This research investigates the impact of the COVID-19 pandemic on consumers’ perspectives of beauty and individual cosmetic products. Since the first confirmed case of COVID-19 was announced on December 31st, 2019, the search volumes of Google News have been updated and information on confirmed cases of the disease has been collected. This study used Python 3.7, NodeXL 1.0.1, and Smart PLS 3.0 to analyze consumer awareness of cosmetic products during the pandemic. The results reveal that consumers’ perspectives of beauty are impacted by a pandemic. Global consumers perceive skincare as an important aspect during the pandemic, while the importance of makeup fell after the outbreak. The awareness of skincare and makeup products has changed. The spread of the pandemic (SOP) has a positive impact on skincare products, but a negative impact on makeup products, except for eye makeup products, which was positive. Finally, the SOP was not significant in terms of consumers’ interest in masks. Fifth, interest in masks showed a positive relationship with interest in skincare products, such as cleansing products, while a negative relationship was observed with interest in makeup products. Overall, this study concludes that pandemics certainly have an impact on global consumers’ perspectives. As a pandemic spread, interest in skincare products increases, while interest in makeup products decreases. This study has academic significance in that it investigates the effects of consumption of cosmetic products during the stay-at-home rules. It can be used as standard information for setting marketing strategies in pandemic-like situations in the future. The coronavirus disease‑19 (COVID‑19) is an infectious disease caused by the severe acute respiratory syndrome coronavirus‑2 (SARS-CoV‑2) Babu, . As the Since consumers now have to stay in their homes longer, they are stressed over difficulties in terms of their appearance  compare the perceptions of cosmetic products before and after the outbreak of COVID-19 using social big data analysis. (2) We establish the causal relationship between COVID-19 variances and purchase behavior of cosmetic products using partial least squares structural equation modeling (PLS-SEM). From a macro perspective, this study reveals the impact of COVID-19 on consumers’ attitude toward cosmetic and skincare products. The multi-dimensional approaches used herein contribute to an in-depth understanding of consumer behavior in the COVID-19 situation.The social self is “a tug-of-war” between societal similarity and individual uniqueness Brewer, . It is aIn the past, makeup was considered the preserve of women : Pandemics will change consumers’ awareness of cosmetic products (skincare and makeup).Hypothesis 1 (H1): Spread of the pandemic (SOP) will positively influence interest in skincare products.Hypothesis 2 (H2): Spread of the pandemic (SOP) will positively influence interest in makeup products.In a pandemic-like situation, people experience death, anxiety, and depression : Spread of the pandemic (SOP) will not influence interest in face masks.Hypothesis 4 (H4): Interest in face masks will positively influence interest in skincare products.Hypothesis 5 (H5): Interest in face masks will negatively influence interest in makeup products.As one of the preventive measures, wearing a mask has become a default option during outdoor activities. In the early phase of the pandemic, there was significant interest in wearing a mask, as it was not a default option. However, before the outbreak of COVID-19, it was considered unusual behavior. More than a year since the outbreak began, mask wearing is no longer considered abnormal or special behavior. In a pandemic situation, the period during which a disease remains contagious is long time, and the interest in preventive measures shows a declining tendency  and central value were measured and then analyzed. In PLS-SEM, development of worldwide confirmed cases was used as an exogenous variable, and search volumes of individual cosmetic products was used as an endogenous variable. Python 3.7 was used to measure Tf-idf value, and NodeXL 1.0.1 was used in the network analysis stage to measure centrality. Tf-idf, a measuring standard that supplements the frequency, is normally used to judge the importance of a certain word in a corpus. Tf-idf weighting is term frequency (tf)inverse document frequency (idf). Given a collection of terms tT that appear in a set of N documents dD, each of length nd, Tf-idf, weighting is computed as shown in Eq. Term frequency-inverse document frequency  Every g is the number of actor i in networks (g − 2)/2) of the theoretical betweenness centrality , and the standardized actor closeness centrality is multiplied by g − 1 to consider the size of the entire network  TheTf-idfEquation iEquation iEquation iEquation i.Equation The occurrence of the first recorded case of COVID-19 on December 31st, 2019 until September 30th 2020 was set as the standard period for collecting data. To compare consumers’ awareness, data between December 31st, 2018 and September 30th, 2019 were also collected. Preliminary investigation was conducted before selecting keywords to be investigated. We analyzed Google News, Twitter posts, and YouTube comments containing the words “corona” and “beauty” for nine months following the outbreak of COVID-19 .As a result of preliminary investigation, according to appearance frequency, “mask” (687), “skincare” (490), “makeup” (459), and “haircare” (330) were identified as the beauty keywords related to COVID-19. In the network analysis, “skincare,” “makeup,” and “beauty” were set as the keywords. “Mask” showed a relationship with “corona,” but it also showed a strong relationship with “face” and “facial.” This suggests it may relate to medical masks and skin management masks, so it was excluded from the analysis. Google News was selected as the collecting channel as the data contained relatively less noise , “product” (315.68), “brand” (276.77), “busy” (215.22), “routine” (200.66), “industry” (142.08), “natural” (140.15), “fashion” (138.77), “trick” (133.73), and “skincare” (132.91) appeared in the upper ranks of consumers’ awareness. Although keywords such as “product” (410.57), “makeup” (389.54), “brand” (328.95), “routine” (221.11), and “skincare” (191.71) appeared in the upper ranks, keywords such as “coronavirus” (191.71) and “pandemic” (85.51) appeared in the infectious disease keywords. These results indicate that a pandemic impacts general consumers’ awareness of cosmetics. Makeup remains the most significant product that composes consumers’ cosmetic awareness, irrespective of the pandemic situation. In the case of skincare, there has been an increase in rank since the pandemic.Before the COVID-19 pandemic, keywords such as “makeup”  except closeness centrality after the outbreak. On this basis, while the influence of makeup products has decreased, that of skincare products has increased. Moreover, in the results of Tf-idf and centrality measurement, keywords of color cosmetics, such as “lipstick,” “foundation,” and “eyeshadow,” which appeared as representative keywords, did not appear in the upper ranks after the outbreak.For centrality measurement, in the case of makeup, both degree and betweenness centrality declined in consumers’ cosmetic awareness after, rather than before, the pandemic. On the other hand, skincare showed an increase in all centrality items , “mask” (47.81), “prevention” (47.50), “maskne” (46.92), “acne” (38.39), and “lockdown” (36.75) appeared as the representative keywords. In terms of consumer’s cosmetic awareness, this indicates the appearance of skin problems (or acne) caused due to wearing masks to prevent infection and the phenomena of self-care at home due to lockdown. The main products are serum (56.61/31.43), sunscreen (41.37/45.55), cream (37.61/28.58), and cleansers (24.29/45.30). Additionally, keywords such as “mask” (47.81) and “Maskne” (46.92) appear as representative keywords in cosmetic awareness, include skincare products for “acne” (38.39).The results of comparing representative keywords of individual cosmetic