the project has been then to analyze MRI/TRUS fusion in prostate brachytherapy from the viewpoint of dose delivery to the organs.

Dose constraints

The objective is to evaluate the potential influence of TRUS/MRI registration on the treatment of the patient. In the Grenoble Hospital, the target dose for treatment of the prostate is 160Gy. The corresponding dose constraint is to deliver between 160Gy and 180Gy to 90% of the volume of the gland. Maximum dose constraints are also specified for the anatomical structures at risks: urethra and rectum. At least 30% of the urethra volume must receive less than 240Gy (150% of the target dose); a dose greater to 160Gy must not be delivered to more than 1.3cc of the rectum. Finally 90% of the rectum volume must receive less than 80Gy.

One common way to represent dose distribution is the so-called Dose Volume Histogram (DVH). The x coordinate represents a dose (percentage of total dose or absolute value in Gy) and the y coordinate denotes a volume (percentage of total volume or absolute value in cc). A point (x,y) on the curve associated to an organ or to an anatomical structure means for instance: y% of the organ volume receives at least x Gy. The constraints listed in the previous paragraph can be summarized in figure 3. D90 is the maximum dose received by 90% of the organ.

Proposed evaluation protocol

At this stage of the study the patient is treated in the conventional way. During the conventional procedure, data are collected and stored in the DICOM-RT format including US images, segmented contours and treatment plan. After patient treatment, those data are postprocessed. MRI data are fused to TRUS information and segmented MRI contours are mapped onto TRUS images using the computed transfer function f. This gives a new set of contours in the US images; the dosimetric plan is evaluated for those two volumes: the US volume and the MRI+US volume.

Up to now 8 patients have been included in this protocol which has been approved by the hospital ethical committee; we plan to include a total of 16 patients. Different parameters have been examined and compared:

-prostate volumes, -percentage of prostate volumes in the 140, 160 and 180Gy isodoses, -values of D90 in the prostate.

Results

Table 2 presents the prostate volume analysis with and without data fusion for the 8 patients.

As can be seen the MRI+US volume is greater than the US volume for 6 of the 8 patients. Most volume differences are in the apex and base regions of the prostate for which TRUS images are often difficult to interpret. For 3 of those 6 patients, the increase of volume exceeds 10% of the initial US volume. Since the number of patients is rather small, a non parametric test has been selected. A Wilcoxon test has been applied to those paired measurements which demonstrates that the two series of measurements are significantly different (p=0.05). The "isodose 160" encloses the volume of the prostate that receives at least 160Gy, the target dose. Table 3 presents the "isodose 160" analysis with and without data fusion. As can be seen, the MRI+US "isodose 160" includes less prostate volume for 7 of the 8 patients. However, all cases still verify the constraint of having 90% of the prostate receiving more than 160Gy. Patient 5 comes close to this inferior limit of the dose. A Wilcoxon test has been also applied to those paired measurements demonstrating that the two series of measurements are significantly different (p=0.05). As expected those dose modifications are correlated to volume ones (Spearman coefficient: 0.904 greater than Spearman threshold=0.88 for n=8, alpha risk=0.01); this is quite visible on figure 4.

Fig. 4. Correlation between volume difference (x) and dose difference (y)

D90 is the maximum dose received by 90% of the prostate. As mentioned below, this dose must be more than 160Gy and less than 180Gy. Table 4 presents a comparison of estimates of the D90 (since the exact value of D90 is difficult to get) with and without data fusion. The exact volume corresponding to the dose is mentioned near the dose value. As can be seen, the MRI+US D90 is smaller for 7 of the 8 patients. However, all cases still verify the constraints of having 160Gy<D90<180Gy. Patient 5 comes close to this inferior limit of the dose. A test of Wilcoxon has been applied to those paired measurements demonstrating that the two series of measurements are significantly different (p=0.05).

Discussion

Results presented below although still partial confirm the hypothesis that TRUS image delineation often underestimates prostate volume due to poor readability of apex and base slices and that it results in overestimating the dose delivered to the patient.

We observed that volume difference for those 8 patients was smaller than for the 11 patients having been included in the first evaluation. On average this volume difference was 15.86% for the 11 first patients instead of 6.79% for the 8 patients included in this work. Since the protocols were slightly different this does not allow a too direct comparison of numbers. Meanwhile, those differences may be explained partly by a side effect of this study having probably resulted in a learning curve associated to prostate TRUS delineation; indeed when the work on MRI/TRUS fusion began, the implantation team (urologist, radiation oncologist and radiophysicist) had still a rather low experience of prostate brachytherapy -implantations began in July 2001. We suppose that post-processing of data and comparison of US data to MRI ones increased the level of knowledge of the urologist who delineates the prostate on the TRUS images.

