St Phane Chevaliez

Jean-Michel Pawlotsky
email: michel.pawlotsky@hmn.aphp.fr

Diagnosis and management of chronic viral hepatitis: antigens, antibodies and viral genomes

Keywords: Antiviral Agents, therapeutic use, Disease Progression, Genome, Viral, Hepacivirus, genetics, Hepatitis B Antibodies, blood, Hepatitis B Antigens, blood, Hepatitis B virus, genetics, Hepatitis B, Chronic, blood, diagnosis, drug therapy, genetics, Hepatitis C Antibodies, blood, Hepatitis C Antigens, blood, Hepatitis C, Chronic, blood, diagnosis, drug therapy, genetics, Humans, Prognosis, RNA, Viral, blood

Approximately 500 million people, i.e. one fifth of the world population, are chronically infected with hepatitis B virus (HBV) or hepatitis C virus (HCV) , . Each year, over 1,5 million people die from HBV-and/or HCV-related chronic liver diseases, such as 1 2

end-stage cirrhosis and hepatocellular carcinoma (HCC). HCC is one of the most common cancers worldwide and in 2002, HBV and HCV have been responsible for at least half a million of these cancers . 3

HBV belongs to the family, genus . HBV is the smallest human enveloped DNA virus, with a Hepadnaviridae Orthohepadnavirus genome of approximately 3,200 base pairs. The partially double-stranded circular DNA genome encodes at least four overlapping open reading frames, including the surface (preS/S), precore/core (preC/C), polymerase (P) and X genes . HBV strains are classified into 8 4 genotypes (A to H) based-on an 8 or more DNA sequence difference over the full genome , . The different HBV genotypes have

% 5 6
distinct geographical distributions and appear to bear different biological properties that may affect the clinical outcome of HBV-related disease . 7 -14

HCV belongs to the family, genus . HCV is an enveloped RNA virus, with a genome of approximately 9,500 Flaviviridae Hepacivirus nucleotides. The single positive-strand RNA genome contains a major open reading frame that encodes a large polyprotein of approximately 3,000 amino acids. The polyprotein co-and post-translational processing yields a number of structural and non-structural proteins . HCV strains are classified into 6 major genotypes, and a seventh one has been recently identified , . The HCV 15 16 17 genotypes also have distinct geographical distributions and the genotype is an essential prognosis marker of the likelihood of HCV eradication during antiviral treatment . 18

Virological tools are needed to diagnose chronic HBV and HCV infections, they may be useful to establish their prognosis, but they have found their principal application in guiding treatment decisions and assessing the virological responses to therapy.

VIROLOGICAL TOOLS

The virological diagnosis and monitoring of HBV and HCV infections is based on the use of a variety of virological markers (Table 1 ). Six HBV markers are used in clinical practice, including HBs antigen (HBsAg), anti-HBs antibodies, HBe antigen (HBeAg), anti-HBe antibodies, anti-HBc antibodies (including total anti-HBc antibodies and anti-HBc IgM) and HBV DNA. Three HCV markers are useful in clinical practice, including total anti-HCV antibodies, HCV genotype and HCV RNA.

Viral antigens and antibodies

Principles of viral antigen and antibody detection and quantification

The detection (and eventually the quantification) of viral antigens and of specific antibodies in body fluids is based on the use of sandwich enzyme immunoassays (EIAs). Recombinant antigens or antibodies are used to capture circulating antibodies or antigens, respectively, onto the wells of microtiter plates, microbeads or specific holders adapted to close automated devices. The presence of antigens or antibodies is revealed by antibodies (in the case of antigen) or anti-antibodies (in the case of antibody) labeled with an enzyme that catalyzes the transformation of a substrate into a colored compound. The optical density (OD) ratio of the reaction (sample OD/internal control OD) is proportional to the amount of antigens or antibodies in the sample. EIAs are cheap, easy to use, can be fully automated and are well adapted to large volume testing.

HBV serological markers

Hepatitis B surface antigen (HBsAg)

Hepatitis B surface antigen is bore by three distinct viral proteins encoded by the pre-S/S gene: the major (or small) surface protein encoded by the S gene, the most abundantly produced surface protein; the middle surface protein, encoded by the preS2 S gene; and the + large surface protein, encoded by the preS1 preS2 S gene. HBsAg is present in great excess in the blood of HBV-infected patients,

+ + 2 13
essentially associated with noninfectious particles including spherical particles and tubular ones (approximately 10 particles per 13 milliliter) . 19

HBsAg is detected early during acute infection, on average 6 to 10 weeks after exposure and several weeks before the onset of clinical and biological symptoms (

). The analytical sensitivity of the available commercial HBsAg EIAs has been improved recently. Figure 1A Indeed, current HBsAg detection assays detect at least 0.15 nanograms (ng) per milliliter (mL) of circulating HBsAg, i.e. approximately 350 international units (IU) per mL . This improvement has reduced the window period , i.e. the post-exposure period during which 20

" "
HBsAg is undetectable, to up to 9 days . In addition, the ability of HBsAg assays to detect HBV variants bearing nucleotide 20 substitutions in the S gene leading to modifications of the tri-dimensional structure of HBsAg has been improved compared to the previous generations of tests . The specificity of current HBsAg detection assays is of more than 99.5 . False-positive results can be 21 -23 % exceptionally observed in pregnant women, autoimmune diseases, and chronic liver diseases of other causes . They can also 23 -25 sometimes be observed in heparinized, hemolyzed (hemoglobin above 1.4 g/dL) or icteric (bilirubin above 52.8 mol) blood specimens μ

24

. In practice, it is recommended that the first detection of HBsAg be confirmed by neutralization in order to eliminate a false-positive result.

Evolution of acute hepatitis B towards chronic HBV carriage is defined by HBsAg persistence for more than 6 months . Under 26 certain circumstances, HBsAg may not be detectable during chronic hepatitis B: (i) in low-replication asymptomatic HBV carriers; (ii) in the case of HBV variants bearing nucleotide substitutions in the S gene leading to the synthesis of an HBsAg that is not recognized by commercial assays , ; (iii) when infection resolves spontaneously or after successful antiviral therapy in chronic HBV-infected 27 28 patients who may subsequently achieve an HBs seroconversion; (iv) in hepatitis delta HBV-co-infected patients, where hepatitis delta virus most often inhibits HBV replication and expression , . 27 29 HBsAg quantification can now be performed by means of a fully automated chemiluminescent microparticle immunoassay. HBsAg quantification is easy, cheap and may provide a mean to establish the prognosis of antiviral therapy in the future. HBsAg quantification indeed appears to be a surrogate marker of the amount of covalently closed circular DNA (cccDNA), the persistent intrahepatic form of HBV DNA, in the hepatocytes and a predictor of a sustained virological response to antiviral treatment off therapy. During antiviral therapy, HBsAg decrease is a predictor of subsequent HBsAg clearance, the principal goal of antiviral treatment, which may be subsequently followed by an HBs seroconversion characterized by the appearance of anti-HBs antibodies . 30 -32

The estimated annual incidence of spontaneous HBsAg clearance from serum in chronically infected patients is 1 to 2 in % %

Caucasians

. It may be lower (0.1 to 0.8 ) in high endemicity areas where infection is usually acquired perinatally or in the early 33

% % childhood . 34 -36

Anti-hepatitis B surface (anti-HBs) antibodies

The presence of anti-HBs antibodies (in the presence of anti-HBc antibodies) witnesses the recovery of chronic HBV infection and life-long immunity against HBV. The anti-HBs titer often varies over time, and anti-HBs antibodies may become undetectable several years after the acute episode. The assessment of anti-HBs antibody levels by different assays is not accurate and consistent, yielding incomparable quantitative results in spite of the calibration with international standards . 37 After vaccination against HBV, isolated anti-HBs antibodies must be present at a titer of more than 10 mIU/mL to confer efficient protection.

Anti-hepatitis B core (anti-HBc) antibodies

Anti-hepatitis B core antibodies are detected early during HBV infection (

). Two isotypes of anti-HBc antibodies can be Figure 1A detected, including: anti-HBc IgM, a marker of acute infection that can be also detected at low levels during the immune elimination phase of chronic hepatitis B and during exacerbations in inactive carriers; anti-HBc IgG which rise in parallel to HBsAg at the acute phase of infection and persist for life-long whatever the outcome of HBV infection (

). Table 1 In contrast to anti-HBs antibodies, anti-HBc IgG are not neutralizing . False-negative detection of anti-HBc antibodies may in vivo rarely occur in immunosuppressed patients. A rare HBV variant harboring an in-frame deletion of the core gene defective for HBc antigen synthesis, named HBV-2, has been reported not to elicit a detectable immune response to HBc antigen in immunocompetent patients. We recently reported the case of an organ donor with low-level HBV DNA (3.0 Log IU/mL) lacking both HBsAg and anti-HBc antibodies; 10 several substitutions in both the HBsAg and HBc antigen sequences were found in this donor .

Hepatitis B e antigen (HBeAg) and anti-HBe antibodies

The HBe protein, which bears the HBe antigen, is a nonstructural HBV protein encoded by the preC/C gene. It is secreted by infected cells under various soluble forms that vary in size between 16 and 20 kDa. The HBe protein contains two epitopes: e1, conformational, and e2, linear. The e1 epitope sequence overlaps that of the conformational HBc epitope, so that e1 is presented at the surface of HBV nucleocapsids and expressed, together with HBc, at the surface of infected cells. Although HBe protein secretion does not appear to be essential for HBV lifecycle, its presence is associated with immune tolerance, high-level HBV replication and high transmissibility.

