Giuseppe Cabibbo

Chiara Genco

Vito Di Marco

Marco Barbara

Marco Enea

Piero Parisi

Giuseppe Brancatelli

Piero Romano

Antonio Craxì

Professor Calogero Cammà

Di Marco

Barbara

TIME-DEPENDENT COX MODEL IS SUPERIOR IN PREDICTION OF SURVIVAL IN PATIENTS WITH HEPATOCELLULAR CARCINOMA TREATED WITH TRANSARTERIAL CHEMOEMBOLIZATION

Keywords:

whether they are published or not. The documents may come

TACE is considered the standard of care in these patients on the basis of two published meta-analyses that cleared demonstrated 2-year overall survival benefit. [START_REF] Llovet | Systematic review of randomized trials for unresectable hepatocellular carcinoma: Chemoembolization improves survival[END_REF][START_REF] Cammà | Transarterial chemoembolization for unresectable hepatocellular carcinoma: meta-analysis of randomized controlled trials[END_REF] There is sufficient evidence from randomized controlled trials (RCTs) on the type of patients who are candidates for TACE. In addition, the American Association for the Study of Liver Diseases (AASLD) Practice Guideline for the management of HCC indicates TACE in nonsurgical patients at intermediate Barcelona Clinic Liver Cancer (BCLC) B stage. [START_REF] Bruix | Practice Guidelines Committee, American Association for the Study of Liver Diseases. Management of hepatocellular carcinoma[END_REF] Nonetheless, application of TACE in real clinical practice remains a matter of debate.

The selection criteria used to identify the candidates for TACE vary nationally and internationally. [START_REF] Cammà | Transarterial chemoembolization for unresectable hepatocellular carcinoma: meta-analysis of randomized controlled trials[END_REF] Optimal candidates are patients with excellent liver functional reserve who have not presented with cancer-related symptoms or vascular invasion. [START_REF] Bruix | Practice Guidelines Committee, American Association for the Study of Liver Diseases. Management of hepatocellular carcinoma[END_REF][START_REF] Llovet | Arterial embolisation or chemoembolisation versus symptomatic treatment in patients with unresectable hepatocellular carcinoma: a randomised controlled trial[END_REF] However, intermediate BCLC B patients may have ascites, which is strongly linked to poor survival in this stage. [START_REF] Cabibbo | A meta-analysis of survival rates of untreated patients in randomized clinical trials of hepatocellular carcinoma[END_REF][START_REF] Raoul | Evolving strategies for the management of intermediate-stage hepatocellular carcinoma: Available evidence and expert opinion on the use of transarterial chemoembolization[END_REF] Moreover, TACE can be performed in early-stage (BCLC A) patients for whom percutaneous radiofrequency thermal ablation (RFTA) is not feasible because of tumor location (proximity to gallbladder, biliary tree, or blood vessel), or on whom surgery cannot be performed because of comorbidities. [START_REF] Cammà | Unità Interdipartimentale Neoplasie Epatiche (U.I.N.E) Group. Treatment of hepatocellular carcinoma in compensated cirrhosis with radio-frequency thermal ablation (RFTA): a prospective study[END_REF] Despite the many RCTs that have been done to identify the optimal chemoembolization procedure, lack of standardization affects some aspects of treatment, including embolization technique and treatment schedules. [START_REF] Marelli | Transarterial therapy for hepatocellular carcinoma: which technique is more effective? A systematic review of cohort and randomized studies[END_REF][START_REF] Piscaglia | The intermediate hepatocellular carcinoma stage: Should treatment be expanded?[END_REF] A relevant clinical question is whether patients should receive repeated courses of TACE at fixed intervals until the planned numbers of courses is reached or until a complete radiological response is achieved. There is no evidence that complete radiological response after TACE is a surrogate end-point strongly linked to overall survival. A major problem in assessing overall survival of patients with HCC secondary to cirrhosis arises from a lack of accurate models able to predict outcome in the individual patient. [START_REF] Bruix | Practice Guidelines Committee, American Association for the Study of Liver Diseases. Management of hepatocellular carcinoma[END_REF][START_REF] Cammà | Survival of patients with hepatocellular carcinoma in cirrhosis: a comparison of BCLC, CLIP and GRETCH staging systems[END_REF][START_REF] Tandon | Prognostic indicators in hepatocellular carcinoma: a systematic review of 72 studies[END_REF][START_REF] Cammà | Prognostic scores for hepatocellular carcinoma: none is the winner[END_REF] Two factors may contribute to a less than satisfactory performance.

First, all previous prognostic models were general, not specialized, models for evaluating patient outcomes within specific populations or allocation treatment groups (e.g., liver transplantation, percutaneous ablation, TACE and systemic therapies).

Second, all the previous prognostic models assumed that the variables noted at one single time point for each patient were sufficient for predicting survival. In HCC, as in most chronic diseases, the clinical situation changes with time, particularly after a treatment.

Conceivably, the weight of prognostic indicators changes in different phases of the disease, and estimates of prognosis could improve if such time-dependent changes were taken into account.

The aims of this prospective cohort study of HCC patients treated with TACE as first-or second-line treatment were:

• to assess the effectiveness of TACE in HCC patients;

• select the optimal candidate for TACE by identification of predictors of overall survival;

• and improve the accuracy of mortality risk estimates with a new prognostic model that accounts for changes during the course of the disease.

MATERIALS & METHODS

Patients

From January 2004 to May 2009, 84 consecutive HCC patients were treated with TACE as first-or second-line treatment at our institution. Follow-up was censored on October 31, 2009. HCC was diagnosed and staged, respectively, according to AASLD criteria and BCLC schedule. [START_REF] Bruix | Practice Guidelines Committee, American Association for the Study of Liver Diseases. Management of hepatocellular carcinoma[END_REF] Patients with early tumors (single tumors measuring less than 5 cm, or three nodules measuring less than 3 cm) were considered for curative therapies. Resection was indicated for patients with single tumors, absence of portal hypertension, and normal bilirubin concentrations. Patients with portal hypertension or abnormal bilirubin concentrations or three nodules of less than 3 cm in diameter were considered for transplantation. Percutaneous treatment was performed when surgery was precluded.

TACE was performed in patients:

• who were not suitable for curative treatments because of locally advanced HCC (tumor size > 5 cm, or multifocal disease);

• in those for whom percutaneous treatments were precluded due to position (pericholecistic, periportal, subfrenic or subcapsular lesions);

• and in those for whom prior curative treatments had failed.

Exclusion criteria were portal vein thrombosis, impaired liver function (Child-Pugh class ≥ B8), widespread cancer (defined as involving more of the 50% of the liver, or with extra hepatic metastasis), hepatic encephalopathy, and ascites. Extra-hepatic disease was assessed with multidetector multiphasic CT and chest radiography. Bone metastases were sought by scintigraphy if clinically suspected.

TACE technique

Each patient underwent standard hepatic angiography with the Seldinger procedure. The catheter tip was advanced as near as possible to the feeding artery. An emulsion of anticancer agent (doxorubicin) and lipiodol, followed by gelatin sponge particles, was carefully injected during the x-ray monitoring. The dose of anticancer agent emulsion and lipiodol, as well as the pieces of embolic materials used for TACE, were based on tumor size and extension of the lesions. TACE was done at baseline and, when there was evidence of any tumor persistence, every 2 months thereafter. It was withheld or

Outcomes and follow-up

The primary outcome was overall survival. Follow-up time was defined as the number of months from first TACE to orthotopic liver transplantation (OLT), other treatments, last contact with the patient, or death.

Response rate magnitude was defined according to the European Association for the Study of the Liver (EASL) criteria. [START_REF] Bruix | EASL Panel of Experts on HCC. Clinical management of hepatocellular carcinoma. Conclusions of the Barcelona-2000 EASL conference. European Association for the Study of the Liver[END_REF] These are addressed by recent guidelines. [START_REF] Llovet | Panel of Experts in HCC-Design Clinical Trials. Design and endpoints of clinical trials in hepatocellular carcinoma[END_REF][START_REF] Lencioni | Modified RECIST (mRECIST) assessment for hepatocellular carcinoma[END_REF] EASL response criteria are defined as follows:

• complete response, defined as absence of any enhancing tissue;

• partial response (PR), defined as > 50% decrease in enhancing tissue;

• and stable disease, defined as < 50% decrease in enhancing tissue.

Progressive disease is defined as any increase in enhancement of the treated tumor.