products before and after the pandemic are shown below. First, in the case of skincare, “self” , “lockdown” (32.80), “home” (26.39), “COVID-19” (26.39), “distance” (26.39), “maskne” (25.05), and “washing” (25.05) appeared after the outbreak. As with skincare, skin problems caused by wearing masks and cleansing the face appeared as the main interest after the spread of the disease. In addition, words related to social distancing and lockdown phenomena related to makeup started to appear. The representative products are “lipstick” (48.85/60.95), “eyeliner” (38.86/ 53.80), and “foundation” (35.07/45.26).The analysis of consumers’ cosmetic awareness of skincare and makeup products before and after the outbreak of the COVID-19 pandemic revealed keywords related to infectious disease . Therefore, it can be argued that consumers’ awareness regarding individual cosmetic products has been affected by the pandemic.R2, f2, and Q2 values , makeup products , and mask (R2 = 0.20). The values of R2 for acne, serum, and foundation are larger than R2 = 0.30. The majority of the other endogenous variables were larger than R2 = 0.20, indicating a high level of suitability.Since the confirmed cases of COVID-19 and search volume of individual cosmetic products’ keywords are measured with a single measurement object, significance and suitability, such as convergent validity, multi-collinearity, outer weights, and outer loading do not need to be judged. The PLS-SEM model is assessed by es Shin, . In invef2) in PLS-SEM is greater than f2 = 0.02, it indicates a small effect size for latent exogenous variables on latent endogenous variables. If it is greater than f2 = 0.15, it indicates a medium effect size. If it is greater than f2 = 0.35, it indicates a large effect size. The interest in cosmetic products due to the spread of disease showed foundation as (f2 = 0.53), which has an effect size larger than f2 = 0.35 and it was identified as having the largest contribution. Serum (f2 = 0.17), acne (f2 = 0.25), lipstick (f2 = 0.28), and mask (f2 = 0.25) have medium effect sizes. Sunscreen (f2 = 0.09), cleanser (f2 = 0.07), and eyeliner (f2 = 0.04) have small effect sizes. Masks, cream (f2 = 0.21), foundation (f2 = 0.24), and lipstick (f2 = 0.26) showed medium effect sizes, and the others showed small effect sizes . Next, by identifying the estimated suitability (Q2) through the blindfolding process, all Q2 values of the latent endogenous variables were larger than 0, indicating the suitability of the entire constitutive model.If the effect size , sunscreen , cream , cleanser , and acne . Therefore, it was clear that as the number of confirmed cases increased, global consumers’ interest in skincare products also increased. This result statistically proves news reports and interviews about changes in cosmetic behaviors due to the pandemic  and foundation . This is statistical proof that the sales of makeup products have decreased  showed a positively influencing relationship with regards to interest in the product. Opposite to the case of lipsticks and foundations, the eyes are still visible when wearing masks, so consumers tend to pay more attention to eye makeup, leading to the increased interest in eyeliners . In the next phase from May to July 2020, SOP also revealed a positive impact on masks , but it was lower than the previous phase. However, since the pandemic has been prolonged, the interest in masks has fallen and it seems to have levelled off. Consequently, the increase of confirmed cases may have influenced the relationship with the interest in masks. However, as the pandemic continues, it does not have a significantly influencing relationship; H3 was therefore accepted.The SOP and consumers’ interest in masks were β = 0.15, p < 0.001) and cleansing . This is similar to the background of the appearance of the word “maskne,” which proves the interest in masks has a relationship with skin problems, such as acne, caused by wearing masks. On the other hand, cream  had a significantly negative influencing relationship. Since “cream” can include moisturizing cream, BB cream, sun cream, and so on, it can be assumed that this affected the result.Although the interest in face masks did not form significantly influencing relationships with serum, sunscreen, and cream, it showed a positively influencing relationship with acne , foundation , and eyeliner . As consumers’ interest in masks increases, interest in makeup products for the entire face decreases. Therefore, H5  was accepted.Therefore, H4a, H4b, and H4c were rejected, and H4d and H4e were accepted. Meanwhile, interest in masks showed a negatively influencing relationship with lipstick . The SOP has increased consumers’ interest in skincare products, while interest in makeup products (lipstick and foundation) has decreased except for eyeliner products. This suggests that anxiety regarding of severity of COVID-19 not only affects interest in skin conditions but also that consumers seek to maintain their social self-esteem by wearing makeup on the exposed areas of their face (Gruenewald et al., The SOP did not have a significantly influencing relationship with consumers’ interest in face masks. In the early stages of increased confirmed cases, a positively influencing relationship with the interest in face masks was observed, but it did not form a significantly influencing relationship as the pandemic progressed. It is obvious that the prolonged pandemic situation makes the preventive measure ineffective compared to the early phase (Bults et al., In terms of practical contribution, this study analyzed global consumers’ macro awareness, allowing cosmetic companies to examine comprehensive opinions about consumers’ beauty habits during a pandemic. Therefore, if future pandemics have similar characteristics to the current COVID-19 outbreak, beauty companies have to pay more attention to the production of sanitary, cleanliness, and so-called trouble-care products. As consumers also consider their social self and social self-esteem as important as skincare despite the spread of pandemic, it is necessary to establish a niche makeup strategy to enable consumers to represent their own identity.This study has the following limitations. We collected data in English, which is the global official language; therefore, it is difficult to apply this study to non-English speaking countries. Newspaper articles and industrial reports were used as references to best measure the social phenomena occurring in real time, and macro data were used to encompass all consumers. Future research should be conducted with much more elaborate theories and accurate measurements. From another viewpoint, demand for cosmetic products decreased in the early stage of the outbreak, and people created new forms of beauty behaviors such as “stay-home makeup” and “makeup for Zoom meetings.” Moreover, consumers’ preferences or behaviors regarding cosmetic products are subject to change, depending on the characteristics of infectious diseases. For example, if a new pandemic is not caused by a respiratory infection, the results derived from this study cannot be applied. Subsequent studies need to analyze new beauty behaviors after COVID-19.Despite the aforementioned limitations, this study is considered important as it has statistically demonstrated that in a pandemic situation, interest in cosmetics may vary depending on their function and category. In addition, the motivations for wearing makeup could be construed as behavior of maintaining the social self. This provides the cosmetic industry some insights into the fact that consumers’ concerns about appearance in pandemic situations are diverse. Consumers are diverse and every case has customized needs for managing their societal appearance. Thus, the results have some managerial implications for the cosmetic industry in terms of which products they should focus on for production and establishing marketing strategies during pandemic situations. Moreover, as a new approach, this study expanded the generalizable scope by using macroscopic data such as social media text and volume of Google keyword searches.