During acute infection, HBeAg can be detected on average 6 to 12 weeks after exposure (

). HBeAg clearance is generally Figure 1A associated with a decrease of viremia and an aminotransferase flare. It is followed by the appearance of anti-HBe antibodies during the HBe seroconversion phase. Persistence of HBeAg is generally observed in the patients who develop chronic infection.

In chronic HBV infection, two phenotypes can be observed, including HBeAg-positive and HBeAg-negative chronic hepatitis B. In HBeAg-positive chronic hepatitis B, the preC/C gene has a wild-type sequence, no anti-HBe antibodies are found, and the presence of HBeAg in peripheral blood is generally associated with a high HBV DNA level. In HBeAg-negative chronic hepatitis B, the patients are infected with a variant virus, bearing nucleotide substitutions in the precore region and/or in the basal core promoter region of the preC/C gene. The most frequent nucleotide substitution occurs at position 1896 (G1896A) in the precore region of the preC/C gene. It inserts a stop codon in the precore sequence that prevents the HBe protein from being synthesized. The second group of nucleotide polymorphisms is located within the core promoter region. The most frequent changes are at positions 1762 (A1762T) and 1764 (G1764A). They down-regulate HBe protein production up to 70 . Other mutations susceptible to alter HBe protein production have also been described

% 33 ,
. Different variants bearing precore and/or basal core promoter mutations can be observed in the same patient in variable proportions. 39

Although a few cases of infection with HBeAg-negative viruses have been described in the literature, HBeAg-negative variants de novo are generally selected during the immune clearance of chronic HBV infection. An important outcome of the immunoelimination phase is indeed seroconversion from HBeAg to anti-HBe, characterized by the clearance of HBeAg followed by the appearance of anti-HBe antibodies. The seroconversion phase may result in an HBeAg-negative chronic hepatitis B or in an inactive carrier state characterized by normal aminotransferase levels and undetectable or low-level (< 2 000 IU/mL) HBV DNA. The estimated annual incidence of spontaneous HBeAg seroclearence in chronically infected patients is 5 to 15 , .

% % 40 41

HCV serological markers Total anti-HCV antibodies

The serological window, characterized by detectable HCV RNA and core antigen in the absence of anti-HCV antibodies, has been estimated to be of approximately 60 days on average . Anti-HCV antibodies appear on average 2 to 8 weeks after the acute phase of 42 infection and persist for life in patients who develop chronic HCV infection (

). The presence of both anti-HCV antibodies and Figure 1B HCV RNA does not allow to distinguish acute hepatitis C from an acute exacerbation of chronic hepatitis C or an acute hepatitis of another cause in a patient with chronic hepatitis C. The anti-HCV IgG avidity index within the first 8 days following the onset of clinical symptoms may be useful in identifying actual acute HCV infection cases . [START_REF] Coppola | Anti-HCV IgG avidity index in acute hepatitis C[END_REF] The significance of the presence of anti-HCV IgM during HCV infection is unclear. Anti-HCV IgM have been reported in 50 to 93 % % of patients with acute hepatitis C and 50 to 70 of patients with chronic hepatitis C . Therefore, anti-HCV IgM cannot be used as

% % 44 -46
a reliable marker of acute HCV infection, and IgM assays have not be used in clinical practice. However, the serial measurements of the anti-HCV IgM titers based on at least three determinations from the fifth to the fifteenth day from the onset of the symptoms may identify patients with acute hepatitis C . 47

Serological determination of HCV genotype

The HCV genotype can be determined by means of a competitive ELISA assay using genotype-specific antigens . This assay 48 allows to identify the 6 HCV genotypes (1 to 6) but not the subtype.

Viral genome

Genome detection and quantification

Principles of genome detection and quantification

Viral genome detection and quantification can be achieved by using two categories of molecular biology-based techniques, including target amplification (such as (PCR)) and signal amplification (such as hybrid capture or the branched DNA polymerase chain reaction assay). Whatever technique used, HBV DNA and HCV RNA international units per milliliter must be preferred to any other quantitative unit and should now be implemented in all commercial quantitative assays. Conversion factors can be used to establish a relationship between the IUs and the non standardized copies , . The classical techniques for viral genome detection and quantification are now 49 50 progressively being replaced by real-time PCR assays in most virology laboratories (

). Table 2 Real-time PCR techniques have a broad dynamic range of quantification, well suited to the clinical needs (upper range of quantification: 7 to 8 Log IU/mL). Real-time PCR is more sensitive than classical PCR, with lower limits of detection of the order of 10 10 to 15 IU/mL for both HBV DNA and HCV RNA. Real-time PCR assays do not yield false-positive results due to carryover contaminations, and they can be fully automated. Real-time PCR has become the technique of choice to detect and quantify viral genomes in clinical practice. Several real-time PCR assays are now commercially available for the detection and quantification of both HBV DNA and HCV RNA ( ). Table 2 HBV DNA detection and quantification HBV DNA detection and quantification is useful in clinical practice to: (i) to diagnose chronic hepatitis B with viral replication; (ii) establish the prognosis of liver disease and assess the risk of progression towards cirrhosis and hepatocellular carcinoma ; (iii) identify 51 patients who need antiviral therapy and offer them the most adapted treatment; (iv) monitor the virological response to therapy and identify amino acid substitutions responsible for resistance to nucleos(t)ide analogues.

The presence of HBV DNA in peripheral blood is a reliable marker of HBV replication. HBV DNA is detectable within a few days after infection. It generally increases to reach a peak at the time of acute hepatitis, and then progressively decreases and disappears when the infection resolves spontaneously . In the patients progressing towards chronic HBsAg carriage, chronic infection evolves through 52 successive phases. HBV DNA levels are not stable over time and depend on the infection phase: the immunotolerance phase is ). These assays have been shown to accurately quantify HBV DNA levels in clinical practice , . Table 2 53 54

HCV RNA detection and quantification

HCV RNA detection and quantification is useful in clinical practice to: (i) diagnose chronic HCV infection; (ii) identify patients who need antiviral therapy; (iii) monitor the virological responses to antiviral therapy, and (iv) in the future, identify amino acid substitutions responsible for resistance to specific inhibitors of HCV viral proteins . 50

The presence of HCV RNA in peripheral blood is a reliable marker of HCV replication. HCV RNA can be detected 1 to 3 weeks after infection, approximately 1 month before the appearance of total anti-HCV antibodies. The presence of HCV RNA after 6 months signs chronic HCV infection. HCV RNA levels remain relatively stable over time in chronically infected patients.

HCV RNA assays based on real time PCR are now used in clinical virology laboratories for RNA detection and quantification. Two 2 ). The intrinsic performances of available tests differ. Indeed, approximately 15 of HCV genotype 2 and 30 of HCV genotype 4 % % samples are substantially underestimated in the CAP-CTM, most likely because of nucleotide mismatches, whereas this problem has not been found with the Abbott assay , . [START_REF] Chevaliez | Overestimation and underestimation of hepatitis C virus RNA levels in a widely used real-time polymerase chain reaction-based method[END_REF] 56

Analysis of the nucleotide sequence of the viral genome

Principles of nucleotide sequence analysis

Viral genome sequence analysis is generally based on direct sequencing (so-called population sequencing) that provides the full sequence of the analyzed fragment, or reverse hybridization that identifies specific nucleotides or motifs at given positions. In practice, signature sequences are used: (i) to classify viral strains into phylogenetic groups of clinical interest, such as the 8 HBV genotype (A to H) or the 6 HCV genotypes (1 to 6); (ii) to identify nucleotide substitutions of the precore and basal core promoter regions of the preC/C gene; (iii) to identify amino acid substitutions known to confer viral resistance to specific antiviral inhibitors.

Genotype determination

The reference method for viral genotype determination is phylogenetic analysis of sequences generated after PCR amplification of a portion of the viral genome relative to reference sequences. Commercial assays have been developed. The Trugene HBV Genotyping Kit The utility of HBV genotype determination in clinical practice is debated. The positive and negative predictive values of the HBV genotype on disease progression and treatment outcomes have not been determined at the individual patient level, and further large clinical studies are warranted before implementing HBV genotype determination in practice . In contrast, HCV genotype determination is 63 mandated before the initiation of therapy with pegylated interferon alpha and ribavirin because it is the best predictor of treatment response and it determines the dose of ribavirin and treatment duration . 18

Identification of amino acid substitutions associated with viral resistance

Direct sequence analysis and reverse hybridization methods are used to identify amino acid substitutions known to confer resistance to antiviral drugs before the viral level increases. At present, early detection of HBV substitutions conferring resistance to nucleos(t)ide analogues is used to alter therapy in order to avoid rebound and hepatitis flare.

PRACTICAL USE OF VIROLOGICAL TOOLS IN THE MANAGEMENT OF CHRONIC HEPATITIS B

Serological and molecular HBV markers are used in clinical practice to diagnose chronic HBV infection, assess the prognosis of the disease, guide therapy and monitor treatment responses.