From the dosimetry point of view experiments confirm that the almost systematic underestimation of prostate volume results in a significant decrease of dose delivered to the prostate. However, prostate dose constraints are still verified on MRI+US contours for those 8 patients. This has to be confirmed on a larger number of patients since some preliminary evaluation exhibited cases where the D90 was substantially lower than expected (see [START_REF] Reynier | MRI/TRUS data fusion for prostate brachytherapy[END_REF]). This has also to be confirmed on organs at risk but this requires software modification which is in progress.

The overestimation of delivered dose has probably a limited effect in terms of treatment quality and therapeutic effects. Nevertheless the implantation team is very enthusiastic about using this system since they expect an improved comfort for image processing and an increased confidence in the planning.

One can see on figure 7 another use of the system where isodoses corresponding to planning from the TRUS images are mapped to the MRI data. The visual validation of those isodoses from MRI data is apparently much easier than the direct evaluation from TRUS images since anatomical substructures are more visible on MRI than on TRUS data. This point has not yet been tested extensively but clinicians and physicists reacted very positively to such a possibility. One prospective development of this project could be to perform the planning directly on MRI data and to transfer this planning to the OR thanks to MRI/TRUS data fusion.

Conclusion

We have presented on-going work concerning the impact of data fusion on dose distribution for prostate brachytherapy. Dose is systematically overestimated due to underestimation of the TRUS prostate volume although the treatment still verifies dose constraints on the prostate for the 8 patients already included in this trial. Clinically using MRI/TRUS data fusion would result in a more reliable delineation of the prostate making real dose delivered to the prostate certainly closer to the planned dose. Further work remains concerning the evaluation of dose distribution on urethra and rectum. However, obtained results are already encouraging. From those preliminary results it is likely that MRI/TRUS data fusion could facilitate treatment planning and improve quality assessment.

Fig. 1 :

 1 Fig. 1: US-guided transperineal brachytherapy operating principles. From http://www.uropage.com/index.htm

Fig. 3 .

 3 Fig. 3. Dose Volume Histogram and treatment constraints

Figure 5

 5 Figure 5 presents the comparative DVH of patient number 7.

Fig. 5 .

 5 Fig.5. Comparative DVH for patient number 7

Fig. 6 .

 6 Fig. 6. Visualisation of MRI+US and US contours plus isodoses on apex (left; middle) and base (right) TRUS images.

Fig. 7 .

 7 Fig. 7. Dose visual assessment (left) from TRUS image (middle and right) from MRI axial and sagital views after MRI/TRUS data fusion. For middle and right views: orange=150Gy isodose; blue=180Gy isodose; red=240Gy isodose.

Table 2 :

 2 Prostate volume analysis

Table 3 :

 3 "Isodose 160" analysis

Table 4 :

 4 D90 analysis

Table 1 :

 1 Accuracy evaluation of elastic registration (see[START_REF] Reynier | MRI/TRUS data fusion for prostate brachytherapy[END_REF] for more details).

	TRE (mm)

Table 2 :

 2 Prostate volume analysis

	Patient	US "isodose 160"	MRI+US	Diff = MRI+US	100 Diff / US
	number	(% of prostate	"isodose 160"	isodose -US	isodose (%)
		volume)	(%)	isodose (%)
	1	96,67	96,76	0,09	0,09
	2	98,08	93,7	-4,38	-4,46
	3	98	91,34	-6,66	-6,79
	4	98,39	95,49	-2,9	-2,94
	5	97,41	90,5	-6,91	-7,09
	6	99,43	93,18	-6,25	-6,28
	7	97,82	92,41	-5,41	-5,53
	8	98,63	97,49	-1,14	-1,15
	Mean value	98,05	93,85	-4,19	-4,27
	Stand. dev.	0,82	2,52	2,63	2,68

Table 3 :

 3 "Isodose 160" analysis

	Patient	US D90 (vol)	MRI+US D90 (vol)	Diff = MRI+US	100 Diff / US
	number	(Gy (%))	(Gy (%))	D90 -US D90	D90 (%)
				(Gy)
	1	175 (89,58)	175 (90,09)	0	0
	2	175 (89,32)	165 (92,25)	10	5,71
	3	175 (88,44)	165 (89,89)	10	5,71
	4	179,2 (90,4)	172,8 (90,44)	6,4	3,57
	5	172,8 (90,71)	160 (90,5)	12,8	7,40
	6	174,4 (90,33)	166,4 (90,45)	8	4,58
	7	174,4 (90,81)	164,8 (90,27)	9,6	5,50
	8	174,4 (90,24)	172,8 (90,07)	1,6	0,91
	Mean value	175,02 (89,97)	167,72 (90,49)	7,3	4,17
	Stand. dev.	1,83 (0,8)	5,19 (0,74)	4,42	2,55

Table 4 :

 4 D90 analysis

Acknowledgments

This work is supported by the French Ministry of Health (Projet Hospitalier de Recherche Clinique PHRC National 2003 Prostate-Echo).