Low back pain (LBP) is a burdensome problem affecting amateur cyclists. This cross-sectional study analysed Italian amateur cycling cohort’s demographic and sport-specific characteristics, the prevalence and characteristics of LBP among this population, its possible association factors, the management strategies adopted to deal with LBP and the sample’s beliefs among possible LBP triggers. A web-based cross-sectional survey was created. The questionnaire included 56 questions divided into six sections, querying the sample’s demographic, clinical, and cycling characteristics. Binomial logistic regression with a Wald backward method was performed to ascertain the effects of some covariates  on the likelihood of developing LBP in the last 12 months.A total of 1274 amateur cyclists answered the survey. The prevalence of LBP appeared to be 55.1%, 26.5% and 10.8% in life, in the last 12 months and the last 4 weeks, respectively. The final model of the logistic regression included the covariates “Sex”, “Work type”, “Cycling year”, “Being supervised by a coach or following a scheduled training”, “Other sports practised regularly”, “Specific pedal training”, “LBP before cycling”, among which “Cycling year” , “Being supervised by a coach or following a scheduled training” , “Specific pedal training” , and “LBP before cycling”  were found to be significant.The prevalence of LBP among Italian amateur cyclists seems to be less frequent compared to the general population. Moreover, undergoing previous specific pedal training and being supervised by a coach or following scheduled training drew a negative association with LBP development. This evidence highlights the importance of being overseen by specific sport figures that could offer a tailored evidence-based training to reach good physical level and to practise sports safely.The online version contains supplementary material available at 10.1186/s40798-021-00370-2. The prevalence of LBP among Italian amateur cyclists seems to be less frequent compared to the general populationFollowing specific training , being supervised by a coach or following structured training seems to be negatively associated with LBP developmentAmateur cyclists should be overseen by specific sport figures that can provide tailored and evidence-based training to practise sports safelyIn the last few years, cycling has raised policymakers’ interest, due to the reported beneficial effects it has on both people’s health  and on tIn particular, low back pain (LBP) is a common and burdensome problem for cyclists. Evidence suggests that this can be due to the fact that prolonged postures are needed to achieve proper aerodynamics aimed at increasing speed and efficiency, including maintained lumbar spine flexion, which is associated with LBP , 8. MoreThe quality of the equipment significantly affects cycling performance and efficiency , 10 sincAs for amateur cyclists, the prevalence of LBP over a long period was measured between 30 and 50%, dropping at 3–16% if measured over a short period (6—8 days) , 13. ConHowever, the data collected so far on amateur cyclists are not easily interpretable, due to the lack of standards for defining LBP, the small sample sizes analysed so far, and the different time frame in which the disease was investigated. Health professionals and physicians, who intend to become involved in the treatment of LBP in cyclists, should be aware of the plethora of issues related to this sport when assessing an injured amateur cyclist, the management strategies adopted, as well as of the possible association factors linked to LBP. In line with this, the primary aims of this study are (1) to depict an Italian amateur cycling cohort’s demographic and (2) sport-specific characteristics, (3) analyse the prevalence, and the characteristics of LBP among this sample, as well as its onset during cycling activities, (4) the management strategies  used to deal with it and the (5) possible association factors related to this pathology. Besides, the secondary aim is to (6) understand the sample’s beliefs among possible LBP triggers related to the cycling activities (e.g. set-up of the bicycle).International Handbook of Survey Methodology through distinct and iterative steps to study Italian amateur cycling cohort’s demographic and sport-specific characteristics, the prevalence and characteristics of LBP among this population, as well as its onset during the cycling activities, its possible association factors, its management and sample’s beliefs among possible LBP triggers  identified any exclusion criteria, in particular having vertebral fractures or back surgery, severe spondylolisthesis (3rd degree or greater), or suffering from any rheumatic disease. Questions 4–10  investigated the characteristics of the participants  and their lifestyle habits . Question 11–24 (3rd section—Cycling-related questions) analysed the participants’ cycling activity , their workout  some technical aspects regarding the pedalling technique , and the bicycle set-up . Questions 25–37  investigated the prevalence of LBP in life, in the 12 months, in the last 4 weeks and the characteristics of the last episode of back pain (intensity and irradiations) and if sciatica, defines as “Pain radiating down the leg below the knee in the distribution of the sciatic nerve” [Questions 37–50 (5th section—LBP and cycling) examined the presence or absence of LBP during cycling, the characteristics of this pain, the factors that participants held responsible for its origin, and their beliefs concerning any correlation between LBP and their cycling activity. Questions 51–56 (6th section—LBP management) examined the participants’ behaviours to manage their LBP.A pool of physiotherapists developed the questionnaire. Throughout the questionnaire, the definition of LBP adopted followed the guidelines for a standardised LBP definition in the prevalence studies . The quec nerve” , was preThis online questionnaire addressed amateur cyclists, i.e. people who had been practising cycling as a sport for more than one year, either at a competitive or non-competitive level, but not at a professional level. Participants were not informed in advance on the fact that the focus of the questionnaire was LBP, since cyclists who experienced this disease could have been more prone to partake in this questionnaire compared to their counterpart without LBP. Participants were informed in advance about the time required to complete the questionnaire, as well as of the anonymity of the information collected in the survey. Amateur cyclists were reached through instant messaging platforms, social network websites and mailing lists of cycling companies previously contacted by telephone. The individual’s decision to fill in the online questionnaire was spontaneous, and there was no incentive. The data were collected from 15 to 30 July 2020.p < 0.01. Based on this assessment, all continuous independent variables were found to be linearly related to the logit of the dependent variable. There was no standardised residual assessing in the casewise list. Odds ratio (OR) and 95% CI were estimated for each covariate reference category.For the analysis of the results, all the incomplete questionnaires were excluded. Descriptive analysis was carried out in order to understand the sample’s characteristics. Continuous variables were reported as mean ± standard deviation (SD), while categorical variables were reported as absolute and percentage frequencies. A prediction model with a logistic regression—Wald backward method—was performed to evaluate the impact of the covariates “Sex”  “Age” (continuous variable), “Body mass index” (continuos variable), “Sleep hours” , “Work type” , “Cycling year” , “Number of training per week” , “Stretching sessions” , “Being supervised by a coach or following a scheduled training” (dichotomous variable: yes/no), “Other sports practised regularly” (dichotomous variable: yes/no), “Number of cycling competitions per year” , “Past biomechanic visit” (dichotomous variable: yes/no), “Specific training pedal” (dichotomous variable: yes/no), “LBP before cycling” (dichotomous variable: yes/no), on the likelihood of developing LBP in the last 12 months (dichotomous variable: yes/no). The final model included the covariates “Sex”, “Work type”, “Cycling year”, “Being supervised by a coach or following a scheduled training”, “Other sports practised regularly”, “Specific training pedal”, “LBP before cycling”. Instead, the variables “Age”, “Body mass index”, “Sleep hours”, “Number of training per week”, “Stretching sessions”, “Number of cycling competitions per year”, “Past biomechanic visit” (dichotomous variable: yes/no) were deleted from the final model. The linearity of the continuous variables for the logit of the dependent variable was assessed via the Box–Tidwell procedure. A Bonferroni correction was applied using all twenty terms in the model, resulting in statistical significance being accepted when X2 = 0.225, p > 0.05), age  and BMI  are concerned when compared to those who completed the whole questionnaire. Moreover, 198 (11.4%) were excluded because of one or more exclusion