Diagnosis of chronic HBV infection

The persistence of HBsAg for more than 6 months defines chronic HBV carriage. In a chronic HBV carrier, chronic hepatitis B is defined by an elevated serum HBV DNA (generally > 2 10 to 2 10 IU/mL), with persistent or intermittent elevation of

× 3 × 4
aminotransferase levels and signs of chronic hepatitis B on liver biopsy . In a chronic HBV carrier, the HBV DNA level should be 67 -70 systematically measured by means of a sensitive and accurate method. Real-time PCR assays should be preferred and the results must be expressed in international units per milliliter . The HBV DNA level is indeed a key determinant of liver disease progression towards 26 cirrhosis or HCC , . HBV DNA level measurement is also crucial for therapeutic decision-making. 51 71 shows the kinetics of HBV markers during chronic HBV infection. HBsAg and total anti-HBc antibodies are always Figure 1A present. The presence of HBeAg (in the absence of anti-HBe antibodies) is generally associated with high-level viral replication and high transmissibility. HBV replication levels are substantially lower on average in HBeAg-negative patients. Inactive HBV carriers have a low level of viral replication (< 2 10 IU/mL), normal aminotransferase levels, no HBeAg and positive anti-HBe antibodies.

Assessment of disease severity and prognosis

The HBV DNA level and aminotransferase activity provide valuable prognostic information. The REVEAL study, which included more than 3,000 Taiwanese patients with chronic HBV infection, showed that an HBV DNA level higher than 4.3 Log (i.e. 2 10 10 × 4 IU/mL) was associated with a significant risk of progression of chronic hepatitis B to cirrhosis and HCC, independently of the HBeAg serostatus and level of aminotransferase activity , . In addition, the risk of HCC is significantly related to the level of HBV 51 71 replication and starts raising above 2 10 IU/mL . The risk of HCC is low in the absence of detectable HBV DNA, except in patients

× 3 72
with cirrhosis.

Treatment of HBV infection

The goal of chronic hepatitis B therapy is to prevent progression of liver disease to its life-threatening complications, cirrhosis and HCC. This can be achieved if HBV replication is durably abolished or significantly reduced. In HBeAg-positive patients, HBeAg clearance followed by the HBe seroconversion phase can be achieved in some cases with short-term therapy and ensures long-term control of viral replication. In HBeAg-negative patients, long-term antiviral suppression of viral replication is needed in most cases. The loss of HBsAg, eventually associated with an HBs seroconversion, is the most desirable endpoint of therapy but is rarely achieved.

Decision to treat

The decision to treat chronic hepatitis B is based on the assessment of multiple parameters including clinical, biological and histologic parameters. Antiviral treatment is currently recommended in patients with an HBV DNA titer above 2,000 IU/mL, elevated serum alanine aminotransferase activity (above the upper limit of normal), and/or evidence of chronic hepatitis with or without cirrhosis. Antiviral treatment should be considered in patients with a low level of viral replication who show mild to moderate necro-inflammatory activity and/or fibrosis. In HBV-infected patients with normal aminotransferase activity and an HBV DNA level below 2,000 IU/mL, repeated HBV DNA and ALT determinations are recommended every 3 to 6 months.

Selection of optimal therapy

The current treatment of chronic hepatitis B is based on the use of two categories of antiviral compounds: pegylated interferon alpha and nucleos(t)ide analogues that inhibit the reverse transcriptase domain of viral polymerase. Five nucleos(t)ide analogues are approved in Europe or in US for the treatment of chronic hepatitis B, including lamivudine, adefovir dipivoxil, entecavir, telbivudine and tenofovir disoproxil fumarate.

In HBeAg-positive patients, first-line treatment with pegylated interferon alpha is recommended if aminotransferase levels are elevated and the HBV DNA level is moderate (below 2 10 IU/mL). Although HBV genotypes A and B globally appear to better respond Most of the other patients, whatever the HBe serostatus, and in HBeAg-positive patients who did not achieve an HBe seroconversion during or after interferon alpha therapy, the use of nucleos(t)ide analogues is recommended. Entecavir or tenofovir must be preferred as first-line treatment because they both potently inhibit HBV replication and they have a high genetic barrier to resistance. Combinations of nucleos(t)ide analogues with no cross-resistance increases the genetic barrier to resistance and thus better prevents resistance on the long-term than mono-or sequential therapy. De novo combinations can be used as first-line treatment in patients with high HBV DNA levels and are unlikely to reach undetectable HBV DNA on monotherapy.

Treatment monitoring

HBV treatment monitoring is based on HBV DNA quantifications and ALT determinations every 3 to 6 months, whatever the HBe serostatus and antiviral treatment . 63

HBeAg-positive patients, treatment efficacy is witness by the loss of HBeAg with may be followed by a seroconversion to anti-HBe antibodies. It is generally associated with a profound reduction of serum HBV DNA levels and normalization of aminotransferase activity.

Ideally in HBe seroconverters, HBV DNA should be undetectable with a sensitive real-time PCR assay (lower limit of detection of the order 10 to 15 IU/mL) and aminotransferase activity should be normal . If this is not the case, the patient may have switched from 73 HBeAg-positive to HBeAg-negative therapy and may need sustained therapeutic suppression of viral replication.

In HBeAg-positive patients with no HBe seroconversion and in HBeAg-negative patients, the goal of antiviral treatment is to achieve a profound and durable HBV DNA suppression. The HBV DNA level should be undetectable on treatment with a sensitive real-time PCR assay (lower limit of detection: 10 to 15 IU/mL) . If the HBV DNA level remains detectable after 48 weeks, a second antiviral 63 compound with no cross-resistance with the first one must be added in order to prevent subsequent resistance.

In the patients who have responded and have been compliant, resistance should be suspected if the HBV DNA level rises by more than 1 Log IU/mL above nadir in two consecutive samples taken one month part , . The identification of selected amino acid substitutions known to be associated with resistance to the administered drug(s) by means of molecular testing can help guide treatment adaptation. Consensus decisional algorithms will need to be established before systematic genotypic resistance testing can be recommended to adapt the treatment strategy to the resistance profile of the infecting viral strain.

Monitoring of untreated chronic HBV infections

Antiviral treatment is not recommended in patients with an HBV DNA level below 2,000 IU/mL and normal aminonotransferase activity . However, a regular monitoring should be performed. Aminotransferase activity should be assessed every month for the three 67 first months, and then every 6 12 months. In untreated patients, the severity of liver inflammation and fibrosis must be evaluated by means of a liver biopsy or non-invasive serological or ultrasound-based testing when persistent or intermittent elevation of aminotransferase levels has been observed. HBV DNA quantification every 6 months is useful to detect an increase in viral replication and eventually reconsider the treatment indication.

PRACTICAL USE OF VIROLOGICAL TOOLS IN THE MANAGEMENT OF CHRONIC HEPATITIS C

Serological and molecular markers are used in clinical practice to diagnose chronic hepatitis C, guide treatment decisions and monitor the antiviral efficacy of treatment.

Diagnosis of chronic HCV infection

The persistence of HCV RNA for more than 6 months defines chronic HCV infection. In patients with clinical and/or biological signs of chronic liver disease, chronic hepatitis C is diagnosed by the simultaneous presence of anti-HCV antibodies and HCV RNA. Detectable HCV replication in the absence of anti-HCV antibodies is exceptional with current anti-HCV enzyme immunoassays. It is almost exclusively observed in profoundly immunodepressed, hemodialysis or agamaglobulinemic subjects , . [START_REF] Lok | Antibody response to core, envelope and nonstructural hepatitis C virus antigens: comparison of immunocompetent and immunosuppressed patients[END_REF] 76

Treatment of HCV infection

The current standard treatment for chronic hepatitis C is the combination of pegylated interferon alpha-2a or -2b and ribavirin . The 77 efficacy endpoint of chronic hepatitis C treatment is the sustained virological response (SVR), defined by an undetectable HCV RNA in serum with a sensitive assay (lower limit of detection of 50 IU/mL or less) 24 weeks after the end of treatment.

Decision to treat and indication of treatment

The decision to treat chronic hepatitis C depends on multiple parameters including a precise assessment of the severity of liver disease, the presence of absolute or relative contra-indications to therapy, and the patient s willingness to be treated.

'

HCV genotype determination should be systematically determined before treatment, as it determines the indication, the duration of treatment, the dose of ribavirin, and the virological monitoring procedure ( ) . Genotypes 2-and 3-infected patients require 24 Figure 2 18 weeks of treatment and a low dose of ribavirin, i.e. 800 mg daily. In contrast, genotype 1-, 4-, 5-and 6-infected patients require 48 weeks of treatment and a high, body-weight based dose of ribavirin, i.e. 1000 to 1400 mg daily.