Since we used an on demand protocol, assessment of response was not done at a fixed time, but after the last performed TACE. The follow-up protocol included clinical assessment by physical examination, ultrasound scan and biochemistry every 3 months, and by multiphasic CT scan every 6 months. In our study, TACE-related morbidity was defined as any complication within 2 weeks of each session of TACE. TACE-related mortality was defined as death from a complication within 2 weeks of each session of TACE. Decompensation of liver disease was defined as appearance of ascites, jaundice and/or hepatic encephalophathy during follow-up. The Kaplan-Meier model was used to estimate survival. Differences in the survival rate were assessed by log-rank testing. Potential prognostic variables were evaluated as predictors of survival both in time-fixed and time-dependent Cox models. [START_REF] Cox | Regression models and life-tables (with Discussion)[END_REF][START_REF] Therneau | Modeling Survival Data: Extending the Cox Model[END_REF] In the timefixed model, only the initial records at the time of first TACE were applied (Table 1). The time-dependent model used the repeated measurements of the potential prognostic variables, with the addition of treatment response, time to progression (TTP) and number of treatments, during follow-up.

All variables studied at univariate analyses were entered into the multivariate analyses. To avoid the effect of co-linearity with performance status, BCLC score was not included in the same multivariate model. Variables with a p value of < 0.10 at univariate analysis were included in the final multivariate models. A Cox model was used to identify prognostic factors for mortality in a multiple regression analysis by time-fixed and timedependent analyses. All p values were two-tailed, and all confidence intervals (CIs) were 95%.

Time-fixed and time-dependent model discrimination were evaluated at 6, 12 and 24 months by the area under incident/dynamic receiver operating characteristic curves (AUROC) determined by the Heagerty and Zheng method. [START_REF] Heagerty | Survival model predictive accuracy and ROC curves[END_REF] At every considered time, AUROCs were tested by a Wilcoxon rank sum test with continuity correction. [START_REF] Wilcoxon | Individual Comparisons by Ranking Methods[END_REF][START_REF] Bauer | Constructing Confidence Sets Using Rank Statistics[END_REF] In order to have a broader view of the differences between the AUROCs, an Integrated Area Under the Curve (IAUROC) calculation was made.

RESULTS

Patient features at baseline

The study population consisted of 84 patients with HCC secondary to cirrhosis of different etiologies. Of these 84 patients, 61 received TACE as first-line treatment, while 23 received it as second-line treatment. The demographic, clinical and tumor staging features of the 84 patients are given in Table 1. A single lesion was observed in 69%, two or three lesions in 25%, and more than three lesions in 6% of patients (Table 1).

At presentation 44 of the 84 patients (52%) were BCLC early (A) stage, 24 BCLC intermediate (B) stage (29%), and 16 BCLC advanced (C) stage (19%). Patients at BCLC C stage were classified in this stage because they had symptomatic disease with PS 1.

Follow-up

Three of the 84 patients (4%) were lost at follow-up. During follow-up, 34 patients died (Table 2), 12 patients (14%) were withdrawn for other treatments, while 26 (31%) were alive at the end of the study (Table 2). Among the 34 deaths, only 3 patients (4%) died cancer-free (i.e., without local recurrence, new lesions, or distant metastases).

Median overall survival after first TACE was 30.5 months (95% confidence interval [CI] 24.0 -38.8) for the entire group. The overall survival rates (Figure 1) were 89.6% (95% CI 82.5-97.2); 58.8% (95% CI 46.2-74.9); 35.4% (95% CI 22.3-56.1); 17.2% (95% CI 7.0-41.7); and 5.7% (95% CI 0.9-35.7) at 12, 24, 36, 48 and 60 months, respectively. Table 2 lists TTP and response rate according to EASL criteria. [START_REF] Tandon | Prognostic indicators in hepatocellular carcinoma: a systematic review of 72 studies[END_REF] Response rate after TACE was 76% (complete response, 30%; partial response 34%), and the safety of TACE was found to be acceptable. No patient death was treatment-related. The most common symptoms were development of transient abdominal pain (18%), fever (14%), and vomiting (9%). The only major complication was acute cholecystitis (1%) (Table 2).

Analysis of factors affecting the survival of patients

Cox regression analysis by time-fixed model showed that performance status (HR 10.9; 95% CI: 4.4-27.1; P < 0.001), multiple nodules (HR 3.7; 95% CI: 1.2-8.6; P = 0.016), and no prior therapy (HR 3.3; 95% CI: 1.3-10.7; P = 0.017) were independent risk factors for mortality (Table 3).

Cox regression analysis by time-dependent model showed that performance status (HR 7.9; 95% CI: 3.63-17.2; P < 0.001); no prior therapy (HR 6.3; 95% CI: 1.8-22.67; P = 0.005); multiple treatments (HR 0.5; 95% CI: 0.3-0.9; P = 0.013); complete response (HR 0.1; 95% CI: 0.03-52; P = 0.005); and elevated bilirubin (HR 4.2; 95% CI: 2.2-7.9; P < 0.001) were independent risk factors for mortality (Table 3).

When relapsing bilirubin levels as a continuous variable with bilirubin levels as categorical variable (cut-off ≤ 3 mg/dl) were measured, we obtained similar results. The shown in Figure 3. The 3-year probability of overall survival for a patient with complete response, stable performance status 0 and normal bilirubin levels on treatment, is 82.5%.

That of a patient with complete response without stable performance status, and abnormal bilirubin levels, is 0.5%.

DISCUSSION

HCC secondary to cirrhosis is a complex and heterogeneous disease with wide variations during its clinical course. [START_REF] Cabibbo | A meta-analysis of survival rates of untreated patients in randomized clinical trials of hepatocellular carcinoma[END_REF][START_REF] Testa | Trans-catheter arterial chemoembolisation for hepatocellular carcinoma in patients with viral cirrhosis: role of combined staging systems, Cancer Liver Italian Program (CLIP) and Model for End-stage Liver Disease (MELD), in predicting outcome after treatment[END_REF] None of the current general prognostic systems has provided confident prediction of survival in individual patients, [START_REF] Cammà | Survival of patients with hepatocellular carcinoma in cirrhosis: a comparison of BCLC, CLIP and GRETCH staging systems[END_REF][START_REF] Cammà | Prognostic scores for hepatocellular carcinoma: none is the winner[END_REF] so we urgently need specialized models to evaluate patient outcomes within specific allocation treatment groups. [START_REF] Orlandi | A consensus conference on prognostic studies in hepatology[END_REF] Another important issue is the lack of prognostic tools able to adequately express the complexity of the interactions during follow-up between tumor factors and degree of liver failure. As a result, we need models that account for changes during the course of the disease.

In this study, which is to our knowledge the first of its kind, the predictive accuracy From a practical point of view, the excellent prediction of survival achieved by our model could be useful for:

• controlling for confounding factors in observational studies;

• calculating the sample size and stratifying patients in RCTs;

• and assessing treatment effect size in order to formulate therapeutic strategies.

Our study also shows that patients with good performance status may benefit from TACE treatment both in the time-fixed and time-dependent models. The finding that a cancer-related variable, such as the number of tumor lesions assessed at baseline, is an independent predictor for better survival at multivariate analysis is in agreement with the results of a previous study by Takayasu. [START_REF] Takayasu | Liver Cancer Study Group of Japan. Prospective cohort study of transarterial chemoembolization for unresectable hepatocellular carcinoma in 8510 patients[END_REF] These two parameters, both included in the BCLC classification, may explain why this staging system provides accurate information on prognosis in the setting of HCC. [START_REF] Varela | Review article: natural history and prognostic prediction of patients with hepatocellular carcinoma[END_REF] An important finding in the present study was the significantly increased risk of death indicated by the time-dependent model in patients with elevating bilirubin levels during follow-up. Therefore, the results of TACE in terms of survival should be carefully evaluated because its indisputable antitumor effects are offset in practice by deterioration in liver function. It is conceivable that a benefit with chemoembolization could be had only with the sort of careful selection that excludes patients with high risk of progressive liver failure after TACE. [START_REF] Giannini | Impact of evidence-based medicine on the treatment of patients with unresectable hepatocellular carcinoma[END_REF] That the median survival observed in our study (30 months) was good was likely due to an accurate selection of patients.

As previously reported in the setting of treatment with RFTA, [START_REF] Raoul | Evolving strategies for the management of intermediate-stage hepatocellular carcinoma: Available evidence and expert opinion on the use of transarterial chemoembolization[END_REF] percutaneous ethanol injection (PEI), [START_REF] Sala | Initial response to percutaneous ablation predicts survival in patients with hepatocellular carcinoma[END_REF] and, more recently, TACE, [START_REF] Olivo | Transcatheter arterial chemoembolisation for hepatocellular carcinoma in cirrhosis: Survival rate and prognostic factors[END_REF] it would seem, from the present study, that overall survival depends strictly on complete radiological response. So, complete response is a relevant surrogate end-point that should be planned and carefully assessed by multiphasic CT scan in all patients who undergo TACE. A general consensus on the optimal schedule of TACE treatment has yet to be reached [START_REF] Raoul | Evolving strategies for the management of intermediate-stage hepatocellular carcinoma: Available evidence and expert opinion on the use of transarterial chemoembolization[END_REF] . In various studies, treatment was repeated at fixed intervals based on a preestablished number of courses, or repeated on-demand based on radiological response.