criteria. Specifically: 89 people (5.1%) had vertebral fractures or back surgery, 23 people (1.3%) had severe spondylolisthesis (grade III or greater), and 106 people (6.1%) suffered from rheumatic diseases. The average time to complete the entire questionnaire was about 11 min. Thus, 1274 (mean age (SD): 43.18 (12.21); women 11%; men 89%) amateur cyclists completed the questionnaire in all its sections and were included in the analysis  completed the questionnaire entirely, 266 (15.3%) did not complete it or did not answer it. Among these, 150 (8.6%) only opened the questionnaire and 116 (6.7%) only reported the major demographic characteristics  and exited the questionnaire. These did not differ significantly as far as sex  reported suffering from LBP at least once in their life during or after a cycling session. In 32.1% of cases, LBP was presented only under load, in 54.9% of cases, it appeared after a few hours no matter the effort was, and in 13% of cases, it appeared immediately before the effort. Moreover, 150 people (25.8%) had never suffered from LBP before starting cycling, whereas 431 (74.2%) had already suffered from LBP before starting cycling. In our cohort of participants, 71.6% of cyclists reported that LBP did not coincide with a particular period of the season, 17.4% said that it coincided with a training period, 6.5% suffered from LBP during the competition period, 3% during the pre-competition period and 1.5% during the rest period. Among those who replied that LBP on bicycles coincided with a particular training period, the primary type of training to which cyclists were subjected at that time was investigated. In particular, 32.6% were riding long climbs (20–40 min) at their anaerobic threshold intensity, 22.7% were performing strength exercises with a low pedalling cadence (Resistant Strength Climb), 14.2% were riding long climbs (> 30 min) but at low intensity climbs, in 14.2% cases, it was plain training at aerobic intensity, in 7.8%, it consisted of short repetitions (2–5 min) uphill at high intensity, in 5.7%, it consisted of long repetitions (10–15 min) uphill at high intensity, and in 2.8%, they were riding maximum shots lasting between 20 and 60 s.χ2(4) = 159.81, p < 0.01. Of the abovementioned predictor variables, only five were statistically significant, as shown in Table A binomial logistic regression was performed to ascertain the effects of “Sex”, “Work type”, “Cycling Year”, “Being supervised by a coach or following a scheduled training”, “Other sports practised regularly”, “Specific Training Pedal”, “LBP before cycling” on the likelihood that participants had suffered from LBP in the last 12 months. The logistic regression model was statistically significant, The main strategies used by cyclists to reduce back pain while cycling were the following: to extend their back (54.4%), to reduce the speed of their pedalling or the intensity of the effort (11.8%), to flex their back (9.3%), to pedal faster (7.8%), to stop and get off the bike (4.7%) or to pedal harder (0.5%). However, in 11.5% of the presented cases, none of the previous strategies exposed reduced LBP while cycling. Finally, 249 participants (19.5%) reported that their LBP had affected their training somehow .Among the cyclists who have suffered from LBP in their life, 52.7% of them never turned to a professional figure to deal with their pain, whereas the remaining 47.3% did. Among these, the professional figures they turned to in order to manage their LBP were physiotherapists (63.3%), osteopaths (50.0%), physicians (38.1%), biomechanics , masseurs (25.5%) and chiropractors (12.2%).Among the cyclists who suffered from LBP in their life, 35.8% took medications to reduce their pain at least once. The most common drugs used were non-steroidal anti-inflammatory drugs , analgesic drugs (13.0%) and cortisone (7.7%). Among those who took drugs, 70.7% said that their physician had prescribed them, 4.5% said that friends or family recommended the drugs, and the remaining 27.8% said they had taken medicines on their initiative.Finally, the participants who declared that they had suffered from back pain were asked if they had ever practised bodyweight exercises to strengthen their back: 22.2% of these had never practised this type of exercises, 29.0% practised them sporadically, 18.2% practised them only in specific periods of the year, 22.7% practised them once or twice a week, and 7.9% practised them almost every day.As far as the perceived correlation between LBP and equipment is concerned, 31.3% of the surveyed population stated that, while riding, LBP arose as a result of a change in the set-up of the bicycle  or a change of some component of the bike itself .Among the cyclists who outlined a possible correlation between LBP and cycling activity, 56.0% believed that cycling does not affect LBP in any way, 26.3% believed that cycling negatively affects LBP, and 17.7% believed that cycling positively affects LBP. Finally, 34.5% of those who, at least once in their lifetime, had suffered from LBP during or after cycling, thought that the position on the bicycle might be the cause of LBP.As far as the prevalence of LBP among amateur cyclists is concerned, our study conveyed that 55.1%, 26.5% and 10.8% of amateur cyclists reported suffering from LBP in life, in the last 12 months and the last 4 weeks, respectively. In line with these results, amateur cyclists seem to have less frequent LBP than the general population, whose lifetime prevalence of non-specific (common) LBP is estimated to be between 60 and 70%, with a one-year prevalence between 15 and 45% and a 4 weeks prevalence of 30.8 –23. It i, since it needs to be tailored on the individual’s capacity, taking into account muscular tissues load resistance without overloading them. Consistent with this, when compared to our data, the annual prevalence reported by professional cyclists (58%) is significantly higher [As a matter of fact, the physical activity is not beneficial per sey higher . These rWhen compared to other sports, one notices that the prevalence of LBP in life among amateur cyclists is similar to what has been found among rowers (64.7%) . These tTraining errors, such as the ones that may occur in the pedalling technique, seem to be major risk factors in cyclists when it comes to pathologies such as patellofemoral pain syndrome and Achilles tendinopathy , 4. HoweSome hypotheses that may explain why pedalling training is a negative association factor for LBP are that a pedalling technique that provides a more uniform delivery of force throughout the pedalling cycle  contribuAs far as being supervised by a coach or following a training programme is concerned, these aspects could be a negative association factors for the LBP as they both involve a planning of training loads, both in terms of intensity, volumes and frequency. The progressiveness and adequacy of training loads are at the basis of the reduction in the risk of onset of LBP , 35. FurIn our sample, 47.3% of the cyclists, who suffered from LBP in their life, turned to a professional figure  to try to solve their disease. Our sample differs from the general population, among which only about 15–20% patients with LBP sought professional intervention . HoweverAs far as pharmacological therapy is concerned, 35.8% of the cyclists with LBP declared using pain relief medications.. These data stand in contrast with the what has been retrieved when looking at the general population and the elite athletes with LBP, among whom 69.4% and more than 50.0%, respectively, reported using pain relief medication , 39. HowSome limitations of this study need to be discussed. First of all, the cross-sectional nature of the study did not allow for an evaluation of the causative relationship between LBP and technical cycling characteristics. Moreover, possible recall biasses may have taken place since some of the information requested was retrospective. Thus, future prospective cohort studies with specific outcome measures evaluating the impact of the different musculoskeletal disorders from which this population seems to suffer  are necessary –46. SecoThis study is the first one to investigate LBP among amateur cyclists starting from an evidence-based definition of LBP, and which deeply depicts the demographic, clinical and technical cycling characteristics of this population. The main results of this study show that amateur cyclists seem to be less subjected to LBP compared to the general population and that undergoing specific training  and being overseen by a coach or following a scheduled training could reduce the possibility of developing LBP. These results bring to the forefront the importance of physical activity as a means to maintain a good level of physical health and its preventive role in the development of pathological conditions, such as LBP. Nevertheless, our results also highlight the fact that physical activity should be individualised and bespoke to one’s needs and capacity in order to set adequate goals and avoid overuse injuries.Additional file 1. Translated version of the questionnaire provided to Italian amateur cyclists.