Treatment monitoring

Monitoring of HCV RNA levels is recommended to tailor treatment to the actual virological response. A sensitive assay with a brioad range of quantification should be used. A real-time PCR assay should ideally be used. In HCV genotype 1-infected patients, the HCV RNA level should be measured before therapy and 12 weeks after its initiation (

). The lack of a 12-week virological response (i.e. Figure 2 no change or an HCV RNA decrease of less than 2 Log at week 12) indicates that the patient has virtually no chance to achieve an SVR 10 and should stop treatment. In contrast, treatment must be continued when a 2 Log drop in HCV RNA level has been observed at week 12, 10 until week 48 if HCV RNA is undetectable, until week 72 if HCV RNA is still detectable at week 12 , . 28 78 Recent studies have suggested that the patients who achive a rapid virological response, defined by an undetectable HCV RNA (< 50 IU/mL) at week 4 of therapy, could benefit from shorter treatment duration, i.e. 24 weeks in patients infected with HCV genotypes 1, 4, 5 or 6 and 12 to 16 weeks in those infected with HCV genotypes 2 or 3 . . These results however need confirmation and new 79 -83 84 algorithms should be drawn to tailor treatment duration to the virological response at week 4 without loosing a chance of viral eradication.

The sustained virological response corresponds to a cure of infection in more than 99 of cases. In the mid-term future, triple % combination therapy with pegylated interferon alpha, ribavirin and a specific HCV inhibitor will likely become the standard treatment of chronic hepatitis C. The SVR will remain the endpoint of therapy. On-treatment monitoring and the corresponding decision algorithms will need to be established.

Monitoring of untreated chronic HCV infections

In patients with no indication or with contra-indications to therapy, the HCV RNA level has no prognostic value. The level of HCV replication does not correlate with the severity of liver disease, nor with the risk of liver disease progression to cirrhosis or HCC. Repeated aminotransferase level assessments are recommended. Assessment of liver inflammation and fibrosis by means of liver biopsy or Best Pract Res Clin Gastroenterol . Author manuscript Page / 8 13 non-invasive serological or ultrasound-based testing is needed in the case of persistent or intermittent elevatiosn of aminotransferase levels . 77

Figure 2

Algorithms for the use of HCV virologicals tools in the treatment of chronic hepatitis C, according to the HCV genotype.

Table 1

Virological markers for the diagnosis and management of chronic HBV and HCV infections

  characterized by high levels of viral replication; the immuno-elimination phase is characterized by generally lower, often fluctuating HBV DNA levels; the inactive carrier stage is characterized by very low or undetectable levels of viral replication, depending on the sensitivity of the assay; reactivation phases, that are facilitated by immunosuppressive therapies, are generally associated with high levels of replication. HBV DNA assays based on real-time PCR technology are now replacing the classical techniques in most virology laboratories. Three real-time PCR platforms are currently available for detection and quantification of HBV DNA: the Cobas Taqman platform, which can ® be used together with automated sample preparation with the Cobas AmpliPrep system (CAP-CTM, Roche Molecular System, ® Pleasanton, California), the Real-Art HBV PCR Assay (Artus-Biotech, Qiagen, Hamburg, Germany), and the Abbott platform (Abbott ® Diagnostic, Chicago Illinois), which uses the 2000 amplification platform together with the 2000 device for sample preparation ( m RT m SP

  Abbott platform (Abbott Diagnostic), which uses the 2000 amplification platform together with the 2000 device for sample m RT

®(

  Siemens Medical Solutions Diagnostics) can determine the HBV genotype after amplification of a region overlapping the open reading frame encoding the S and P genes. The Trugene 5 NC HCV Genotyping kit (Siemens Medical Solutions Diagnostics) has been developed ® ′ for HCV genotype determination by direct sequencing of a portion of the 5 non-coding region (NCR) of the viral genome. Direct sequence ′ analysis is the gold standard for genomic sequence analysis. However, it only identifies viral variants representing at least 20 to 25 of the % circulating viral populations. Reverse hybridization of PCR amplicons to membrane-bound probes is more sensitive than direct sequence analysis to detect minor variants representing as few as 5 the whole viral population . Line probe assays (INNO-LiPA, Innogenetics, Gent, Belgium) use a % 57 series of short immobilized oligonucleotide probes to discriminate among different PCR fragments. A commercial assays has been developed for HBV genotype determination (INNO-LiPA HBV Genotyping) . The most recent version of the line probe assay for HCV 58 genotype determination (VERSANT HCV Genotype 2.0 Assay, Siemens Medical Solutions Diagnostics) bears consistently improved ® accuracy for HCV genotype 1 subtype and HCV genotype 6 determination compared to the previous assays . 59 -62

  Commercial assays are available. The Trugene HBV ® Genotyping Kit (Siemens Medical Solutions Diagnotics) is based on direct sequence analysis of a portion of the reverse transcriptase domain of the HBV polymerase gene . A new generation of reverse hybridization assay, INNO-LiPA HBV DR v3, has been developed 64 in 2008 to detect amino acid substitutions associated with lamivudine, adefovir and entecavir resistance. Reverse hybridization methods have been shown to detect changes in viral quasispecies composition early, on average 6 months before direct sequencing analysis , . 65 66

× 3

 3

× 6 to

 6 interferon-based therapy than genotypes C and D, HBV genotype determination is not yet recommended to guide the therapeutic decision in the absence of strong individual predictive value.

10

 10

Table 2

 2 Commercially available real-time PCR assays for HBV DNA and HCV RNA detection and quantification

				Lower limit of
	Assay	Manufacturer	Method	detection	Dynamic range
	Hepatitis B virus
	Cobas Taqman HBV	Roche Molecular Systems, Pleasanton,	Real-time PCR on Cobas Taqman after automated extraction (Cobas	12 IU/mL	54 IU/mL -110 000 000 IU/mL
		California	Ampliprep)
	Real-Art HBV PCR	Qiagen, Hamburg, Germany	Real-time PCR after manual extraction	4 IU/mL	4 to 9 IU/mL -100 000 000
	assay				IU/mL
	Abbott Real-time HBV	Abbott Diagnostic, Chicago, Illinois	Real-time PCR on 2000 after automated extraction ( 2000 ) m RT m SP	10 IU/mL	10 UI/mL -1 000 000 000 IU/mL
	Hepatitis C virus
	Cobas Taqman HCV	Roche Molecular Systems, Pleasanton,	Real-time PCR on Cobas Taqman after automated extraction (Cobas	15 IU/mL	46 IU/mL -69 000 000 IU/mL
		California	Ampliprep)
	Abbott Real-time HCV	Abbott Diagnostic, Chicago, Illinois	Real-time PCR 2000 after automated extraction( 2000 ) m RT m SP	12 to 30 IU/mL	12 IU/mL -100 000 000 UI/mL

[START_REF] Livingston | Hepatitis B virus genotypes in Alaska Native people with hepatocellular carcinoma: preponderance of genotype F[END_REF]

[START_REF] Livingston | Hepatitis B virus genotypes in Alaska Native people with hepatocellular carcinoma: preponderance of genotype F[END_REF]

[START_REF] Livingston | Hepatitis B virus genotypes in Alaska Native people with hepatocellular carcinoma: preponderance of genotype F[END_REF]

[START_REF] Livingston | Hepatitis B virus genotypes in Alaska Native people with hepatocellular carcinoma: preponderance of genotype F[END_REF]

[START_REF] Livingston | Hepatitis B virus genotypes in Alaska Native people with hepatocellular carcinoma: preponderance of genotype F[END_REF]

[START_REF] Livingston | Hepatitis B virus genotypes in Alaska Native people with hepatocellular carcinoma: preponderance of genotype F[END_REF]

[START_REF] Livingston | Hepatitis B virus genotypes in Alaska Native people with hepatocellular carcinoma: preponderance of genotype F[END_REF]


Thomas Gilles
email: thomas.gilles@mines-paristech.fr

Stefano Sabatini
email: stefano.sabatini@huawei.com

Dzmitry Tsishkou
email: dzmitry.tsishkou@huawei.com

Bogdan Stanciulescu
email: bogdan.stanciulescu@mines-paristech.fr

Fabien Moutarde
email: fabien.moutarde@mines-paristech.fr

THOMAS: TRAJECTORY HEATMAP OUTPUT WITH LEARNED MULTI-AGENT SAMPLING

In this paper, we propose THOMAS, a joint multi-agent trajectory prediction framework allowing for an efficient and consistent prediction of multi-agent multimodal trajectories. We present a unified model architecture for simultaneous agent future heatmap estimation, in which we leverage hierarchical and sparse image generation for fast and memory-efficient inference. We propose a learnable trajectory recombination model that takes as input a set of predicted trajectories for each agent and outputs its consistent reordered recombination. This recombination module is able to realign the initially independent modalities so that they do no collide and are coherent with each other. We report our results on the Interaction multi-agent prediction challenge and rank 1 st on the online test leaderboard.

INTRODUCTION

Motion forecasting is an essential step in the pipeline of an autonomous driving vehicle, transforming perception data into future prediction which are then leveraged to plan the future moves of the autonomous cars. The self-driving stacks needs to predict the future trajectories for all the neighbor agents, in a fast and coherent way.