Our study suggests the possibility that repeated courses of treatment are more efficient than single treatment, and that a complete radiological response should be achieved because it is a relevant surrogate end-point. The possibility of achieving this surrogate end point with TACE should be carefully assessed before determining treatment failure after TACE, and then switching to sorafenib.

What are the implications of these results for current practice? In accordance with current AASLD guidelines, [START_REF] Bruix | Practice Guidelines Committee, American Association for the Study of Liver Diseases. Management of hepatocellular carcinoma[END_REF] we confirmed that mortality risk estimates should be made at baseline with the BCLC staging system. Our study provides further evidence that the evaluation of other simple parameters during the course of treatment, namely performance status, radiological response, and bilirubin levels, by a time-dependent model can reliably aid in determining whether further sessions of TACE are needed. In the subgroup of patients with the most favorable on-treatment predictors, the probability of 3-year overall survival was 82%. In patients with complete response, but with coexistence of the most unfavorable on-treatment predictors (worsening of the performance status and increasing of bilirubin levels) the prognosis was very poor. Accordingly, TACE should be repeated until achieving complete necrosis in patients with a good and stable performance status and with relatively preserved liver function (bilirubin level < 3 mg/dL).

Our analysis, specifically designed to identify prognostic factors of survival, shows that patients who received TACE as first-line treatment had a higher risk of death than those who received TACE as second-line treatment. The worse survival observed in the first group could be explained by the fact that the first group had a greater number of patients in a more advanced stage than did the second group. Moreover, in our prospective cohort study, 44 of 84 patients (52%) were in BCLC class A, and received Moreover, the fact that multiple treatments appeared to be a predictor of good outcome may reflect a selection bias due to which patients receiving multiple treatments were those that were healthy enough to tolerate multiple treatments over a long period.

Another weakness of our prognostic model is the lack of data on molecular factors, such as gene expression profiling, which can have some impact on patient's outcome. [START_REF] Giannini | Impact of evidence-based medicine on the treatment of patients with unresectable hepatocellular carcinoma[END_REF][START_REF] Sala | Initial response to percutaneous ablation predicts survival in patients with hepatocellular carcinoma[END_REF] The predictive ability of our model, including simple and easy clinical and radiological predictors was excellent, underscoring the applicability of our results to new populations and settings, particularly in real clinical practice, where complex and expensive tests are not available.

Finally, we should be particularly concerned about the small number of patients included in this single center study compared with other prospective, multicenter studies. Further large-scale prospective studies may prove useful in substantiating the benefit of this new approach.

The available evidence is sufficient to conclude that: 1) the time-dependent Cox model better predicts overall survival than the time-fixed model;

2) patients with a good performance status, and with a low number of nodules at baseline, are good candidates for TACE;

3) a complete radiological response after TACE significantly increases overall survival, and should therefore be considered a surrogate endpoint of treatment; repeated courses of treatment are more efficient than a single treatment; Funding/Support: This study was not supported by any pharmaceutical company or grants; the cost was borne by the authors' institutions. We have made the article more succinct, and simplified many sentences. Moreover, we have tried to clarify the doubts and questions raised by the reviewers.

We hope that the study is now acceptable for publication. In any event, we wish to thank the two referees for their many helpful comments on the earlier version of this paper.

You will also find a letter itemizing the changes we have made, as point-by-point replies. In First of all, we would like to thank the reviewers for their comments, which were of great help in improving the manuscript.

Reviewer 1:

1) A number of sentences have been shortened by making them two sentences. Some of the longer, and perhaps more tortuous, sentences have been put into bullet points.

Reviewer 2:

1-2)
As requested, we have changed the expressions "number of nodules" in "multiple nodules," "number of treatments," in "multiple treatments," and "bilirubin" in "elevated bilirubin" as follows: (pages 9, lines 6-10) "Cox regression analysis by timedependent model showed that performance status (HR 7.9; 95% CI: 3.63-17.2; P < 0.001); no prior therapy (HR 6.3; 95% CI: 1.8-22.67; P = 0.005); multiple treatments (HR 0.5; 95% CI: 0.3-0.9; P = 0.013); complete response (HR 0.1; 95% CI: 0.03-52; P = 0.005); and elevated bilirubin (HR 4.2; 95% CI: 2.2-7.9; P < 0.001) were independent risk factors for mortality (Table 3)".

Moreover, each variable is now explained in Table 3, and we discuss the unexpected prediction of good outcomes of multiple treatments as follows: (page 13, lines 6-9)

"Moreover, the fact that multiple treatments appeared to be a predictor of good outcome may reflect a selection bias due to which patients receiving multiple treatments were those that were healthy enough to tolerate multiple treatments over a long period."

3) This was an error, plain and simple. We have corrected it as follows: (page10, line1) "…mortality by the time-dependent model…".

INTRODUCTION

  Transarterial chemoembolization (TACE) is the most widely used first-line treatment in the Western world and Asia for patients with unresectable hepatocellular carcinoma (HCC).

  contraindications, poor hepatic function, severe adverse effects, or progressive disease developed. One month after every TACE, a multiphasic CT scan was done.

  All multivariate analyses were done with PROC PHREG in SAS version 8.1 (SAS Institute, Inc, Cary, NC, USA). Model discrimination analyses were carried out with the R Statistical Computing, version 2.10 (R Foundation for Statistical Computing, Vienna, Austria).

  discriminating ability of time-fixed and time-dependent models in predicting overall survival was evaluated by AUROC values at 6 months (0.901 for the time-dependent model, and 0.848 for the time-fixed model [Figure 2A]); at 12 months (0.903 for the time-dependent model, and 0.817 for the time-fixed model [Figure 2B]); and at 24 months (0.908 for the time-dependent model, and 841 for the time-fixed model [Figure2C]). AUROC of the timedependent model was significantly higher than that of the time-fixed model at all time points (the time-dependent vs. time-fixed models two-sided P-values were < 0.001, < 0.001 and = 0.01 at 6, 12 and 24 months, respectively [Figures2A,B,C]).The Integrated AUC (IAUC) of the time-dependent model was significantly higher than that of the time-fixed model (time-dependent model vs. time-fixed model, P-value < 0.0001), demonstrating a better discriminating capacity of the time-dependent model (Figure2D).The estimated probability of survival in the 4 hypothetical patients treated with TACE who achieved complete response, according to factors significantly predicting time-dependent model (i.e., performance status and bilirubin levels) are

  of a time-dependent Cox model for overall survival prediction in patients with unresectable HCC and compensated cirrhosis treated with TACE was prospectively compared with that of the most widely-used time-fixed models. The performance of the time-dependent model was significantly better than that of the time-fixed model, and the overall predictive ability of this model, including simple and easy clinical and radiological predictors, was excellent. Moreover, it was uniform over the 3 time points considered: 6, 12 and 24 months.This study shows that the key prognostic factors of HCC treated with TACE change over time, and that they can be combined into a specialized model that accurately estimates the risk of mortality at different time points during the post-treatment disease course.

  these, more-curative treatment failed in 23 patients, who then received TACE as second-line therapy. The remaining 21 could not receive curative treatment because of tumor location and/or comorbidities. It should be recognized that not all patients in real clinical practice defined by each stage of BCLC are ultimately candidates for the suggested treatment modality.

  bilirubin elevation during follow-up significantly increases the risk of death; Therefore, treatment should be discontinued when bilirubin exceeds the value of 3 mg%.

Figure 1 .

 1 Figure 1. Probability of Overall Survival According to BCLC in 84 Patients with HCC in Compensated Cirrhosis Treated with TACE.

Figure 2 .

 2 Figure 2. Receiver Operating Characteristic (ROC) Curves and Area Under the ROC Curve for Time-Fixed and Time-Dependent Cox Regression Models At 6 (A), 12 (B) and 24 Months (C). (D) Comparison between the Time-Dependent and Time-Fixed Cox Models in Terms of Integrated AUROCs.

Figure 3 .

 3 Figure 3. Estimated Probability of Overall Survival for Different Patients with HCC Treated with TACE, According to Variability in Predicting Factors by Time-Dependent Cox Regression Model. Patients with Complete Response and 1) Stable Performance Status and Bilirubin Levels; 2) Stable Performance Status and Impaired Bilirubin Levels; 3) Impaired Performance Status and Stable Bilirubin Levels; 4) Impaired Performance Status and Bilirubin Levels.

Figure 1 .Figure 2 .Figure 3 .

 123 Figure 1. Probability of overall survival according to BCLC in 84 patients with HCC in compensated cirrhosis treated with TACE. 211x158mm (96 x 96 DPI)

  the letter, all sentences added to the revised version are underlined. I look forward to hearing from you,

Table 1 . Demographic, Laboratory, Clinical and Tumor Staging Characteristics of 84 Patients with HCC in Compensated Cirrhosis Treated with TACE.