It has been shown that there is no information on absorption coefficient values for filter materials operating in a two-stage “multi-cyclone–porous partition” separation system. Original methodology and conditions for determining dust absorption coefficient (mk) of a separation partition, operating under the conditions of two-stage filtration, were presented. The following characteristics were tested: separation efficiency, filtration performance, and pressure drop characteristics of three different filtration partitions. These were A (cellulose), B (cellulose and polyester), and C , working individually and in a two-stage system—behind the cyclone. Granulometric dust composition dosed into the cyclone and cyclone downstream was determined. During tests, conditions corresponding to air filter’s actual operating conditions, including separation speed and dust concentration in the air, were maintained. For the pressure drop values, the dust absorption coefficient (mk) values of three different filtration partitions , working individually and in a two-stage system—behind the cyclone—were determined experimentally.Pollutant properties in intake air to internal combustion engines were analyzed. Mineral dust particles’ influence on accelerated engine components’ wear was discussed. Dust concentration values in the air under various operating conditions in trucks and special vehicles were presented. The idea and necessity for using two-stage filters, operating in a “multi-cyclone–porous partition” system for vehicles operated in dusty air conditions, are presented. Information from the literature information has been presented, showing that impurities in small grain sizes reduce fiber bed absorbency. It has been shown that such a phenomenon occurs during filter material operation, located directly behind the inertial filter (multi-cyclone), which off-road vehicles are equipped with. It results in a greater pressure drop intensity increase and a shorter proper filter operation period. It has been shown that filter material selection for the motor vehicle air filter requires knowledge of the mass of stopped dust per filtration unit area (dust absorption coefficient  Air flow, sucked in by the internal combustion engine, depends in direct proportion to the engine’s displacement (ssV), rotational crankshaft speed (n), and cylinder filling degree (υη)—the values of which depend on engine type  and charge air cooler presence. As examples of the maximum, theoretically determined air demands for a given engine, see the following: Peugeot 306 Sedan 1.9 D—about 220 m3/h; Volkswagen T4 1.9 TDI—about 385 m3/h; BWP-1 infantry fighting vehicle—about 1250 m3/h; Scania R420 6 × 4—around 1650 m3/h; T-72 tank—around 3400 m3/h; Leopard 2A1—around 6000 m3/h.A basic working medium component in every internal combustion engine is air taken from the atmosphere. The amount taken in depends proportionally on engine power. In piston engines, about 700 kW of power is obtained from 1 kg/s , the piston, and the piston sealing ring are most exposed to abrasive wear. Abrasive wear to engine elements is intensified by mineral particles with sizes in the range 1–40 µm. However, most aggressive are dust particles, whose size does not exceed 20 µm ,4,5,6. Ezd) of equivalent size as the oil film thickness (minh) between two surfaces at a given moment. Oil film thickness, in connections lubricated with engine oil, depends on operating engine conditions , temperature, and oil viscosity. For this reason, oil film assumes various values, most often in the range of minh = 0–10 µm .Filtration speed is conventional average speed, defined as quotient of air stream flowing through the filter cartridge and filter paper active surfaces. Maximum filtration speed (Fmaxυ) is the basic criterion used when selecting active surface (cA) filter paper for car engine air filters. Experience has shown that this factor is not sufficient to ensure required air filter operating time, and thus vehicle mileage. The significant air filter working time limitation is achieved by the filter flow resistance permissible value (Δfdopp)—this being the criterion for the end of its life. Filter operation time to obtain the Δfdopp value depends not only on filtration speed (air stream) in porous partition, but also on its absorption, which directly depends on filter material structure and dust grain sizes.The maximum filtration speed (pd = 80 µm. In a two-stage air separation system (multi-cyclone–filter paper) in truck engines and special vehicles, “after passing” through the cyclones, dust has a substantially different fractional composition; then, dust grains of much smaller sizes (not exceeding pd = 15–35 µm) are transferred to the second separation stage (paper filter) [fdopp value much earlier, with a smaller retained dust mass. Such a phenomenon was observed during the experiments in [A single-stage filter, the filtering element of which is most often a pleated filter paper cartridge, along with air, sucks up dust grains directly from the environment, with dimensions not exceeding the value of  filter) ,54,55,56ments in ,59,60,61ments in ,63 fibroments in ,65.mk = 400 g/m2) and for loading it obtained the value of 7 kPa. Dust with larger particle sizes of 0–20 µm caused a lower intensity increase in pressure drop of the tested bed, hence the value of 7 kPa was obtained for the larger value of mk = 800 g/m2. A similar phenomenon was observed during tests of a synthetic bed, with three dusts with different granulometric compositions: dust with a size of 0–10 µm, AC fine (0–80 µm), and AC Coarse (0–200 µm) [Fυ = 0.05 m/s and a determined pressure drop value of 0.25 kPa, bed loading with dust was mk = 125 g/m2, mk = 165 g/m2 and mk = 360 g/m2, respectively. For greater separation velocity (Fυ) values, bed dust loading—for a predetermined pressure drop value—assumes, irrespective of dust type, proportionally lower and lower values due to a more intensive increase in pressure drop.For example, the authors of  investig–200 µm) . The smafp = 5 kPa), loading the filter bed with dust takes the following values: mk1 = 75 g/m2, mk2 = 210 g/m2, mk3 = 310 g/m2, and mk4 = 560 g/m2.In , changesmk = 32 g/m2, and for 1.40 µm particles it is mk = 53 g/m2, which is almost twice as much.It was shown in  that a f2 dust with different diameters, as follows: pd = 52, 103, 310, and 553 nm. Fine dusts caused a more intensive increase in bed pressure drop than coarse dusts. Dust grains with the size pd = 52 nm cause the bed to achieve a pressure drop of Δfp = 0.6 kPa when loaded with dust, mk = 1.2 g/m2. With the increase in dust grains size, bed loading with dust increases for smaller and smaller pressure drop (Δfp) values. The bed into which dust size pd = 553 nm was dosed, obtained a dust load of mk = 5.5 g/m2 with a pressure drop of Δfp = 2.5 kPa.The authors of  presente3. Results showed that dust load depends on particle size distribution and filter type. Submicron particles cause filter beds pressure drop to increase much faster than when SAE Fine dust particles are operating. Moreover, cellulose filters with a layer of very fine fibers on the surface showed the fastest increase in pressure drop due to dust loading.The authors of  tested s3, and coarse Arizona dust with the chemical composition of SiO2 (65–75%), Al2O3 (11–17%), Fe2O3 (2.5–5%), Na2O (2–4%), CaO (2–5%), MgO (1–2%), and TiO2 (0.5–1%). They found that pressure drop was strongly dependent on the ratio of fine to coarse particles.The authors of  examinedmk = 1.5 mg/cm2 (mk = 15 g/m2). Such a pressure drop value on the filter bed for Arizona dust (coarse) was obtained for a much higher dust load mk = 15 mg/cm2 (mk = 150 g/m2). The greater the mass ratio of fine particles to coarse particles, the faster the pressure drop increased. If filter bed received only fine dust, a pressure drop of 850 kPa was obtained for dust loading g = 2.5 mm, operating in the conditions of one-stage and two-stage filtration, using the multicyclone of axial flow cyclones.The authors of  conductepmaxd = 80 µm was used. A permissible pressure drop value Δwp = 5 kPa was achieved by the non-woven filter element operating in the conditions of single-stage filtration with dust absorption coefficient m1k = 700 g/m2, i.e., with a value twice as high as in the conditions of two-stage filtration—m2k = 325 g/m2 [pd < 20–35 µm)—is 50% lower than that of the non-woven fabric on which dust flows directly from the environment (pd < 80 µm).Polydisperse dust with particle size 325 g/m2 . Thus, tg = 0.56 mm, operating in the conditions of one-stage and two-stage filtration. A single axial flow cyclone was used as the first separation stage. Polydisperse dust with particle size pmaxd = 80 µm was used. Working in the conditions of single-stage separation, dust absorption coefficient of the tested filter paper, with the resistance