The interactivity between agents plays an important role for accurate trajectory prediction. Agents need to be aware of their neighbors in order to adapt their speed, yield right of way and merge in neighbor lanes. To do so, different interaction mechanisms have been developed, such as social pooling [START_REF] Alahi | Social lstm: Human trajectory prediction in crowded spaces[END_REF][START_REF] Lee | Desire: Distant future prediction in dynamic scenes with interacting agents[END_REF][START_REF] Deo | Convolutional social pooling for vehicle trajectory prediction[END_REF], graphs [START_REF] Salzmann | Trajectron++: Dynamically-feasible trajectory forecasting with heterogeneous data[END_REF][START_REF] Zeng | Lanercnn: Distributed representations for graph-centric motion forecasting[END_REF] or attention [START_REF] Mercat | Multi-head attention for multi-modal joint vehicle motion forecasting[END_REF][START_REF] Messaoud | Multi-head attention with joint agent-map representation for trajectory prediction in autonomous driving[END_REF][START_REF] Luo | Probabilistic multi-modal trajectory prediction with lane attention for autonomous vehicles[END_REF][START_REF] Gao | Vectornet: Encoding hd maps and agent dynamics from vectorized representation[END_REF][START_REF] Liang | Learning lane graph representations for motion forecasting[END_REF], benefiting from the progress of powerful transformer architectures [START_REF] Lingyun | End-to-end contextual perception and prediction with interaction transformer[END_REF][START_REF] Yuan | Agentformer: Agent-aware transformers for socio-temporal multi-agent forecasting[END_REF][START_REF] Girgis | Autobots: Latent variable sequential set transformers[END_REF][START_REF] Ngiam | Scene transformer: A unified multi-task model for behavior prediction and planning[END_REF] . These mechanisms allow agents to look at and share features with neighbors and to take them into account in their own predictions.

Multi-modality is another important aspect of the possible future trajectories. A car can indeed chose to turn right or left, or decide to realise a certain maneuver in various ways. Uncertainty modeled as variance of Gaussians is insufficient to model these multiple cases, as it can only represent a continuous spread and cannot show multiple discrete possibilities. Therefore, current state-of-the-art produces not one but K possible trajectories for each agent predicted, and most recent benchmarks [START_REF] Caesar | nuscenes: A multimodal dataset for autonomous driving[END_REF][START_REF] Chang | Argoverse: 3d tracking and forecasting with rich maps[END_REF][START_REF] Zhan | Interaction dataset: An international, adversarial and cooperative motion dataset in interactive driving scenarios with semantic maps[END_REF][START_REF] Ettinger | Large scale interactive motion forecasting for autonomous driving: The waymo open motion dataset[END_REF] include multimodality in their metrics, taking only the minimum error over a predicted set of K trajectories.

However, up until very recently and the opening of multi-agent joint interaction challenges [START_REF] Ettinger | Large scale interactive motion forecasting for autonomous driving: The waymo open motion dataset[END_REF][START_REF] Zhan | Interpret: Interactiondataset-based prediction challenge[END_REF], no motion forecasting prediction datasets were taking into account the coherence of modalities between different agents predicted at the same time. As a result, the most probable predicted modality of a given agent could crash with the most probable modality of another agent.

Our THOMAS model encodes the past trajectories of all the agents present in the scene, as well as the HD-Map lanelet graph, and then predicts for each agent a sparse heatmap representing the future probability distribution at a fixed timestep in the future, using hierarchical refinement for very efficient decoding. A deterministic sampling algorithm then iteratively selects the best K trajectory endpoints according to the heatmap for each agent, in order to represent a wide and diverse spectrum of modalities. Given this wide spectrum of endpoints, a recombination module takes care of addressing consistency in the scene among agents.

Our contributions are summarized as follow:

• We propose a hierarchical heatmap decoder allowing for unconstrained heatmap generation with optimized computational costs, enabling efficient simultaneous multi-agent prediction.

• We design a novel recombination model able to recombine the sampled endpoints to obtain scene-consistent trajectories across the agents.

RELATED WORK

Learning-based models have quickly overtaken physics-based methods for trajectory prediction for several reasons. First, the sequential nature of trajectories is a logical application for recurrent architectures [START_REF] Alahi | Social lstm: Human trajectory prediction in crowded spaces[END_REF][START_REF] Altché | An lstm network for highway trajectory prediction[END_REF][START_REF] Lee | Desire: Distant future prediction in dynamic scenes with interacting agents[END_REF][START_REF] Mercat | Multi-head attention for multi-modal joint vehicle motion forecasting[END_REF][START_REF] Khandelwal | What-if motion prediction for autonomous driving[END_REF]. Then, benefiting from the latest progresses in computer vision, convolutional layers can easily be applied to bird-view rasters of the map context [START_REF] Lee | Desire: Distant future prediction in dynamic scenes with interacting agents[END_REF][START_REF] Yichuan | Multiple futures prediction[END_REF][START_REF] Cui | Multimodal trajectory predictions for autonomous driving using deep convolutional networks[END_REF][START_REF] Hong | Rules of the road: Predicting driving behavior with a convolutional model of semantic interactions[END_REF][START_REF] Salzmann | Trajectron++: Dynamically-feasible trajectory forecasting with heterogeneous data[END_REF][START_REF] Chai | Multipath: Multiple probabilistic anchor trajectory hypotheses for behavior prediction[END_REF]Gilles et al., 2021b). A more compact representation closer to the trajectory space can encode surrounding HD-Maps (usually formalized as connected lanelets), using Graph Neural Networks [START_REF] Gao | Vectornet: Encoding hd maps and agent dynamics from vectorized representation[END_REF][START_REF] Liang | Learning lane graph representations for motion forecasting[END_REF][START_REF] Zeng | Lanercnn: Distributed representations for graph-centric motion forecasting[END_REF]Gilles et al., 2021a). Finally, some pointbased approaches [START_REF] Yuan | Agentformer: Agent-aware transformers for socio-temporal multi-agent forecasting[END_REF] can be applied in a broader way to trajectory prediction, as both lanes and trajectories can be considered as ordered set of points.

Multi-modality in prediction can be obtained through a multiple prediction head in the model [START_REF] Cui | Multimodal trajectory predictions for autonomous driving using deep convolutional networks[END_REF][START_REF] Liang | Learning lane graph representations for motion forecasting[END_REF][START_REF] Ngiam | Scene transformer: A unified multi-task model for behavior prediction and planning[END_REF][START_REF] Deo | Multimodal trajectory prediction conditioned on lane-graph traversals[END_REF]. However, some methods rather adopt a candidate-based approach where potential endpoints are obtained either from anchor trajectories through clustering [START_REF] Chai | Multipath: Multiple probabilistic anchor trajectory hypotheses for behavior prediction[END_REF][START_REF] Phan-Minh | Covernet: Multimodal behavior prediction using trajectory sets[END_REF] or from a model-based generator [START_REF] Song | Learning to predict vehicle trajectories with model-based planning[END_REF]. Other approaches use a broader set of candidates from the context graph [START_REF] Zhang | Map-adaptive goal-based trajectory prediction[END_REF][START_REF] Zhao | Tnt: Target-driven trajectory prediction[END_REF][START_REF] Zeng | Lanercnn: Distributed representations for graph-centric motion forecasting[END_REF][START_REF] Kim | Lapred: Lane-aware prediction of multi-modal future trajectories of dynamic agents[END_REF] or a dense grid around the target agent (Deo & Trivedi, 2020;[START_REF] Gu | Densetnt: End-to-end trajectory prediction from dense goal sets[END_REF]Gilles et al., 2021b;a). Another family of approaches use variational inference to generate diverse predictions through latent variables [START_REF] Lee | Desire: Distant future prediction in dynamic scenes with interacting agents[END_REF][START_REF] Rhinehart | R2p2: A reparameterized pushforward policy for diverse, precise generative path forecasting[END_REF][START_REF] Yichuan | Multiple futures prediction[END_REF][START_REF] Casas | Implicit latent variable model for scene-consistent motion forecasting[END_REF] or GAN [START_REF] Gupta | Social gan: Socially acceptable trajectories with generative adversarial networks[END_REF][START_REF] Rhinehart | R2p2: A reparameterized pushforward policy for diverse, precise generative path forecasting[END_REF][START_REF] Amir Sadeghian | Sophie: An attentive gan for predicting paths compliant to social and physical constraints[END_REF] but the sampling of these trajectories is stochastic and does not provide any probability value for each sample.

While very little work has directly tackled multi-agent prediction and evaluation so far, multiple methods hint at the ability to predict multiple agents at the same time [START_REF] Liang | Learning lane graph representations for motion forecasting[END_REF][START_REF] Ivanovic | Mats: An interpretable trajectory forecasting representation for planning and control[END_REF][START_REF] Zeng | Lanercnn: Distributed representations for graph-centric motion forecasting[END_REF] even if they then focus on a more single-agent oriented framework.

Other works [START_REF] Alahi | Social lstm: Human trajectory prediction in crowded spaces[END_REF][START_REF] Yichuan | Multiple futures prediction[END_REF][START_REF] Rhinehart | Precog: Prediction conditioned on goals in visual multi-agent settings[END_REF][START_REF] Girgis | Autobots: Latent variable sequential set transformers[END_REF]) use autoregressive roll-outs to condition the future step of an agent on the previous steps of all the other agents. SceneTransformer [START_REF] Ngiam | Scene transformer: A unified multi-task model for behavior prediction and planning[END_REF] repeats each agent features across possible modalities, and performs self-attention operations inside each modality before using a loss computed jointly among agents to train a model and evaluate on the WOMD dataset [START_REF] Ettinger | Large scale interactive motion forecasting for autonomous driving: The waymo open motion dataset[END_REF] interaction track. ILVM [START_REF] Casas | Implicit latent variable model for scene-consistent motion forecasting[END_REF] uses scene latent representations conditioned on all agents to generate scene-consistent samples, but its variational inference does not provide a confidence score for each modality, hence LookOut [START_REF] Cui | Lookout: Diverse multi-future prediction and planning for self-driving[END_REF] proposes a scenario scoring function and a diverse sampler to improve sample efficiency. AIR 2 [START_REF] Wu | Air 2 for interaction prediction. Waymo Open Dataset Challenges Reports[END_REF] extends Multipath [START_REF] Chai | Multipath: Multiple probabilistic anchor trajectory hypotheses for behavior prediction[END_REF] and produces a cross-distribution for two agents along all possible trajectory anchors, but it scales exponentially with the number of agents, making impractical for a real-time implementation that could encounter more than 10 agents at the same time.