 1 Values are mean ± SD. Abbreviations: IU, international units; AFP, alpha fetoprotein; HCV, hepatitis C virus; HBV, hepatitis B virus; BCLC, the Barcelona Clinic Liver Cancer; °, Eastern Cooperative Oncology Group -Performance Status; MELD, Model for End-Stage Liver Disease.

	Characteristic

Table 2 . Follow-up of 84 Patients with HCC in Compensated Cirrhosis Treated with TACE.

 2

	Characteristics

Table 3 . Multivariate Cox Regression Models for Predicting Overall Survival in Patients with HCC in Compensated Cirrhosis Treated with TACE.

 3

	Variable (Code)	HR	95%CI	p-value
		Time-Fixed Approach
	Performance Status° (0/1)	10.9	4.4 -27.1	<0.001
	No Prior Therapy	3.3	1.3 -10.7	0.017
	Number of Nodules (≥3)	3.7	1.2 -8.6	0.016
		Time-Dependent Approach
	Performance Status° (0/1)	7.90	3.63 -17.23	<0.001
	No Prior Therapy	6.3	1.77 -22.63	0.005
	Number of Treatments (Continuous)	0.5	0.31 -0.87	0.013
	Complete Response after TACE (yes/no)	0.1	0.03 -0.52	0.005
	Log -Bilirubin (Continuous)	4.2	2.18 -7.89	<0.001
	Note: °, Eastern Cooperative Oncology Group -Performance Status.
	Abbreviations: HR, hazard Ratio; CI, confidence interval; TACE, transarterial chemoembolization.

ACKNOWLEDGEMENTS

This article is dedicated to the memory of Professor Luigi Sandonato.

The authors thank Professor Jordi Bruix for his many suggestions.

The authors thank Warren Blumberg for his forbearance in editing the manuscript.


Arm coordination, power, and swim efficiency in national and regional front crawl swimmers

Keywords: biomechanics, motor control, expertise, drag, swimming. PsycINFO Classification: 2330, 3720

The effects of skill level on index of arm coordination (IdC), mechanical power output (P d ), and swim efficiency were studied in front crawlers swimming at different speeds. Seven national and seven regional swimmers performed an arms-only intermittent graded speed test on the MAD-system and in a free condition. The MAD-system measured the drag (D) and P d . Swimming speed (v), stroke rate (SR), stroke length (SL), stroke index (SI), relative entry, pull, push, and recovery phase durations, and IdC were calculated. Swim efficiency was assessed from SI, the coefficient of variation of calculated hip intracyclic velocity variations (IVV), and the efficiency of propulsion generation, i.e., the ratio of v² to tangential hand speed squared (u²). Both groups increased propulsive continuity (IdC) and hand speed (u) and applied greater P d to overcome active drag with speed increases (p < .05). This motor organization adaptation was adequate because SI, IVV, and v²/u² were unchanged. National swimmers appeared more efficient, with greater propulsive continuity (IdC) and P d to reach higher v than regional swimmers (p < .05). The regional swimmers exhibited a higher u and lower SI, IVV, and v²/u² compared to national swimmers (p < .05), which revealed lower effectiveness to generate propulsion, suggesting that technique is a major determinant of swimming performance.

Introduction

Swimming is a cyclic form of locomotion in the aquatic environment whereby propulsion is generated to overcome resistive forces. Therefore, the goal for competitive swimmers is to maximize propulsion while minimizing drag, given a finite metabolic capacity. As expressed in Equation 1, swimming speed (v) depends on total energy expenditure rate ( ), propulsive efficiency (e P ), mechanical efficiency (e m ), and resistive forces (D):

v = • e P • e m • D -1
(Equation 1)

In variable swimming movement, the same change in speed (v) considering a given period of time defines the acceleration (a) and is dependent on the applied resultant force (F) and the inertial term of the equation of movement:

F = m • a (Equation 2)
where F is the resultant force from propulsion (P) and drag (D):

P + D = m • a (Equation 3) Thus, variable movement is: (i) the result of a circumstantial prevalence of P or D, or (ii) a consequence of an increased (or reduced) added mass effect during a given swim cycle.

To assess some of the performance characteristics of a swimmer in practice, several stroking parameters are measured (swimming speed, v; stroke rate, SR; stroke length, SL; and stroke index, SI) [START_REF] Costill | Energy expenditure during front crawl swimming: Predicting success in middle-distance events[END_REF][START_REF] Craig | Relationships of stroke rate, distance per stroke, and velocity in competitive swimming[END_REF], where v relates to SR and SL according to Equation 4: 4)

v = SR • SL (Equation
and SI to v and SL according to Equation 5 [START_REF] Costill | Energy expenditure during front crawl swimming: Predicting success in middle-distance events[END_REF]: 5)

SI = v • SL (Equation
In uniform movement, acceleration is null (a = 0 and v = v 0 ), which means P = D. Thus, to swim at constant speed, swimmers must overcome the resistive forces of water, i.e., the active drag (D) that increases with speed squared [START_REF] Toussaint | Biomechanical aspects of peak performance in human swimming[END_REF]) (Equation 6): 6)

D = K• v 2 (Equation
where K is a constant of proportionality depending on body size and shape: K = 0.5 • Cd • Ap • , Cd is the drag coefficient, Ap is the projected frontal area, and is the density of water.

To overcome this active drag, the swimmer applies a certain amount of work per stroke (W d )

corresponding to the product of SL and drag force (Equation 7):

W d = D • SL (Equation 7) Thus, the mechanical power output to overcome drag (P d in W) is related to the product of the work generated per stroke and the swimmer's SR (Equation 8): 8)

P d = W d • SR (Equation
Combining Equations 7 and 8: 9)

P d = D • v (Equation
While part of the total mechanical power output (P o ) is used beneficially to overcome active drag (P d ),

another part is dissipated in the water as kinetic energy when water is accelerated in the process of propulsion generation (P k ) [START_REF] Toussaint | Propelling efficiency of front crawl swimming[END_REF], so total power output P o equals:

P o = P k + P d (Equation 10)

The mechanical efficiency (e m ) is calculated as the ratio of the energy equivalence of oxygen uptake to the P o delivered, while the propulsive efficiency (e P ) quantifies the useful power for body translation (Equation 11) [START_REF] Lighthill | Mathematical biofluid dynamics[END_REF][START_REF] Toussaint | Propelling efficiency of front crawl swimming[END_REF]):

e P = P d / P o (Equation 11)

Propulsion is generated by the movement of propelling surfaces, e.g., the hands and feet; however, the relative contribution of the feet is much reduced [START_REF] Deschodt | Relative contribution of arms and legs in humans to propulsion in 25-m sprint front-crawl swimming[END_REF]. [START_REF] Wiegand | The division of swimming strokes into phases, based upon kinematic parameters[END_REF] were the first to relate swimming v and hand speed to determine propulsive and resistive phases in the arm stroke; [START_REF] Martin | A simple analytical model for the crawl stroke[END_REF] later proposed a model to assess arm stroke efficiency, which was then adapted by [START_REF] Zamparo | An energy balance of front crawl[END_REF]. This model assumes that the arm is a rigid segment of length l rotating at constant angular speed ( ) about the shoulder, which enables the calculation of tangential hand speed (u) (Equations 12 and 13):

= 2 • SR (Equation 12) 13)

u = • l (Equation
In this model, the efficiency of propulsion generation (e pg ) is quantified as the ratio between v and SR, which is directly related to u and calculated over the underwater part of the cycle, corresponding to half of a complete arm cycle (Equation 14): 14)

e pg = (v / (2 • SR • l)) • (2 / ) (Equation
The e pg was close to 0.42-0.55 when expert front crawl swimming speed varied from 1 to 1.4 m.s -1 [START_REF] Zamparo | An energy balance of front crawl[END_REF]; it did not change with gender but varied with age (0.31 before puberty, 0.38-0.40 at about 20 years, 0.25 at about 40 years) [START_REF] Zamparo | Effects of age and gender on the propelling efficiency of the arm stroke[END_REF]. [START_REF] Toussaint | Effect of fatigue on stroking characteristics in an arms-only 100-m front-crawl race[END_REF] showed that during four 25-m bouts of a 100-m all-out, mechanical power output and hand speed (u) respectively decreased from 200 to 150 W and from 2.14 to 1.91 m.s -1 while the e pg , calculated as the v²/u² ratio, tended to slightly (but not significantly) decrease from 0.63 to 0.60. Performance seemed linked to high hand forces, mechanical power output, and hand speed, and it was found to decrease with fatigue [START_REF] Toussaint | Effect of fatigue on stroking characteristics in an arms-only 100-m front-crawl race[END_REF].

The previous calculation of e pg does not take into account the intra-cyclic velocity variation (IVV).