value of Δwp = 5 kPa, reaches following values: mk = 278 g/m2 for standard dust and mk = 210 g/m2 when the paper element worked as the second filtration stage.The authors of  conductefp value much earlier and with a smaller retained dust mass per unit of filtration area—lower dust absorption coefficient value (mk). This phenomenon occurs during operation of two-stage air filter “multi-cyclone–paper partition”, where large-size dust grains are retained by the multi-cyclone, and small ones are directed to filtration partition. Therefore, for the proper design of a two-stage air filter, it is necessary to know the dust absorption coefficient mk of the filter material, determined in the conditions of two-stage filtration. Coefficient mk value is particularly important when forecasting the distance traveled by the vehicle until the filter reaches the permissible flow resistance value Δfdopp. Filter material producers do not provide such data, only providing the following paper structure parameters: pore size, air permeability, and thickness. There is no data on filtration properties with dust use, in particular, filter bed dust absorption, i.e., dust mass per material unit area. Such data can be obtained during numerical tests as well as experimental material samples. Experimental research is costly and labor intensive; however, it is the most reliable research method. The problems of small-grain dust separation in a pleated (non-woven) paper filter, working directly downstream of an inertia filter, is not sufficiently researched or described in the available literature. In order to fill the gap in this respect, this paper presents an experimental determination methodology of the dust absorption coefficient of any filter material operating in a two-stage system—directly after the inertial filter. The methodology consists in examining the separation characteristics of any material sample, working directly downstream of a single cyclone in laboratory conditions, while maintaining the flow conditions of an actual air filter.The above data shows that the dust absorption of the barrier for small grains is much lower than when the barrier is loaded with large-grained dust particles. When small-sized dust flows with the air onto the porous barrier , grains retained on the fibers form expanding dendrites that fills free spaces (pores) between the fibers, creating a more compact and thus less permeable structure. Pressure drop increases more rapidly as a result of lower air permeability through the dust layer. Therefore, the filter obtains a Δmk)—of three different filter materials formed into a cylindrical cartridge , but with different filter material chemical composition. Filter material A was cellulose. Filter material B was a composite of cellulose and polyester layer. Filter material C is a composite of cellulose, polyester, and nanofiber layer.The subjects of the research were filter inserts  of the sA—cellulose;B—cellulose and polyester;C—cellulose, polyester, and nanofibers.The characteristic parameters of the tested filter materials are summarized in GQ stream:w = fφ(mk);separation efficiency zmax = fd(mk);filtration performance w = fp(mk);pressure drop Δwhere mk—dust absorption coefficient, defining the total dust mass (zm), retained and evenly distributed over 1 m2 of active filter material surface, which is expressed by the following:The test’s scope of filter materials A, B, and C, working in the “cyclone–filter cartridge” system, without a cyclone, included the determination of the following characteristics, with a fixed value of the Tests were carried out on the stand , the verD = 36 mm; total length H = 124 mm; outlet pipe internal diameter wd = 23.5 mm; four-blade steering wheel  caused a slow increase in separation efficiency. After reaching maximum value of cmaxφ = 90.9% at GQ = 27.47 m3/h, it decreased. Air stream change in the range of GQ = 7.32–36.62 m3/h caused a continuous increase in pressure drop to the value of Δc =p 638 Pa (cφ = f(GQ) and Δc = fp(GQ), were consistent with research results provided in the literature [Increase in the air stream = 638 Pa . Such chterature ,54,56,59GQ = 27.47 m3/h. This is the value at which the cyclone, during preliminary experimental tests, obtained maximum separation efficiency , an intensive increase in cyclone separation efficiency, but only up to a certain value (m0 = 12–18%) [m0, the increase in cyclone separation efficiency was not so intense, but there was a significant increase in cyclone flow resistance resulting from the increasing flow velocity.Assumed value  12–18%) ,67. WithGQ), to the tested filter cartridge. Directly behind the cartridge there was a measuring line, to which the end of the U-tube water pressure gauge line was connected, used to measure the filter cartridge pressure drop (Δwp). The measuring cable ends with a filter that protects the rotameter against dust getting into it, and at the same time is a measuring filter used to collect the AGm dust mass passed through the test filter cartridge and, consequently, to determine cartridge separation efficiency w.φDust that hasd not been separated by the cyclone was directed, along with the main air stream  behind tested filter cartridge. As soon as measurement was started, air and dust were sucked into the Pamas 2132 particle counter. The particle counter sensor registered the number and size of dust grains in the air stream (GQ) behind the tested filter cartridge. Particle analysis was carried out in the range of zakresie 0.7–100 µm in i = 32 measuring intervals, which were limited by diameters (pimind–pimaxd).A dust probe tip was mounted centrally in the axis at a distance of 6w = fp(GQ) in the air stream range GQ = 7.32–36.6 m3/h.Before starting filter inserts tests with test dust use, their flow characteristics were performed Δw = fφ(mk) and filtration performance pmax = fd(mk)—were determined indirectly using the gravimetric method. For air stream QG = 27.47 m3/h, dust mass retained on the tested filter element Fzm, the absolute filter Am, and dust mass dosed into the Dm system in successive measurement cycles (j) with a specific duration (pτ) were determined. Measurement duration was determined as pτ = 120 s in the initial period (I) and pτ = 240–480 s in the second (II) period of filter cartridges operation. Dust mass retained on tested filter cartridge, the absolute filter, and the dosed mass were determined with an analytical balance with a measuring range of 220 g and an accuracy of 0.1 mg.Cartridges filtering characteristics—separation efficiency During the measurement cycle (60 s before scheduled end of measurement), the procedure for measuring the number and dust grains size in the air after the filter cartridge was started in the particle counter.j), measurements were made in quantities that allowed filter cartridge operating parameters calculation: dust absorption coefficient, filtration efficiency and accuracy, and flow resistance.fjp) was determined as the drop in static pressure before and after the filter on the basis of the measured (after the end of dust dosing) height (Δmjh) on a U-tube water manometer.Filter cartridge pressure drop (ΔFzjm) retained by the filter element and dust mass (Fdjm) supplied to the filter element during the next measurement cycle j based on the following:Filter element separation efficiency was determined as the quotient of dust mass (3.mjk) of tested filter material was determined from the following:Dust absorption coefficient (4.ziN) in the air stream after the filter  was determined in measuring intervals limited by diameters (pimin–dpimaxd).Dust grains number (5.pjd = pmaxd) in the air stream after the filter.Filtration performance was defined as the largest dust grain size , filtration performance zmax = fd(mk), and pressure drop Δw = fp(mk) of A, B, and C filter elements, operating in a single and two-stage system. Tests were carried out until the filter cartridge reached the assumed permissible resistance value Δfdopp = 2.5 kPa.According to the above methodology, the following separation characteristics were determined: separation efficiency wp = f(wQ)) of cartridges with different types of filter materials are shown in Flow characteristics testing results (ΔThe C cartridge with a three-layer (cellulose–polyester–nanofibers) filter material obtained the highest pressure drop value in the entire air stream range. Cellulose filter medium is characterized by the lowest pressure drop, which results from its high permeability in relation to other materials.mk) function characteristics, including filtration efficiency (w= fφ(mk)), flow resistance (Δw = fp(mk)), and filtration accuracy (zmax = fd(mk)) were obtained during filter material A tests (cellulose). Two variants of filter element operation A were tested: in a single-stage system (without cyclone) and in a two-stage system, as the second