Muscle strength is important for health and can affect how well people live, even increasing the risk of death in adults and older people. The one-repetition maximum (1RM) test is relatively easy compared to other tests and is commonly used to measure muscle strength in various groups, including healthy individuals and those with chronic diseases. It assists in prescribing resistance training and understanding training results. Knee extensors, especially the quadriceps femoris, are often studied because they play a key role in standing and walking. However, there are no standard reference values or equations for measuring knee extensors using the 1RM test. The existing methods rely on the evaluator's judgment, making them hard to replicate and standardize. The goal of this study is to provide reference equations and values for the 1RM of knee extensors and to establish a standardized methodology for the test.

The project consists of two phases: in order to develop the final standardized 1RM protocol, a pilot study (phase 1) will be conducted to identify the best objective load to start the 1RM attempts. The protocol will then be defined according to the results of the pilot study, and the main study (phase 2) will be initiated using this protocol.

The one-repetition maximum test (1RM) will be conducted using a leg extension machine (MacSport, Sigma). This test aims to determine the maximum weight that can be lifted in a single movement by the tested muscle group (in this study, knee extensors) through its full range of motion and without compensatory movements. The knees should be aligned with the axis of the equipment (adjust the backrest if necessary), and hands should firmly grip the handles. The equipment will be set so that individuals start the knee extension from a 90 degree flexion and extend until reaching a 0 degree flexion. Standardized verbal encouragement will be given during the tests.

All recruited individuals, both those participating in the pilot study (phase 1) and those in the main study (phase 2), will be evaluated at two different moments. In the first evaluation (pilot study test 1, or pilot study T1), participants will be assessed for anthropometric data, presence of comorbidities, self-reported regular physical activity, cognitive screening and knee extensor muscle strength using the 1RM test, following the protocol proposed by the authors (details below). Specifically for the pilot study, which is a methodological study aimed at identifying the best initial load for the first 1RM attempt, three initial load options based on body weight (40%, 60%, and 80% of body weight) will be randomly assigned via envelopes. The pilot study will include 72 individuals in total, distributed across six age groups with an average interval of ten years (i.e., 18-29, 30-39, 40-49, 50-59, 60-69 and 70-80 years). Each age group will have 12 participants, with four performing the first 1RM attempt at 40% of body weight (two men and two women), another four at 60% of body weight (two men and two women), and the remaining four at 80% of body weight (two men and two women). This way, participants will be evenly distributed among age groups, gender and percentage of body weight for the initial 1RM attempt. In the assessment of the pilot study (pilot study T2), 48-72 hours after the first assessment pilot study T1, individuals will be re-evaluated for knee extensor strength (following the same protocol and the same percentage of body weight as in pilot study T1) to investigate the reproducibility and familiarization (e.g., learning affect) of the test.

The porposed protocol for the pilot study will follow this sequence: (1) warm-up with a set of 10 repetitions with a light load (20% of body weight); (2) two minutes of rest; (3) the frist attempt will be with the percentage of body weight randomly chosen before the start of the pilot (i.e., 40%, 60% or 80% of body weight); (4) the load progression will be based on the Likert scale of difficulty from 1 to 5 (1-Very easy, 2-Easy, 3-Moderate, 4-Very difficult, and 5-Extremely difficult); responses from 1 to 3 will have an increment of 20% of the last load, and responses from 4 to 5 will have an increment of 10% of the last load. Individuals will have two minutes of rest between each progression; (5) if the attempt is unsuccessful, the load should be decreased by 5% or 10%; upon success, this will be the 1RM value, and upon failure, the 1RM will be the last value successfully lifted; (6) the 1RM value should ideally be obtained in 4 to 6 attempts, provided that the last attempt is not the highest value. As mentioned earlier, after 48-72 hours, individuals will perform the pilot study T2 following the same protocol and initial load drawn in pilot study T1. The best initial load for the 1RM test will be the one that allows reaching the highest 1RM value in the fewest attempts in the best tests conducted in pilot study T1 and pilot study T2, as long as they fall within the range of 4 to 6 attempts.

After the completion of the pilot study with the result of the best initial load for the 1RM test, the main study will begin and follow the same protocol previously proposed. However, it will use the best percentage of body weight identified as the ideal initial load in the pilot study during both main study tests (main study T1 and main study T2). In both the pilot and main studies, the same evaluator should perform the test in both T1 and T2, allowing for the analysis of intra-evaluator reproducibility and avoiding potential inter-evaluator bias. The 1RM value used for analysis will be the highest value obtained from the evaluations in main study T1 and main study T2.

The sample size will be calculated based on the pilot study. The variable used for the calculation will be knee extensor strength, as this is the main outcome of the study. A power of 80% and an alpha of 0.05 will be adopted.

Microsoft Excel 2010 (Microsoft, USA) and SPSS 21.0 version (IBM, USA) will be used for data tabulation and statistical analysis, respectively. The Shapiro-Wilk test will be used for the analysis of normality in data distribution. Data with normal distribution will be described as mean ± standard deviation and statistically treated with parametric tests, whereas data with non-normal distribution will be described as median [interquartile range 25-75%] and statistically treated with non-parametric tests. To identify the best initial load for the 1RM test in the pilot study and to compare different age groups, one-way ANOVA or Kruskal-Wallis test with Dunn's post hoc test will be used when necessary. Pearson or Spearman coefficients will be used to identify simple correlations between the 1RM test and anthropometric variables, while multiple linear regression analysis will be used to establish reference equations. A value of P<0.05 will be adopted as statistical significance, except for the multiple linear regression model where variables showing a correlation with 1RM of knee extensors up to P<0.20 will be included in the model.

Inclusion Criteria:

• Individuals aged between 18-80 years of both sexes;
• Absence of any condition (e.g., orthopedic, neuromuscular, cardiorespiratory) that may limit the assessment or directly interfere in its results.

Exclusion Criteria:

• Failure to complete the proposed assessments for any reason;
• A score on the Mini-Mental State Examination lower than18 for illiterate individuals and lower than 24 for literate individuals;
• Body mass index (BMI) lower than 18 kg/m2 and higher than 40 kg/m2;
• The manifestation of the desire to leave the study at any time for any reason.

Apparently healthy individuals from the local community, as well as students, employees of the involved institution and their families will be recruited, provided they do not have any condition that may limit the performance of the knee extensor muscle strength testing and/or do not have contraindications for its execution.