In fact, the swimming speed is not uniform as the application of propulsive forces in water leads to acceleration and deceleration within the cycle, i.e., of the center of gravity IVV [START_REF] Fujishima | Velocity degradation caused by its fluctuation in swimming and guidelines for improvement of average velocity[END_REF][START_REF] Miller | Biomechanics of swimming[END_REF][START_REF] Miyashita | An analysis of fluctuations of swimming speed[END_REF][START_REF] Nigg | Selected methodology in biomechanics with respect to swimming[END_REF]. Therefore, to accurately measure efficiency, an estimation of the extra power output wasted with IVV is required [START_REF] Miller | Biomechanics of swimming[END_REF][START_REF] Nigg | Selected methodology in biomechanics with respect to swimming[END_REF]. Generally, higher IVV has been correlated to an increased rate of the energy expenditure of swimming [START_REF] Alves | Determinants of energy cost of front crawl and backstroke swimming and competitive performance[END_REF][START_REF] Barbosa | Energy cost and intracyclic variation of the velocity of the centre of mass in butterfly stroke[END_REF][START_REF] Barbosa | Relationships between energy cost, swimming velocity and speed fluctuation in competitive swimming strokes[END_REF] caused by a power term related to the acceleration and deceleration of the center of gravity. Notably, [START_REF] Nigg | Selected methodology in biomechanics with respect to swimming[END_REF] predicted that a speed change of 10% within a stroke cycle resulted in an additional work demand of about 3%, suggesting that the best solution to increase the capacity to produce propulsive forces while minimizing power output seems to be to reduce IVV.

One way to minimize IVV would be to organize the inter-limb coordination well, as the propulsive continuity of the two arms in front crawl would permit the swimmer to minimize the deceleration between two propulsions and, therefore, increase swim efficiency. To assess the inter-arm coordination in front crawl swimming, [START_REF] Chollet | A new index of coordination for the crawl: Description and usefulness[END_REF] developed an index of coordination (IdC) which quantifies the lag time between the propulsive actions of the two arms. When the swimming speed increased from slow to fast paces, SR increased while SL decreased, and IdC increased to reflect a shift from catch-up (lag time between the propulsions) to a relative superposition (overlap of the propulsions) coordination mode [START_REF] Chollet | A new index of coordination for the crawl: Description and usefulness[END_REF][START_REF] Seifert | Swimming constraints and arm coordination[END_REF]. Expert swimmers reached greater v, which could be ascribed to their greater SL and propulsive continuity (greater IdC) than less expert swimmers, both during speed incremental tests [START_REF] Chollet | A new index of coordination for the crawl: Description and usefulness[END_REF][START_REF] Seifert | Swimming constraints and arm coordination[END_REF] and 100-m races [START_REF] Seifert | Kinematic changes during a 100-m front crawl: Effects of performance level and gender[END_REF]. A study on the effect of fatigue on stroking characteristics revealed that fatigue development induced an increase in SR and IdC to compensate for the reduced capacity to generate a propulsive impulse per stroke. The change in arm coordination allowed a better chain of the propulsive actions and led to more time allotted to propulsion per distance unit. Such motor adaptation ensured that the overall propulsive impulse remained constant, whereas average propulsive force per arm stroke was reduced [START_REF] Alberty | Stroking characteristics during time to exhaustion tests[END_REF]. [START_REF] Seifert | Swimming constraints and arm coordination[END_REF] postulated that an increase in environmental constraints, notably active drag, would necessitate the increase in IdC. In fact, above a critical speed (1.8 m.s -1 ) and SR (0.83 Hz) [START_REF] Potdevin | Does stroke rate determine swimming velocity values and coordination[END_REF][START_REF] Seifert | Swimming constraints and arm coordination[END_REF], superposition coordination was the main motor solution observed. For expert swimmers, the changes in inter-limb coordination appeared efficient because IVV did not increase over eight trials of 25-m at increasing speed [START_REF] Schnitzler | Arm coordination adaptations assessment in swimming[END_REF]. However, this assumption has not yet been supported by published data showing the implied relationships between active drag and inter-limb coordination changes with speed and the efficiency of these changes with regard to the swimmer's skill level.

The aim of the present study was thus to examine how a combined group of national and regional swimmers organized their stroke (i.e., their inter-limb coordination and their power output application) to increase v, and more particularly how the national swimmers changed their coordination when swimming at higher speeds. It was also examined whether, for a given speed, the stroke organization of the national swimmers would be more efficient (the latter assessed by IVV and changes in SI and the e pg , i.e., v²/u²). It was hypothesized that the increase in speed would lead to greater IdC, mechanical power output, and efficiency for the national swimmers, indicating that their change in coordination was more efficient and enabled them to reach higher v than regional swimmers.

Method

Participants

Fourteen French male swimmers separated into two skill levels volunteered for this study. The first group was composed of seven national swimmers for whom the mean ± standard deviation of age, body mass, height, arm span, and arm length was: 21.9 ± 4.2 years, 80.7 ± 7.0 kg, 1.86 ± 0.04 m, 1.93 ± 0.07 m, 0.65 ± 0.03 m, respectively. At the time of the experiment, they were training 20.0 ± 1.0 hours per week and had 11.6 ± 2.5 years of practice, which indicates expert skill, according to [START_REF] Ericsson | Expert and exceptional performance: Evidence of maximal adaptation to task constraints[END_REF].

Their mean performance for the 100-m front crawl in the long pool was 51.3 ± 2.3 s, which corresponds to a national rank and is 90.2 ± 3.9% of the 2007 world speed record. The second group was composed of seven regional swimmers for whom the mean ± standard deviation of age, body mass, height, arm span, and arm length was: 21.7 ± 3.1 years, 73.6 ± 9.4 kg, 1.81 ± 0.07 m, 1.84 ± 0.07 m, 0.64 ± 0.02 m, respectively. At the time of the experiment, they were training 9.4 ± 4.3 hours per week and had 8.0 ± 4.3 years of practice. Their mean performance for the 100-m front crawl in the long pool was 56.8 ± 1.9 s, which corresponds to a regional rank and is 81.5 ± 2.8% of the 2007 world speed record. The protocol, approved by the university ethics committee, was explained to the swimmers, who then gave their written consent to participate.

Protocol

The swimmers performed two intermittent graded speed tests in randomized order, using an arms-only front crawl stroke (using a pull-buoy): one on the MAD-system (10 bouts of 25-m) and one in the free swimming condition (8 bouts of 25-m), from slow (~60%) to 100% of maximal speed (with an absolute increment of 0.05 m.s -1 , which corresponded to a relative increment of 5% of maximal speed). The bout was self-paced to avoid the speed variations that can arise when the swimmer follows a target. Thus to be sure that the normalized v (expressed in % of maximal speed) on the MAD-system and in the free condition were close for each bout, two more bouts were allowed on the MAD-system as this condition was uncommon for the swimmers. Four minutes of rest were given before the next bout was swum.

a. 2.3. Video analysis in the free condition

Swimmers were video-taped by two underwater video cameras (Sony compact FCB-EX10L, f = 50 Hz), with one camera placed to obtain a frontal view and the other to obtain a side view. The frontal underwater camera was fixed on the edge of the pool, 0.4 m below the water. The side underwater camera was fixed on a trolley and an operator followed the swimmer's head to avoid parallax. Both cameras were connected to a double-entry audio-visual mixer, a video timer, a video recorder, and a monitoring screen to mix and genlock the frontal and side views on the same screen. A third camera mixed with the side view for time synchronization video-taped all trials with a profile view from above.

b. 2.4. Graded speed test on MAD-system

For the graded speed test, the swimmers swam on the MAD-system, which allowed them to push off from fixed pads with each stroke. These push-off pads were attached to a 22-m rod and the distance between them was 1.35 m. The rod was mounted 0.8 m below the water surface and was connected to a force transducer, enabling direct measurement of push-off forces for each stroke. Assuming a constant mean swimming speed, the mean propelling force equals the mean drag force (D in N). Hence, swimming one bout on the system yields one data-point for the speed-drag curve [START_REF] Toussaint | Biomechanical aspects of peak performance in human swimming[END_REF]. Using Equation 6, the relationship between drag force and speed was established for each swimmer and thus the individual K factor was determined. The mechanical power output (P d ) was then calculated for each speed, according to Equation 9. Finally, the power output for each swimmer was assessed through the ratio P d max /K, where P d max represents the maximal power output developed at the fastest bout.

c. 2.5. Stroking parameters

The lateral view of the free swimming condition allowed the calculation of the average speed (v free in m.s - 1 ) over a 10-m distance (from 10-m to 20-m) using the swimmer's head as the marker. Over this distance, a mean period (defined as the time that separates two consecutive entries of the same hand in the water)

was determined with the video timer on three consecutive arm stroke cycles (T cycle ) taken in the 10-m central part of the pool. An average stroke rate value (SR free = 1/T cycle in Hz) was calculated. The stroke length (SL in m) was calculated from v and SR using Equation 4. The stroke index (SI) was calculated from v and SL according to Equation 5. During the MAD-system condition, the average speed (v MAD ) was calculated from the time spent to cover the 18.9-m distance between the second and last pads. The average stroke rate (SR MAD ) was calculated from the duration of each stroke, which was the time separating the push-off between two pads. As has been done previously [START_REF] Toussaint | Effect of fatigue on stroking characteristics in an arms-only 100-m front-crawl race[END_REF], the v and SR data were normalized in percentage of the maximal value reached at the fastest bout. Eight of the ten bouts performed on the MAD-system, corresponding to the same intensity of the eight bouts swum in the free swimming condition, were selected. Then the normalized v and SR were compared between the free swimming and MAD-system conditions.

d. 2.6. Coordination of arm movements

In line with [START_REF] Chollet | A new index of coordination for the crawl: Description and usefulness[END_REF], four arm phases per stroke were determined from the two underwater views recorded in the free condition. Phase A: entry and catch of the hand in the water. This corresponded to the time from the hand's entry into the water to the maximal forward coordinate of the hand, which also marked the beginning of its backward movement. Phase B: pull. This corresponded to the time from the beginning of the hand's backward movement to the hand's arrival in the vertical plane to the shoulder.