stage of filtration (after passing through the cyclone).mk). φ = 99.5% by the inserts. After the first measurement cycle, the effectiveness of A cartridge (cellulose) working without a cyclone reaches value of wφ = 93.9%, and when working with a cyclone, cartridge efficiency is much lower and amounts to wcφ = 53.6%—Obtained characteristics differ significantly in terms of the course and values. Due to the achieved separation efficiency values, tested cartridge working time can be conventionally divided into two periods. The first period  is characterized by small separation efficiency values, which systematically increase (sometimes very rapidly) with the amount of dust mass retained by filtration bed, and thus with an increase in dust absorption coefficient (pmaxd) (from 40 µm to 6 µm) in the GQ outlet stream and lasts until the mk = 11.9 g/m2 coefficient is reached  in the fibrous bed. For this reason, filter element working after cyclone reaches determined separation efficiency value faster than 5–99.98% .pmaxd = 40 µm in the air behind the A filter cartridge, tested in the cyclone unit , the grain diameters of zmaxd assume smaller and smaller values. They faster decrease in diameter occurs for contribution tested in set with a cyclone  in the outlet stream from filter cartridge A (cellulose) working in the “cyclone–cartridge” set is shown in pd and their zN number. As dust grains size increases, their number decreases until they disappear completely. Grains (or a single grain) in the last dimensional range have the largest size pd = pmaxd (pmaxd) in exhaust air stream from test filter cartridge expresses filtration performance of filter material in the next measuring cycle (j). Additionally, for comparison, a number of test dust grains corresponding to the individual size ranges are shown, in a cyclone inlet stream (line 1) and in a cyclone outlet stream–inlet to filter cartridge , which were compared with dust particle size composition in cyclone inlet stream, which is test dust.Dust grains number pU dust grains in the outlet stream from filter cartridge take larger and larger values for increasingly larger grain sizes, followed by their decrease. This changes nature in numerical shares of pU is similar to particle size composition of dust dosed into the cyclone—test dust (pmaxU = 15.8% for dust grains with size pd = 2 µm. For the first measurement (mk = 0.506 g/m2), maximum dust grains share in the air behind filter element takes greater value, pmaxU = 23.1%. In subsequent measurements, maximum particle size assumes ever greater values, but for ever smaller dust particles. For mk = 9.85 g/m2 (measurement no. 25), numerical dust grains share has value pmaxU = 34.5% for pd = 1 µm. In last measurement (mk = 99.5 g/m2), maximum dust grains number pmaxU = 44.9% occurs for pd = 0.7 µm, while dust grains share above pd = 2 µm is only pU = 1.1%.Numerical fractions of est dust . MaximumThe above phenomenon is caused by the fact that tested filter bed (A—cellulose) is characterized by high permeability. In initial filtration period, mainly larger dust grains are retained. However, as dust accumulates in filter bed, voids (pores) fill up in it.mk), pressure drop Δp of tested filter inserts is systematically growing all the time. This is due to the dendrites formed on the fibers and growing to large sizes, which fill free spaces between the fibers.Along with the increase in dust mass retained by the filter material , is more intense, despite smaller dust mass retained by the bed. This is because small-sized dust particles form dendrites on the fibers that grow faster when bed is loaded with smaller particles. Small-sized dust grains, the number of which is much greater when cartridge is operated with a cyclone, penetrate into filter paper structure much more easily and fill it more tightly compared with grains with larger diameters. Free spaces created between the anchored dust particles of small sizes are much smaller than in case of large dust particles, which makes aerosol flow velocity through them higher, and thus pressure drop increases.d) made of regularly arranged spheres, where d is also sphere diameter.Mineral dust grains have irregular, lumped shapes. Therefore, for simplicity, during theoretical considerations, equivalent grain diameters are assumed. Most often, it is grain diameter, which is shaped like a sphere. V1) between spherical particles equals cube volume (V) minus volume 2V, occupied by particles according to the following equations:For the model shown in V1 between spherical dust grains depends only on grain diameter (d) in the third power. After combining successive volumes V1 between the particles, a channel is obtained, with an assumed diameter (εd), through which air flows. According to Equation (10), for particles with smaller diameters (d), space volume between particles (V1) assumes smaller and smaller values. For a bed composed of particles with equivalent diameter of d = 80 µm, space volume (V1) takes value, as follows:Presented Equation (10) shows that space volume V1) between particles with equivalent diameter d = 40 µm  has value V1(40) = 30,506 µm3, and thus is 8 times smaller. For the diameter of d = 8 µm, space volume V1(8) is 1000 times smaller, and for d = 2 µm, V1(2) is 64,000 times smaller.Accordingly, space volume (Q (separation velocity Fυ), flowing through the filter bed made of particles with smaller diameters, the actual velocity (ευ) in the channels between the particles assumes higher and higher values. Therefore, pressure drop (Δp) of the filter bed loaded with small-diameter dust particles will assume even greater values in accordance with modified Darcy Weisbach formula.ρ—fluid density; λ—friction coefficient; wg—filter bed thickness; εd—conventional channels diameter formed by particles; ευ—actual velocity in channels between particles.For the same air stream value Ac) to its volume (cV) expresses the following relationship:Moreover, small-sized dust grains have a higher surface to volume ratio. Therefore, they get a greater pressure drop per unit volume–particles mass. Spherical particle ratio surface , pressure drop Δw = fp(Dm), and filtration performance pmax = fd(Dm), as dust mass function Dm is supplied to the filter element A, operating in one-stage and two-stage “cyclone–cartridge” separation system.Presented characteristics show that working time of “cyclone–cartridge” unit reaching permissible resistance (2.5 kPa) is three times longer than that of the same single working cartridge. It happens despite the fact that filter element in two-stage system obtains much lower dust absorption.When an inertial filter (multi-cyclone) is used as the first filtration stage before the paper filter cartridge, the vast majority of supplied dust (in case of tested set—about 80% of dust mass) is retained by the multi-cyclone. Thus, only 20% of dust mass, which was introduced into the “multicyclone–partition” separation system, goes to filter cartridge. Cyclones are characterized by the fact that they are able to trap large dust masses from the stream of flowing aerosol, but with low efficiency and accuracy. Retained dust is accumulated in settling tank, which must be periodically removed, or it is continuously removed outside the vehicle by dust extraction system. Therefore, multicyclone pressure drop (at a constant stream of flowing air) is unchanged, in contrast to barrier filter materials, where dust mass retention causes an increase in pressure drop.w= fφ(mk)), filtration performance (pmax = fd(mk)), and pressure drop (Δw = fp(mk)) as a function of dust absorption coefficient mk of filter material C tested in the “set filtration“ as a second filtration stage downstream of the through-flow cyclone and without the cyclone. Tests were performed as a function of dust absorption coefficient (mk) according to same methodology as filter element A tests. Filter material C is a composite of cellulose, polyester, and nanofibers layer  than when it works in a single-stage system (without a cyclone). In case of material C, on filter bed surface there is nanofibers layer on which surface filtration and faster accumulation of dust layer take place. Permeability of dust layer made of small dust grains is much lower due to their tight mutual adhesion and easier penetration into the structure of the filter paper compared with grains with larger diameters. For this reason, pressure drop increases more intensively, and a set value of 2.5 kPa for the filter cartridge C, working in a set with a cyclone, reaches a dust absorption coefficient of pmaxd) in the air stream downstream of C cartridge working in “filter set” initially assume considerable dimensions (measurement no. 1 pmaxd = 12.5 µm) which results from greater proportion of small-diameter dust grains in the air, but with the accumulation of dust in the bed, they quickly assume lower