The approach most related to this paper is GOHOME (Gilles et al., 2021a), which uses a similar graph encoder and then leverage lane rasters to generate a probability heatmap in a sparse manner. However, this lane-generated heatmap remains constrained to the drivable area and to fixed lanewidths. Another close approach is the one of DenseTNT [START_REF] Gu | Densetnt: End-to-end trajectory prediction from dense goal sets[END_REF], which also uses attention to a grid of points in order to obtain a dense prediction, but their grid also remains constrained to a

METHOD

Our goal is to predict the future T timesteps of A agents using their past history made of H timesteps and the HD-Map context. Similar to recent works [START_REF] Zhao | Tnt: Target-driven trajectory prediction[END_REF][START_REF] Zeng | Lanercnn: Distributed representations for graph-centric motion forecasting[END_REF][START_REF] Gu | Densetnt: End-to-end trajectory prediction from dense goal sets[END_REF], we will divide the problem into goal-based prediction followed by full trajectory reconstruction. Our prediction pipeline is displayed in Fig. 1. We first encode each agent trajectory and the HD-Map context graph into a common representation. We then decode a future probability heatmap for each agent in the scene, which we sample heuristically to maximize coverage. Finally, we recombine the sampled endpoints into scene-consistent modalities across agents and build the full trajectories for each agent.

Our pipeline shares the same graph encoder, sampling algorithm and full trajectory generation as GOHOME (Gilles et al., 2021a), but uses a novel efficient hierarchical heatmap process that enables to scale to simultaneous multi-agent prediction. Furthermore, we add a novel scene-consistency module that recombines the marginal outputs into a joint prediction.

MODEL BACKBONE

GRAPH ENCODER

We use the same encoder as the GOHOME model (Gilles et al., 2021a). The agent trajectories are encoded though T rajEncoder using a 1D CNN followed by a UGRU recurrent layer [START_REF] Rozenberg | Asymmetrical bi-rnn for pedestrian trajectory encoding[END_REF], and the HD-Map is encoded as a lanelet graph using a GNN GraphEncoder made of graph convolutions. We then run cross-attention Lanes2Agents to add context information to the agent features, followed by self-attention Agents2Agents to observe interaction between agents. The final result is an encoding F a for each agent, where history, context and interactions have been summarized. This encoding F a is used in the next decoder operations and is also stored to be potentially used in modality recombination described in Sec. 3.2. The resulting architecture of these encoding operations is illustrated in the first half of Fig. 2. Figure 3: Hierarchical iterative refinement of the grid probabilities. First, the full grid is evaluated at a very low resolution, then the highest cells are up-sampled and evaluated at a higher resolution, until final resolution is reached. We highlight in grey the restricted area considered for refinement at each step.

HIERARCHICAL GRID DECODER

Our aim here is to decode each agent encoding into a heatmap representing its future probability distribution at prediction horizon T . Since we create this heatmap for each agent in the scene, the decoding process has to be fast so that it can be applied to a great number of agents in parallel. We use hierarchical predictions at various levels of resolutions so that the decoder has the possibility of predicting over the full surroundings of the agent but learns to refine with more precision only in places where the agent will end up with high probability. This hierarchical process is illustrated in Fig. 3.

Starting from an initial full dense grid probability at low resolution R 0 × R 0 by pixels, we iteratively refine the resolution by a fixed factor f until we reach the desired final resolution R f inal × R f inal .

At each iteration i, we select only the N i highest ranking grid points from the previous iteration, and upsample only these points to the R i × R i = Ri-1 /f × Ri-1 /f. At each step, the grid points features are computed by a 2-layer MLP applied on the point coordinates, these features are then concatenated to the agent encoding and passed through a linear layer, and finally enriched by a 2layer cross-attention on the graph lane features, before applying a linear layer with sigmoid to get the probability.

For a given W output range, this hierarchical process allows the model to only operate on

W /R0 × W /R0 + i N i × f 2 grid points instead of the W /R f inal × W /R f inal available.
In practice, for a final output range of 192 meters with desired R f inal = 0.5m resolution, we start with an initial resolution of R 0 = 8m and use two iterations of (N 1 , N 2 ) = (16, 64) points each and an upscaling factor f = 4. This way, we compute only 1856 grid points from the 147 456 available, with no performance loss.

The heatmap is trained on each resolution level using as pixel-wise focal loss as in Gilles et al. (2021b), detailed in Appendix A.3, with the ground truth being a Gaussian centered at the target agent future position.

FULL TRAJECTORY GENERATION

Having a heatmap as output grants us the good property of letting us decide to privilege coverage in order to give a wide spectrum of candidates to the scene recombination process. From each heatmap, we therefore decode K end points using the same MissRate optimization algorithm as Gilles et al. (2021b). We then generate the full trajectories for each end point using also the same model, a fully-connected MLP. The MLP takes the car history and predicted endpoint as input and produces T 2D-coordinates representing the full future trajectory. At training time, this model is trained using ground-truth endpoints. The difficulty in multimodal multi-agent prediction resides in having coherent modalities between each agent. Since the modalities are considered scene-wise, each agent's most probable modality has to match with the most probable prediction of the other agents, and so on. Moreover, these modalities must not collide with each other, as they should represent realistic scenarios.

… 𝑝 1 1 𝑝 𝑙 1 𝑝 1 𝑎 𝑝 𝑙 𝑎 Linear recombination L x D A x K x D L x A x 2 L x A x K 𝑐 𝑙 𝑘,𝑎 A x K x D
Initially, the prediction output of the model can be defined as marginal, as all A agents have been predicted and sampled independently in order to get K possible endpoint each. Our goal is to output a set of scene predictions J = (L, A) from the marginal prediction M = (A, K), where each scene modality l belonging to J is an association of endpoints p a l for each agent a. To achieve this, our main hypothesis lays in the fact that good trajectory proposals are already present in the marginal predictions, but they need to be coherently aligned among agents to achieve a set of overall consistent scene predictions. For a given agent a, the modality selected for the scene l would be a combination of this agent available marginal modalities p a k ∈ M. Each scene modality l would select a different association between the agents. We illustrate our scene modality generation process in Fig. 4. The model learns L scene modality embeddings S l of D features each. K × A agent modality vectors A a k are also derived from each agent modality endpoint. These vectors are obtained through a 2-layer MLP applied on the agent modality coordinates p a k , to which the stored agent encoding F a (previously described in Sec. 3.1.1) is concatenated in order to help the model recognise modalities from the same agent. The scene modality vectors S l are 'specialized' by querying the available modality proposals A a k of each agent through cross-attention layers. Subsequently, a matching score c k,a l between each scene modality S l and each agent modality A a k is computed. This matching score can be intuitively interpreted as the selection of the role (maneuver k) that the agent a would play in the overall traffic scene l:

c k,a l = S l .A a k T
Since argmax is non-differentiable, we employ a soft argmax as a weighted linear combination of the agent modalities p a k using a softmax on the c k,a l scores:

p a l = k sof tmax(c k,a l )p a k
The recombination module is trained with the scene-level minimum displacement error, where for each modality inside a single scene all predicted agent displacement losses are averaged before taking the minimum (winner-takes-all loss) over the L scene modalities. A formal definiton of this loss, also used as a metric, is given in Eq. 2 in Sec. 4.2 (minSFDE k ).

EXPERIMENTS 4.1 DATASET

We use the Interaction v1.2 dataset that has recently opened a new multi-agent track in the context of its Interpret challenge. It contains 47 584 training cases, 11 794 validation cases and 2 644 testing cases, with each case containing between 1 and 40 agents to predict simultaneously.

METRICS

For a set of k predictions p a k for each agent a in a scene, we report the minimum Final Displacement Error (minFDE k ) to the ground truth pa and the MissRate (MR k ), whose definition of a miss is specified according to the evaluated dataset in Appendix A.1. In their usual marginal definition, these metrics are averaged over agents after the minimum operation, which means that the best modality of each agent is selected independently for each and then averaged:

minF DE k = 1 A a min k p a k -pa 2 , M R k = 1 A a min k 1 a miss k (1)
For consistent scene multi-agent prediction, we report the joint scene-level metrics, where the average operation over the agents is done before the minimum operator. In this formulation, the minimum is taken over scene modalities, meaning that only the best scene (joint over agents) modality is taken into account:

minSF DE k = min k 1 A a p a k -pa 2 , SM R k = min k 1 A a 1 a miss k (2)
In other words, the marginal metrics pick their optimal solutions in a pool of k to the power of a predicted solutions, while the joint metrics restrict this pool to only k possibilities, making it a much more complex problem.