This phase was the beginning of propulsion. Phase C: push. This corresponded to the time from the hand's position below the shoulder to its release from the water. Phase D: recovery. This corresponded to the time from the hand's release from the water to its following entry into the water.

The key motor points of the arm phase were determined every 0.02 s (since f = 50 Hz) by three independent operators measuring with a blind technique, i.e., without knowing the results of the analyses of the two other operators, as previously described [START_REF] Seifert | Comparison of subjective and objective methods of determination of stroke phases to analyse arm coordination in front-crawl[END_REF]. The three analyses were then compared. When the differences were < 0.04 s, the mean of the analyses was accepted to quantify the key point. When the error was > 0.04 s, the three operators proceeded to a new assessment of the key points.

Three strokes were analyzed and the data were then averaged.

The duration of each phase was measured for each arm stroke cycle with an accuracy of 0.02 s ( 50 15)

The index of coordination (IdC) calculated the time gap between the propulsions of the two arms as a percentage of the duration of the complete arm stroke cycle [START_REF] Chollet | A new index of coordination for the crawl: Description and usefulness[END_REF]. IdC was the mean of IdC left (Equation 16) and IdC right (Equation 17): (Equation 17)

IdC left = [(
When IdC was < 0%, the arm coordination was called "catch-up" because there was a lag time between the propulsive phases of the two arms. When the propulsive phase of one arm started at the time the other arm finished its propulsive phase, the coordination was called "opposition" (IdC = 0%). In fact, the opposition coordination for IdC = 0 is theoretical; in practical terms, opposition coordination is accepted for -1% < IdC < 1%. When the propulsive phases of the two arms overlapped, the coordination was called "superposition" (IdC > 0%).

e. 2.7. Swim Efficiency

Three indicators of swim efficiency were calculated from the test in free swimming condition: (i) SI (Equation 5), (ii) the coefficient of variation (CV) of the hip intra-cyclic velocity variation (IVV), and (iii)

the efficiency of propulsion generation, i.e., the v²/u² ratio.

Concerning IVV, a video-velocity-meter device was used, as previously reported [START_REF] Schnitzler | Arm coordination adaptations assessment in swimming[END_REF].

The underwater side view was synchronized with a velocity-meter (Fahnemann 12® 045, Bockenheim, Germany, f = 50 Hz). The swimmers were connected to a very stiff cable driving an electromagnetic angular velocity tachometer. The measurements were taken using 30 m of stainless steel light cable coiled around the tachometer and connected at the distal end to a harness belt attached to the swimmer's waist.

This provided a linear velocity measurement of the hip and was relayed into a computer. For each participant, the three strokes of the 10-m central part were averaged. The corresponding time-velocity curves were filtered with Origin 5.0 software (Microcal Inc., Northampton, England, 1997) with a lowpass filter. The cut-off frequency was set at 6 Hz. The IVV was analyzed by calculating its coefficient of variation (CV) [START_REF] Alberty | Intracyclic velocity variations and arm coordination during exhaustive exercise in front crawl stroke[END_REF][START_REF] Alves | Determinants of energy cost of front crawl and backstroke swimming and competitive performance[END_REF][START_REF] Barbosa | Energy cost and intracyclic variation of the velocity of the centre of mass in butterfly stroke[END_REF][START_REF] Miller | Biomechanics of swimming[END_REF][START_REF] Schnitzler | Arm coordination adaptations assessment in swimming[END_REF] obtained from Equation 18:

CV = standard deviation / mean (Equation 18)

where mean is the mean swimming v and standard deviation is the SD of the instantaneous swimming v from the three stroke cycles.

The efficiency of propulsion generation was calculated from an adaptation of Equation 10proposed by [START_REF] Zamparo | An energy balance of front crawl[END_REF]. Instead of using SR and the total underwater part of the cycle, which includes the non-propulsive entry + catch phase in the calculation, the calculation of the tangential hand speed (u) in the present study considered (Equation 19): (i) the sum of the absolute duration (s) of the propulsive Then, according to [START_REF] Toussaint | Effect of fatigue on stroking characteristics in an arms-only 100-m front-crawl race[END_REF], the efficiency of propulsion generation (e pg ) of the arm stroke was the v²/u² ratio, assuming that v² is proportional to the drag force and u² is proportional to the propulsive force. When the swimming speed increased, assuming that propulsive force increases with drag force, the e pg should remain constant. Thus, a decrease in e pg could be indicative of a less effective propulsion "generating pattern" since a relatively higher tangential hand speed is necessary for force generation.

f. 2.8. Statistical analysis

Before using parametric statistics (Minitab 14.10, Minitab, Inc., 2003), the normal distribution (Ryan-Joiner test, equivalent to the Shapiro-Francia test) was checked and the homogeneity of variance (Bartlett test) was controlled for each variable.

For both free swimming and MAD-system conditions, the normalized v and SR were compared between the two skill groups by Student t tests. On the whole population, two-way ANOVA (condition and pace) compared the normalized v and SR between the free swimming and MAD-system conditions for the eight bouts of speed.

Two-way ANOVA (group and speed) analyzed the effect of graded speed on (i) the stroking parameters (v, SR, SL), (ii) the IdC and arm stroke phases, (iii) the swim efficiency (SI, CV, of IVV, u, v²/u²), and (iv) D and P d . When a significant main effect was obtained, a post hoc pairwise multiple comparison analysis was performed with the Tukey test to identify differences. Then, the K obtained from Equation 3 and the ratio P d max /K were compared between the two groups by Student t test.

The relationships between IdC and the other variables, and between v and the other variables, were assessed by Pearson's correlation test, as well as stepwise regression analysis. The variables entered the equation if F > 4 and removed if F < 3.96. For all tests, the level of significance was set at .05.

Results

Stroking parameters

The Student t test did not show any significant between-group differences for the normalized v and SR in the free swimming and MAD-system conditions. For the whole population, a non-significant difference of 0.6±2.2% was noted between normalized v free and normalized v MAD , while a significant difference of 15.5±8.1% was noted between normalized SR free and normalized SR MAD , F(1, 195) = 468.27, p < .05 (Fig. 1).

< < Insert Fig. 1 > >

The stroking parameters significantly changed with the increase in speed and significantly differed between groups. Indeed, v free , F(7, 96) = 94.02, SR free , F(7, 96) = 1125.67, v MAD and SR MAD , F(7, 96) = 74.57, increased through the eight bouts of speed (all p < .05), while SL decreased, F(7, 96) = 42.68, p <

.05 (Fig. 2). For these bouts, the national swimmers had greater v free , F(1, 96) = 36.44, SL, F(1, 96) = 9.74, v MAD and SR MAD , F(1, 96) = 30.85, than the regional swimmers (all p < .05) and non-significantly different SR free (Fig. 2).

Drag and mechanical power output on MAD-system

For both groups, the drag force increased through the bouts of speed, F(7, 96) = = 30.92, p < .05. This was not the case for the last two bouts where performance was at or near the maximum. The increase in speed led to a significant increase in the mechanical power output through the eight bouts, F(7, 96) = = 39.02, p < .05. For most of these bouts, greater drag force, F(1 ,96) = 5.77, p < .05, and P d , F(1, 96) = 7.81, p < .05, were noted for the national swimmers than for the regional swimmers (Fig. 3). Although the Student t test did not show significance difference in K between national (K = 25.54±5.11) and regional swimmers (K = 28.01±3.51), the ratio between P d max (at the last bout) and K was significantly higher for the national swimmers (P d max /K = 8.61±2.00) than for the regional swimmers (P d max /K = 6.44±1.10) (p < .05). Apparently the national swimmers were able to produce significantly more power output relative their drag profile than the regional swimmers.

< < Insert Fig. 3 > >

Coordination of arm movements

For both groups, IdC increased with speed, F(7, 96) = = 51.21, p < .05, except between the first and second bouts and the seventh and eighth bouts (Fig. 4). The observed changes in IdC were related to the decrease in the relative duration of the entry+catch phase, F(7, 96) = = 49.90, p < .05, and to the increase in the relative duration of both pull phase, F(7, 96) = = 36.38, p < .05, and push phase, F(7, 96) = 21.44, p < .05 (Fig. 4). The relative duration of the recovery phase did not change significantly with the increase in speed for either group and was close to 26.2±2.4%. The angle of arm propulsion (i.e., angle between the arm and horizontal axis from the beginning of pull phase to the end of push phase) did not change significantly with the increase in speed for either group and was close to 156.1±4.2°. The national swimmers had greater IdC, F(1, 96) = 33.94, p < .05, that was related to their shorter entry+catch phase, F(1, 96) = 21.23, p < .05, and longer push phase, F(1, 96) = 64.36, p < .05, which was mostly noted for the last four bouts (Fig. 4).

13

< < Insert Fig. 4 > >

Swim Efficiency

The tangential hand speed (u) increased through the eight bouts of speed [F(7,96) = 35.61; p < .05],

except between the last two bouts, while SI, the CV of IVV and v²/u² did not change significantly (Table 1). The national swimmers had greater SI, F(1, 96) = 28.17, and v²/u², F(1, 96) = 41.00, smaller u, F(1, 96) = 7.60 (all p < .05) and non-significantly different CV of IVV (Table 1).

< < Insert Table 1 > >

Relationships among variables

The results of the Pearson's correlation and stepwise regression tests studying the relationships between IdC and the other variables, and between v and the other variables, are presented in Tables 2 and3. The stepwise regression showed that SR, v²/u², drag force, and hand speed explained 95.3% of the IdC changes, while SR, v²/u² and hand speed explained 92.5% of the v changes.

< < Insert Tables 2 and3 > >

Discussion

The first aim of this study was to examine how the combined group of national and regional swimmers organized their stroke to increase v, and more particularly how the national swimmers achieved higher speed. The second aim was to explore the swim efficiency of the stroke organization in relation to the skill level and swimming speed.

Relevance of the protocol

The MAD-system was used to assess the drag force, and it was assumed that the maximal mechanical power production in the free swimming condition would be similar to the recorded power production on the MAD-system. Therefore, as shown by the normalized v (Fig. 1), all the swimmers were put in situations of equal relative effort when swimming 25-m at their maximal speed on the MAD-system and in free condition (as previously done to study the 100-m event, [START_REF] Toussaint | Effect of fatigue on stroking characteristics in an arms-only 100-m front-crawl race[END_REF], as well as when swimming the other bouts at submaximal speed. Only the normalized SR changed between the two conditions, being higher on the MAD-system due to the fixed SL (as previously observed, [START_REF] Toussaint | Effect of fatigue on stroking characteristics in an arms-only 100-m front-crawl race[END_REF]. The scale of the absolute values of v achieved in the free condition was smoothly lower than those observed in the literature [START_REF] Seifert | Swimming constraints and arm coordination[END_REF] and in competition [START_REF] Haljand | Race analysis of European Short Course Championships Debrecen[END_REF] due to the absence of leg kick in our study.

Stroke organization according to speed and skill

Drag and mechanical power output on MAD-system

Our results showed an increase in drag force with speed that led both groups to develop higher mechanical power output to overcome higher active drag. However, the national swimmers were able to develop higher mechanical power output and stroke length than the regional swimmers, which enabled them to reach higher swimming speed. This phenomenon was not due to significant differences in overall drag coefficient (drag factor: K), but could be attributed to the capacity of the national swimmers to demonstrate higher propulsive force to overcome higher environmental constraints (i.e., higher drag force). Indeed, the relative power output (P d max /K) and the absolute power output (P d ) were significantly higher for the national than for the regional swimmers.

Coordination of arm movements

As the speed increased, the temporal organization of the stroke cycle was modified. Correlation and stepwise regression showed that stroke rate is the main predictor of IdC and swimming speed changes (in accordance to [START_REF] Seifert | Swimming constraints and arm coordination[END_REF]. Indeed, for both groups of swimmers, stroke rate increased by shortening the duration of the catch+entry phase, thus at the expense of the non-propulsive underwater phase [START_REF] Chollet | A new index of coordination for the crawl: Description and usefulness[END_REF][START_REF] Seifert | Swimming constraints and arm coordination[END_REF]. In other words, both groups of swimmers favored the time dedicated to propulsion (pull + push phases) within the stroke cycle (according to [START_REF] Alberty | Stroking characteristics during time to exhaustion tests[END_REF]. In whole stroke swimming (arm + leg), superposition coordination appeared as the main solution over a critical speed of 1.8 m.s -1 and/or a critical stroke rate of 0.83 Hz [START_REF] Potdevin | Does stroke rate determine swimming velocity values and coordination[END_REF][START_REF] Seifert | Swimming constraints and arm coordination[END_REF]. With arms only, Figs. 2A and4A show that for slow speed, the swimmers adopted catch-up coordination (IdC ~ -18%). Then, above a critical speed of 1.6 m.s -1 opposition coordination was required (IdC~0%), which implies a better chain of consecutive propulsive actions in both arms. Moreover, the national swimmers demonstrated higher propulsive continuity (i.e., higher IdC) in relation to their higher stroke length, stroke index and higher efficiency of propulsion generation (i.e., higher v²/u² ratio).

Swim efficiency according to speed and skill

Throughout the eight bouts of 'free' swimming, IVV did not significantly change for either group and remained low (0.12 < CV < 0.16), while the propulsive continuity of the two arms increased. This indicated that the swimmers were able to adapt their stroke technique to minimize IVV and reach higher speed, confirming the results of previous studies in which the IVV of national swimmers did not increase with speed (0.11 < CV of IVV < 0.16) while IdC increased from -13.2±4.4% to -2.7±0.8% [START_REF] Schnitzler | Arm coordination adaptations assessment in swimming[END_REF]. The low IVV was related to higher propulsive continuity, which ensured low energy cost [START_REF] Alves | Determinants of energy cost of front crawl and backstroke swimming and competitive performance[END_REF][START_REF] Barbosa | Relationships between energy cost, swimming velocity and speed fluctuation in competitive swimming strokes[END_REF]. Indeed, through an incremental set of 200-m swims until exhaustion, [START_REF] Barbosa | Relationships between energy cost, swimming velocity and speed fluctuation in competitive swimming strokes[END_REF] confirmed that IVV is correlated with the energy cost in the four strokes, and particularly in freestyle (r = 0.62), suggesting that IVV is a relevant indicator of swim efficiency.

However, in our rather homogeneous group of swimmers no clear difference was seen in IVV.

Although the two groups showed similar low CV of IVV through the eight bouts, the national swimmers revealed greater propulsive continuity of the two arms than the regional swimmers, suggesting that if the propulsive surface and orientation are correct, a greater IdC could be associated with higher mechanical power output (as shown by the correlation and stepwise regression analyses of Tables 2 and3).

However, a greater IdC does not automatically ensure efficiency of propulsion generation and high swimming speed because swimmers can slip through the water [START_REF] Counsilman | Hand speed and acceleration[END_REF] or spend a long time in the propulsive phase due to slow hand speed [START_REF] Aujouannet | Effects of a highintensity swim test on kinematic parameters in high-level athletes[END_REF][START_REF] Seifert | Kinematic changes during a 100-m front crawl: Effects of performance level and gender[END_REF]. According to hydrodynamic theories of propulsion, the orientation, surface and speed of the body segments involved in propulsion are crucial factors to determine lift and drag force magnitudes. In our study, the motor organization of the two groups appeared adequate in relationship to the given swimming speed because it did not lead to significant changes in SI and the v²/u² ratio through the eight bouts. Nevertheless, the regional swimmers showed higher hand speed (u) for lower swimming speed (v) than the national swimmers, reflecting lower efficiency of propulsion generation (v²/u² = 0.15±0.02 for regionals vs. 0.19±0.05 for nationals), meaning that regional swimmers have to modify their technique to swim faster. Indeed, whether or not a great hand speed enables a high stroke rate and contributes to swimming speed, the stepwise regression analyses showed that v²/u² appeared as the second main predictor of a high IdC and v. Thus, in agreement with the conclusion of [START_REF] Toussaint | Differences in propelling efficiency between competitive and triathlon swimmers[END_REF], who compared triathletes and swimmers, our results suggested that a relative lack of skill and technique could lead to lower efficiency of propulsion generation. In our study, several proposals could be made to explain the lower u and greater v²/u² ratio of the national swimmers:

(i) The hand speed concerned solely the sagittal plane, so hand sweeps that may have occurred in the frontal plane were missed. The national swimmers might have preferred lift forces that resulted in greater hand sweeps which would enlarge the hand path and explain a lower antero-posterior hand speed [START_REF] Ichikawa | Relationship between kinematical parameters in the propulsive phase and the sprint performance in front crawl swimming[END_REF][START_REF] Matsuuchi | Unsteady effect on the propulsive force in the arm pull of crawl swimming[END_REF][START_REF] Schleihauf | Three-dimensional analysis of hand propulsion in the sprint front crawl[END_REF]. Indeed, using a 3-D analysis of hand trajectories recorded in a flume, [START_REF] Ichikawa | Relationship between kinematical parameters in the propulsive phase and the sprint performance in front crawl swimming[END_REF] found no significant correlation between swimming speed and either hand speed or the distance covered by the hand during the propulsive phase (considered as the backward displacement of the hand). (ii) The national swimmers could have used a greater propulsive surface by swimming with higher elbow position during the catch and subsequent propulsive phases. They may also have better oriented their hands to avoid slippage through the water. Indeed, the dropped elbow position has often been observed in less expert swimmers [START_REF] Arellano | Qualitative evaluation of technique in international Spanish junior and pre-junior swimmers: An analysis of error frequencies[END_REF], as well as slippage through water [START_REF] Counsilman | Hand speed and acceleration[END_REF], which would explain the greater hand speed than the national swimmers but the lower SL, SI and v²/u² ratio.