We also report the scene collision rate (SCR) which is the percentage of modalities where two or more agents collide together, and the consistent collision-free joint Miss Rate (cSMR), which is SM R where colliding modalities are also counted as misses.

COMPARISON WITH STATE-OF-THE-ART

We compare our THOMAS model performance with other joint predictions methods ILVM [START_REF] Casas | Implicit latent variable model for scene-consistent motion forecasting[END_REF] and SceneTransformer [START_REF] Ngiam | Scene transformer: A unified multi-task model for behavior prediction and planning[END_REF]. For fair comparison, we use a GOHOME encoder for each of the method, and adapt them accordingly so that they predict only endpoints similar to our method. For each method, we focus on implementing the key idea meant to solve scene consistency and keep the remaining part of the model as close as possible to our approach for fair comparison:

ILVM [START_REF] Casas | Implicit latent variable model for scene-consistent motion forecasting[END_REF] uses variational inference to learn a latent representation of the scene conditioned of each agent with a Scene Interaction Module, and decodes it with a similar Scene Interaction Module. The required number of modalities is obtained by sampling the latent space as many times as require. Even though the sampling is independent for each agent, the latent space is generated conditionally on all the agents.

SceneTransformer [START_REF] Ngiam | Scene transformer: A unified multi-task model for behavior prediction and planning[END_REF] duplicates the agent encoding with the number of modalities required and adds a one-hot encoding specific to each modality. They then apply a shared transformer architecture on all modalities to encode intra-modality interactions between agents and generate the final trajectories.

More details on the state-of-the-art method and the re-implementations we used are given in Appendix A.4. The results are reported in Tab. 1. While having comparable marginal distance performance (demonstrating that our model is not inherently more powerful or leveraging more information), THOMAS significantly outperforms other methods on every joint metric. SMR is improved by about 25% and SCR by almost 30%, leading to a combined cSMR decreased by also more than 25%. We also report our numbers from the Interpret multi-agent online test set leaderboard in Tab. 6 of Appendix A.5. For better comparison with existing single-agent trajectory prediction state-ofthe-art, we provide evaluation numbers on the single-agents benchmarks Argoverse [START_REF] Chang | Argoverse: 3d tracking and forecasting with rich maps[END_REF] and NuScenes [START_REF] Caesar | nuscenes: A multimodal dataset for autonomous driving[END_REF] in Appendix A.7.

ABLATION STUDIES

RECOMBINATION MODULE

We establish the following baselines to assess the effects our THOMAS recombination.

Scalar output: we train a model with the GOHOME graph encoder and a multimodal scalar regression head similar to [START_REF] Liang | Learning lane graph representations for motion forecasting[END_REF]. We optimize it with either marginal and joint loss formulation.

Heatmap output with deterministic sampling: we try various sampling methods applied on the heatmap, with either the deterministic sampling as described in Gilles et al. (2021a) or a learned sampling trained to directly regress the sampled modalities from the input heatmap.

We report the comparison between the aforementioned baselines and THOMAS in Tab. 3. Compared to these baselines, THOMAS can be seen as an hybrid sampling method that takes the result of deterministic sampling as input and learns to recombine it into a more coherent solution. With regard to the joint algorithmic sampling that only tackled collisions but has little to no effect on actual consistency, as highlighted by the big drop in collision rate from 7.2% to 2.6% but a similar joint SMR, THOMAS actually brings a lot of consistency in the multi-agent prediction and drops the joint SMR from 14.8% to 11.8%. Usually, scalar marginal models already suffer from learning difficulties as only one output modality, the closest one to ground, can be trained at a time. Some modalities may therefore converge faster to acceptable solutions, and benefit from a much increased number of training samples compared to the others. This problem is aggravated in the joint training case, since the modality selected is the same for all agents in a training sample. The joint scalar model therefore actually fails to learn multi-modality as illustrated by a higher marginal minFDE 6 than any other model, and an extremely high crossCollisionRate since some modalities never train and always point to the same coordinates regardless of the queried agent. Note that, despite a similar training loss, SceneTransformer doesn't suffer of the same pitfalls in Tab. 1 as is shares the same weights between all modalities and only differentiates them in the initialization of the features. We assess the speed gain of our proposed hierarchical decoder compared to the lane rasters of GO-HOME Gilles et al. (2021a). In Tab. 4. We report training time for 16 epochs with a batchsize of 16, and inference time for 32 and 128 simultaneous agents. For additional comparison, the other existing dense prediction method DenseTNT [START_REF] Gu | Densetnt: End-to-end trajectory prediction from dense goal sets[END_REF] reports an inference speed of 100ms per sample for their model.

QUALITATIVE EXAMPLES

In this section, we will mostly compare the model before recombination, which we will refer by the Bef ore model, to the model after recombination, referenced as the Af ter model. We display four qualitative examples in Fig. 5 with colliding modalities in the Bef ore model (in dashed orange) and the solved modality (in full line orange) after recombination. For each model (Bef ore-dashed or Af ter-full), the highlighted modality in orange is the best modality according to the SM R 6 metric among the 6 available modalities. We also display in dashed grey the other 5 predicted Bef ore modalities, and highlight that the recombination model indeed selects modalities already available in the vanilla set and reorders them so that non-colliding modalities are aligned together. We also show more qualitative examples in Fig. 6, where we highlight the comparison in modality diversity between the Bef ore model (in dashed lines) and the Af ter model (in full lines). While the Bef ore model tries to spread the modalities for all agents to minimize marginal miss-rate, the recombined model presents much less spread compared to the original model, maintaining a multimodal behavior only in presence of very different possible agent intentions such as different possible exits or turn choices. For most other agents, almost all modalities are located at the same position, that is, the one deemed the most likely by the model. Thus, if the truly uncertain agents have to select the second or third most likely modality, the other agents still have their own most likely modality

CONCLUSION

We have presented THOMAS, a recombination module that can be added after any trajectory prediction module outputing multi-modal predictions. By design, THOMAS allows to generate sceneconsistent modalities across all agents by making the scene modalities select coherent agent modalities and restricting the modality budget on the agents that truly need it. We show significant performance increase when adding the THOMAS module compared to the vanilla model and achieve state-of-the-art results compared to already existing methods tackling scene-consistent predictions.

. From N = 16 and lower, coverage performance starts to diminish while little speed gains are made. We still kept a relatively high N=64 in our model as we wanted to insure a wide coverage, and the time loss between 41 ms and 46 ms remains acceptable. [START_REF] Liang | Learning lane graph representations for motion forecasting[END_REF] 3.78 59.1 0.87 1.36 16.3 Autobot [START_REF] Girgis | Autobots: Latent variable sequential set transformers[END_REF] 0.89 1.41 16 TPCN [START_REF] Yuan | Agentformer: Agent-aware transformers for socio-temporal multi-agent forecasting[END_REF] 3.64 58.6 0.85 1.35 15.9 Jean [START_REF] Mercat | Multi-head attention for multi-modal joint vehicle motion forecasting[END_REF] 4.24 68.6 1.00 1.42 13.1 SceneTrans [START_REF] Ngiam | Scene transformer: A unified multi-task model for behavior prediction and planning[END_REF] 4.06 59.2 0.80 1.23 12.6 LaneRCNN [START_REF] Zeng | Lanercnn: Distributed representations for graph-centric motion forecasting[END_REF] 3.69 56.9 0.90 1.45 12.3 PRIME [START_REF] Song | Learning to predict vehicle trajectories with model-based planning[END_REF] 3.82 58.7 1.22 1.56 11.5 DenseTNT [START_REF] Gu | Densetnt: End-to-end trajectory prediction from dense goal sets[END_REF] 3.70 59.9 0.94 1.49 10.5 GOHOME (Gilles et al., 2021a) 3.65 57.2 0.94 1.45 10.5 HOME (Gilles et al., 2021b) 3

Figure 1 :

 1 Figure 1: Illustration of the THOMAS multi-agent prediction pipeline

Figure 2 :

 2 Figure 2: Model architecture for multi-agent prediction with shared backbone

Figure 4 :

 4 Figure 4: Illustration of THOMAS methods for generation of scene-consistent agent modalities

Figure 5 :

 5 Figure5: Qualitative examples of recombination model assembling collision-free modalities together compared to initial colliding modalities. For each example we display the general context with highlighted agents and area of interest, then two zooms in on the agents, one displaying the initial best modality before recombination in dashed orange and all the other available modalities in grey. The second zooms shows the best modality after recombination in full line orange.

Figure 6 :

 6 Figure6: Qualitative examples of recombination model selecting fewer but more pronounced and impactful agent modalities compared to initial colliding modalities. For each example we display on the left the vanilla model modalities with dashed lines, with the initial best modality in dashed orange and all the other available modalities in grey. On the right we display the selected modalities after recombination, where the model focuses on the most likely occurrence in most agents.

Figure 7 :

 7 Figure 7: Curve of MissRate 6 with regard to inference time with varying number of points upsampled at the last hierarchical refinement iteration.

Table 1 :

 1 Comparison of consistent solutions on Interpret multi-agent validation track

		Marginal metrics		Joint metrics
		mADE mFDE MR mFDE MR SCR cMR
	ILVM (Casas et al., 2020)	0.30	0.62	10.8	0.84	19.8	5.7	21.3
	SceneTranformer (Ngiam et al., 2021)	0.29	0.59	10.5	0.84	15.7	3.4	17.3
	THOMAS	0.31	0.60	8.2	0.76	11.8	2.4	12.7

Table 2 :

 2 Comparison of consistent solutions on Interpret multi-agent validation track

				Marginal metrics		Joint metrics
	Output Sampling Objective mADE mFDE MR mFDE MR Col cMR
	Scalar		Marg	0.28	0.59	10.4	1.04	23.7 6.4 24.9
	Scalar		Joint	0.34	0.77	16.2	0.90	19.9 49	21.7
	Heat	Learned	Marg	0.26	0.46	4.9	0.98	20.9 4.1 21.9
	Heat	Learned	Joint	0.29	0.58	9.8	0.88	15.2 3.0 16.4
	Heat	Algo	Marg	0.29	0.54	3.8	0.83	14.8 7.2 15.9
	Heat	Algo	Joint	0.29	0.54	3.8	0.83	14.8 2.6 15.6
	Heat	Combi	Joint	0.31	0.60	8.2	0.76	11.8 2.4 12.7

Table 3 :

 3 Ablation study of the recombination module

		Marginal metrics		Joint metrics
		mADE mFDE MR mFDE MR Col cMR
	No recombination	0.29	0.54	3.8	0.83	14.8 7.2 15.9
	With recombination	0.31	0.60	8.2	0.76	11.8 2.4 12.7
	4.5 HIERARCHICAL HEATMAP REFINEMENT

Table 4 :

 4 Comparison of consistent solutions on Interpret multi-agent validation track

		Training	Inference 32 agents Inference 128 agents
	GOHOME 12.8 hours	36 ms	90 ms
	THOMAS	7.5 hours	20 ms	31 ms

Table 7 :

 7 Argoverse Leaderboard(Chang et al.)

	K=1	K=6
	minFDE MR minADE minFDE MR
	LaneGCN

We use the publicly available Interaction 1.2 dataset (Zhan et al., 2019) available at http:// challenge.interaction-dataset.com/dataset/download. We detail dataset preprocessing in Appendix A.2, training process in Appendix A.3 and give a precise illustration of our model architecture with each layer size in A.8.

A APPENDIX

A.1 METRIC DETAILS We adopt for each dataset evaluation the miss definition as specified by the dataset benchmark. Argoverse [START_REF] Chang | Argoverse: 3d tracking and forecasting with rich maps[END_REF] and NuScenes [START_REF] Caesar | nuscenes: A multimodal dataset for autonomous driving[END_REF] define a miss as the prediction being further than 2 meters to the ground truth, while Waymo [START_REF] Ettinger | Large scale interactive motion forecasting for autonomous driving: The waymo open motion dataset[END_REF] and Interaction [START_REF] Zhan | Interaction dataset: An international, adversarial and cooperative motion dataset in interactive driving scenarios with semantic maps[END_REF]count a miss when the prediction is closer than a lateral (1m) and an longitudinal threshold with regard to speed:

We use the training/validation split provided in Interaction 1.2. We select for each scene a reference agent on which the scene will be centered and oriented according to its heading at prediction time.

At training time, this reference agent is chosen randomly across all agents. At validation and testing time, we compute the barycenter of all agents and select the closest agent as the scene reference point. We use for training all agents that have ground-truth available at prediction horizon T=3s.

We use the provided dataset HD-Maps to create the context graphs. As in [START_REF] Liang | Learning lane graph representations for motion forecasting[END_REF], we use four relations:{predecessor, successor, lef t, right} obtained from the lane graph connectivity. We upsample long lanelets to have a maximum of 10 points in each lanelet.

For each agent, we use their trajectory history made of position, yaw and speed in the past second sampled at 10Hz. We also provide the model a mask indicating if the agent was present in a given time-frame, and pad with zeros when the agent is not tracked at a specific timestep.

A.3 TRAINING DETAILS

We train all models with Adam optimizer and batchsize 32. We initialize the learning rate at 1e -3 and divide it by 2 at epochs 3, 6, 9 and 13, before stopping the training at epoch 16. We use ReLU activation after every linear layer unless specified otherwise, and LayerNormalization after every attention and graph convolution layer.

During training, since a scene can contain up to 40 agents, which is too much for gradient computation in batches of 32, we restrict the number of predicted agents to 8 by randomly sampling them across available agents. We do not use other data augmentation.

The final heatmap Y predicted cover a range of 192 meters at resolution 0.5m, hence a (384, 384) image. For heatmap generation, we use the same pixel-wise focal loss over the pixels p as in Gilles et al. (2021b):

where Ŷ is defined as a Gaussian centered on the agent future position at prediction horizon T with a standard deviation of 4 pixels, equivalent to 2m.

A.4 BASELINES IMPLEMENTATIONS

A.4.1 IMPLICIT LATENT VARIABLE MODEL

We use a GOHOME encoder for the prior, posterior and decoder Scene Interaction Modules. We weight the KL term with β = 1 which worked best according to our experiments.

A.4.2 SCENE TRANSFORMER

The initial paper applies a transformer architecture on a [F, A, T, D] tensor where F is the potential modality dimension, A the agent dimension and T the time dimension, with D the feature embedding, with factorized self-attention to the agent and time dimensions separately, so that agents can look at each-other inside a specific scene modality. The resulting output is optimized using a jointly formalized loss. For our implementation, we get rid of the T dimension as we focus on endpoint prediction and coherence between the A agents. The initial encoded [A, D] tensor is obtained with a GOHOME encoder, multiplied across the F futures and concatenated with a modality-specific one-hot encoding as in [START_REF] Ngiam | Scene transformer: A unified multi-task model for behavior prediction and planning[END_REF] to obtain the [F, A, D] tensor. We then apply two layers of agent self-attention similar to the original paper, before decoding the endpoints through a MLP.

A.4.3 COLLISION-FREE ENDPOINT SAMPLING BASELINE

We designed a deterministic sampling algorithm based on the heatmaps generated in previous section in order to sample endpoints for each agent in a collision aware manner. We use the same sampling algorithm as Gilles et al. (2021a) based on MR optimization, but add a sequential iteration over the agents for each modalities.

For a single modality k, we predict the possible endpoint of a first agent a by taking the maximum accumulated predicted probability under an area of radius r. We then not only set to zero the heatmap values of this agent heatmap I a k around the sampled location so not to sample it in the next modalities k , but we also set to zero the same area on the heatmaps I a k of the other agents a on the same modality k, so that these other agents cannot be sampled at the same position for this modality. This way, we try to enforce collision-free endpoints, and expect that considering collisions brings logic to improve the overall consistency of the predictions. However, as will be highlighted in Sec. 4.4, this methods significantly improves the collision rate without the need for any additional learned model but it does barely improve the multi agent consistency.

A.5 RESULTS ON INTERPRET CHALLENGE

We also report our numbers from the Interpret multi-agent track challenge online leaderboard in Table 6. It is to be noted that the DenseTNT solution explicitely checks for collisions in the search for its proposed predictions, which we don't, hence their 0% collision rate (SCR) and its direct impact on consistent collision-free joint Miss Rate (cSMR). We also display the trade-off between inference speed and coverage from hierarchical refinement in Fig. 7, evaluated on the Interpret multi-agent dataset with marginal MissRate 6 . The curve is obtained setting the number N of upsampled points at the last refinement iteration from 2 to 128.

Published as a conference paper at ICLR 2022 [START_REF] Salzmann | Trajectron++: Dynamically-feasible trajectory forecasting with heterogeneous data[END_REF] 1.88 70 1.51 57 9.52 ALAN [START_REF] Narayanan | Divide-and-conquer for lane-aware diverse trajectory prediction[END_REF] 1.87 1.22 49 9.98 SG-Net [START_REF] Wang | Stepwise goal-driven networks for trajectory prediction[END_REF] 1.86 67 1.40 52 9.25 WIMP [START_REF] Khandelwal | What-if motion prediction for autonomous driving[END_REF] 1.84 55 1.11 43 8.49 MHA-JAM [START_REF] Messaoud | Multi-head attention with joint agent-map representation for trajectory prediction in autonomous driving[END_REF] 1.81 59 1.24 46 8.57 CXX [START_REF] Luo | Probabilistic multi-modal trajectory prediction with lane attention for autonomous vehicles[END_REF] 1.63 69 1.29 60 8.86 LaPred [START_REF] Kim | Lapred: Lane-aware prediction of multi-modal future trajectories of dynamic agents[END_REF] 1.53 1.12 8.12 P2T (Deo & Trivedi, 2020) 1.45 64 1.16 46 10.50 GOHOME (Gilles et al., 2021a) 1.42 57 1.15 47 6.99 Autobot [START_REF] Girgis | Autobots: Latent variable sequential set transformers[END_REF] 1.37 62 1.03 44 8.19 PGP (Deo & Trivedi, 2020) 1 Step Grid decoder 1

Top N 1

Upsample

Mid res grid G 1 x 2

Step Grid decoder 2

Top N 2

Upsample

High res grid G 2 x 2

Step Grid decoder 3

Final res grid (G 2 , 1)

Sparse2Dense

Agent features

Graph features

Top K lanelets A x K x 32