Conclusion

For both groups, the increase in speed led them to increase their propulsive continuity and hand speed and to apply greater mechanical power output to overcome the active drag. This adaptation of the motor organization appeared adequate because it did not lead to changes in SI, IVV or the v²/u² ratio through the eight bouts. The national swimmers appeared more efficient (i.e., higher SI and v²/u² ratio) and they also showed greater propulsive continuity (higher IdC). In addition, their higher mechanical power output enabled them to reach higher v. Conversely, the higher hand speed of the regional swimmers may have reflected hand slippage through the water, suggesting that great hand force and speed need to be associated with a correct path and orientation of the hand.

Figure Captions

Fig. 1. Comparison between free swimming (white) and MAD-system (gray) conditions for the normalized v (1A) and the normalized stroke rate (1B) at each speed the mean of the two groups; *: significant difference between the two conditions, p < .05.

Fig. 2. Effect of skill level on v free (2A), v MAD (2B), stroke rate free (2C), stroke rate MAD (2D) , and stroke length (2E). *: significant difference between national (white) and regional (gray) swimmers, p < .05.

Fig. 3. Effect of skill level on drag force (3A) and mechanical power output (3B). *: significant difference between national (white) and regional (gray) swimmers, p < .05.

Fig. 4. Effect of skill level on index of coordination (4A). *: significant difference between national (black point) and regional (white point) swimmers, p < .05. Effect of skill level on arm stroke phases (4B): entry+catch phase (gray), pull phase (white) and push phase (black). *: significant difference between national (first column) and regional (second column) swimmers, p < .05.

Figure 1. Comparison between free swimming (white) and MAD-system (gray) conditions for the normalized v (1A) and the normalized stroke rate (1B) at each speed the mean of the two groups; *: significant difference between the two conditions, p<.05. . Effect of skill level on index of coordination (4A). *: significant difference between national (black point) and regional (white point) swimmers, p < 0.05. Effect of skill level on arm stroke phases (4B): entry+catch phase (gray), pull phase (white) and push phase (black). *: significant difference between national (first column) and regional (second column) swimmers, p<.05.

Table 1. Effect of skill level on the efficiency parameters: stroke index, swimming speed / hand speed ratio, intra-cyclic velocity variation. M: mean, SD: standard deviation; *: significant difference with regional swimmers, p<.05.

Swim Bout

Stroke Index (m²/stroke/s) Tangential hand speed (u in m.s -1 )

Swimming speed / Tangential hand speed (v²/u²) Coefficient of variation of hip intra-cyclic velocity National Regional National Regional National Regional

  Hz) and was expressed as a percentage of the duration of the complete arm stroke cycle. The duration of the propulsive phases was the sum of phases B and C. The duration of the non-propulsive phases was the sum of phases A and D. The duration of a complete arm stroke cycle was the sum of the durations of the propulsive and non-propulsive phases (Equation 15). Duration Complete cycle = [(Phase A + Phase B + Phase C + Phase D) left arm + (Phase A + Phase B + Phase C + Phase D) right arm ] / 2 (Equation

  Time End of phase C for left arm -Time Beginning of phase B for right arm ) • 100] / Duration Complete cycle (Equation 16) IdC right = [(Time End of phase C right arm -Time Beginning of phase B for left arm ) • 100] / Duration Complete cycle

  phases B and C, and (ii) the angle of the propulsive phase measured between the arm (wrist-shoulder) and the horizontal axis angle from the beginning of phase B to the end of phase C. Two body marks (wrist and shoulder on the right side) were digitized with Dartfish© software (Dartfish ProSuite4.0, 2005, Switzerland) from the underwater side view to calculate the arm-horizontal axis angle at the beginning of phase B. The angle between the arm and the horizontal axis at the end of the phase C is 0°. u = [angle of the propulsion phase / (phase B + phase C)] • l (Equation 19)

  Figure4. Effect of skill level on index of coordination (4A). *: significant difference between national (black point) and regional (white point) swimmers, p < 0.05. Effect of skill level on arm stroke phases (4B): entry+catch phase (gray), pull phase (white) and push phase (black). *: significant difference between national (first column) and regional (second column) swimmers, p<.05.

  Figure2. Effect of skill level on v free (2A), v MAD (2B), stroke rate free (2C), stroke rate MAD (2D) and stroke length (2E). *: significant difference between national (white) and regional (gray) swimmers, p<.05.Figure3. Effect of skill level on drag force (3A) and mechanical power output (3B). *: significant difference between national (white) and regional (gray) swimmers, p<.05.

	160																					3A	280											3B
	0 20 40 60 80 100 120 Normalized v (%) 0.0 0.4 0.8 1.2 1.6 2.0 v free (m.s -1 ) 0 20 40 60 80 100 120 140 Drag (N) *	62.2 1 64.1 1 0.94 0.90 * 45.0 36.8 1 *	70.6 2 69.3 2 1.09 1.00 * 50.0 44.3 2 * -16.	74.9 3 74.1 3 1.15 1.06 * 58.2 51.0 3 -15.3 81.0 79.0 4 Swim Bout 89.3 87.7 5 4 5 Swim Bout 1.25 1.36 1.15 1.28 * * 63.5 79.7 61.4 76.0 4 5 * -11.9	93.0 6 92.7 6 1.44 1.31 * 88.8 88.6 6 -7.8	97.8 7 97.3 7 1.49 1.40 * 107.3 96.3 7 * -6.2 100.0 8 100.0 1A 8 1.52 1.44 2A * 111.0 101.6 * 8	1 39.8 64.1 1 1.25 1.12 * * 57.4 41.8 -2.3 0 20 40 60 80 100 120 Normalized SR (%) * 0.0 0.4 0.8 1.2 1.6 2.0 v M AD (m.s -1 ) 240 40 80 120 160 200 * Mechanical power out-put (W) -2.8 0 1	2 48.7 69.3 2 1.34 1.22 * * 68.2 54.5 * 2	3 52.6 74.1 3 1.44 1.31 * * 86.2 66.9 * 3	4 Swim Bout 5 4 5 Swim Bout 62.5 73.8 79.0 87.7 * 1.50 1.66 1.42 1.59 * * 96.8 133.2 87.7 121.4 * 4 5	6 6 83.2 92.7 * 1.74 1.68 * 155.5 150.5 6	7 7 95.2 97.3 1.88 1.72 * * 202.3 166.9 7	8 8 100.0 100.0 1B 1.93 1.77 2B * * 214.2 181.0 8
												Swim Bout																Swim Bout
		1.2																						2C		1.2											2D
		1.0																								1.0
	Stroke Rate free (Hz)	0.2 0.4 0.6 0.8	0.41	0.42	0.47	0.47	0.51	0.51	0.64	0.58	0.76	0.69	0.83	0.79	0.93	0.92	0.97	0.98	Stroke Rate M AD (Hz)	0.2 0.4 0.6 0.8	0.46 *	0.42	0.50 *	0.45	0.53 *	0.48	0.55 *	0.53	0.61 *	0.59	0.65 *	0.62	0.70 *	0.64	0.71 *	0.66
		0.0																								0.0
			1	2	3	4	5	6	7	8			1	2	3	4	5	6	7	8
												Swim Bout																Swim Bout
	Stroke Length (m)	0.4 0.8 1.2 1.6 2.0 2.4	2.30 *	2.17	2.32 *	2.10	2.27 *	2.08	1.98 *	1.98	1.83 *	1.87	1.74 *	1.68	1.61 *	1.52	1.58 *	1.47 2E
		0.0
			1	2	3		4	5	6	7	8
												Swim Bout

Table 2 .

 2 Significant correlation (r) at p < 0.05.

	National	Regional

Acknowledgments

No funding was received for this work. The authors thank Franck Bouzard for the video system assistance and Cathy Carmeni for language editing.

Conflict of interest

The authors have no professional relationships to disclose with companies or manufacturers who will benefit from the results of the present study.