and lower values. After reaching absorption coefficient mk = 6.15 g/m2, they are in range pmaxd = 1–3 µm. In the same period, in air stream downstream of the C element working in a single-stage system (without a cyclone), maximum dust grains diameters zmaxd assume much greater values in the range pmaxd = 2–10 µm.Maximum dust grains diameters (w= fφ(mk), filtration performance pmax = fd(mk), and pressure drop Δw = fp(mk), as a function of dust absorption coefficient mk of filter materials A, B, and C tested in the “filter assembly” as the second stage of separation downstream of through-cyclone. Characteristics were performed as a function of dust absorption coefficient (mk) according to the same methodology, maintaining same test conditions.wφ = 99.5% than filter cartridge made of material A (cellulose), and thus the initial filtration period of the B and C filter material lasts a much shorter time. Maximum dust grains diameters in the air stream after the B and C inserts assume much smaller sizes  than after the A insert—pmaxd = 50 µm. This makes use of B and C filter materials more favorable in real engine operating conditions.Presented tested filter materials characteristics A, B, and C  differ iwp = 2.5 kPa for mk = 99.5 g/m2.As dust mass retained on filter cartridges increases, value and pressure drop intensity of filter cartridges increase, resulting from different properties of filter materials A, B, and C . The leawp = 2.5 kPa, the B and C cartridges are achieved with absorption coefficient mk = 57.2 g/m2, which is 50% less than cartridge A. This is due to the fact that cartridges B and C use composite filter materials, unlike cartridge A, which has a conventional cellulose bed.The most intense (parabolic)—but only in the first filtration period—increase pressure drop was recorded for the B element. With particle deposition increase on sample B (cellulose and polyester), there is a slow exponential increase in pressure drop, until a linear trend is reached, the slope of which is the same as pressure drop of linear A trend (cellulose) and C (cellulose–polyester–nanofibers) cartridge—pmaxd = 25 µm and pmaxd = 17.5 µm, respectively) than after the A insert—pmaxd = 50 µm. This makes the use of B and C filter materials more favorable for real engine operating conditions. However, it is related to increased frequency of filter inserts replacement, resulting from a more intensive increase in pressure drop and permissible resistance achievement Δfdopp.After the first measurement, maximum dust grains diameters in air stream after the B and C inserts assume much smaller sizes (mk)—of three different filter materials, formed into a cylindrical cartridge, which worked individually (one-stage system) and directly after the axial flow cyclone (two-stage system) with the same constant separation speed Fυ = 0.045 m/s. The aim of the study was to compare the characteristics of several filter media types when loaded with different dust grain size range and to show that, if dust with small grain sizes flows onto the filter material, it has an impact on separation process and filter material characteristics. Such a case occurs when filter element works in a two-stage system of air inlet filtration to the “multi-cyclone–porous partition” engine. During the experiment, original methodology was used, which consisted in the fact that filter cartridge material, which worked behind the cyclone, was filled with dust. It was stripped of large grains, whose grain size composition was changed and shaped as a result of the actual air filtration process in the cyclone.This paper presents an experimental filtration properties evaluation—of the separation efficiency, filtration performance, pressure drop, and dust absorption coefficient (mk) knowledge of the filter material working directly after the inertial filter as the second filtration stage.Analysis was performed in the context of using research results to design paper filters partitions for trucks. Air filter selection for a truck engine requires dust absorption coefficient . This is related to a more intensive pressure drop increase and has a direct impact on filter operation time limited by permissible resistance achievement, and thus on vehicle mileage.φ = 63–92%) tested filter materials A, B, and C efficiency and large (zmaxd = 17.5–50 μm) dust grains presence in purified air in the initial operation period is fibrous materials characteristic feature which has been demonstrated. In real operating conditions of air filter and engine, this may have a direct impact on accelerated engine couplings wear that cooperate in the form of a tray, especially piston–piston rings–cylinder (P–P–C).Low  before the main filter can improve entire filtration system performance by extending the main filter’s service life, despite a decrease in its absorption capacity due to small-sized dust grains inflow.As a result of the research, the following conclusions were formulated:


Background and Objectives: This study aimed to compare the calculated running velocity at the anaerobic lactate threshold (cLTAn), determined by a mathematical model for metabolic simulation, with two established threshold concepts  and modified maximal deviation method (mDmax)). Additionally, all threshold concepts were correlated with performance in different endurance running events. Materials and Methods: Ten sub-elite runners performed a 30 s sprint test on a cycle ergometer adjusted to an isokinetic mode set to a cadence of 120 rpm to determine maximal lactate production rate (VLamax), and a graded exercise test on a treadmill to determine maximal oxygen uptake (VO2max). Running velocities at OBLA, mDmax, and cLTAn were then compared with each other, and further correlated with running performance over various distances . Results: The mean difference in cLTAn was −0.13 ± 0.43 m∙s−1 and −0.32 ± 0.39 m∙s−1 compared to mDmax (p = 0.49) and OBLA (p < 0.01), respectively. cLTAn indicated moderate to good concordance with the established threshold concepts . In comparison with other threshold concepts, cLTAn exhibited comparable correlations with the assessed running performances . Conclusion: Our data show that cLTAn can be applied for determining endurance performance during running. Due to the consideration of individual physiological profiles, cLTAn offers a physiologically justified approach to assess an athlete’s endurance performance. An), which is generally considered to be a good indicator of individual aerobic endurance performance and can be used for prescribing endurance training intensities [Determination of the blood lactate response during exercise is among the most widely used performance diagnostic tools ,2. Bloodensities ,9.An. Most LTAn concepts are usually applied to lactate performance curves derived from graded incremental exercise tests [An concepts use either fixed lactate concentrations [An has shown to be strongly dependent on the applied test protocol [An concepts have been questioned [In recent decades, researchers have developed several concepts to determine LTse tests . Most extrations ,10 or intrations ,12 as thprotocol ,14 and oprotocol , which iestioned .Lactate production and removal are ongoing processes, which are closely related to metabolic rate but not necessarily to oxygen delivery ,6,16,17.An may be influenced by aerobic  or anaerobic (glycolytic) capacity  separately [2max and VLamax can result in two identical lactate performance curves with equal LTAn [An), at which the extent of lactate formation by glycolysis is exactly equal to the maximal elimination rate of lactate by combustion. Thus, no lactate accumulation in blood lactate over time occurs  was then compared with other established experimentally determined LTAn concepts. Additionally, we aimed to validate cLTAn against the athlete’s recent performance in endurance running events.Based on Mader’s approach, Hauser et al.  applied  of MLSS . However of MLSS  has only of MLSS . Therefoand Heck  and Hausand Heck . The cal2max = 69.8 ± 6.7 mL∙kg−1 min−1, VLamax = 0.39 ± 0.09 mmol L−1 s−1) participated in this study. Prior to signing the written informed consent of the investigation, all participants were informed about the experimental procedures. The protocols used in this investigation were approved by the Ethics Committee of the university and are in line with the Declaration of Helsinki.Ten sub-elite male middle- and long-distance runners . Participants were instructed to arrive in the laboratory in a rested, 2 h postprandial, and well-hydrated state. They were ordered to avoid strenuous exercise for at least 24 h before the test.max. After a 60 min break, a graded exercise test on a treadmill (second test) was performed to determine VO2max and running velocity at the onset of blood lactate accumulation  [An was determined according to the calculation scheme described by Mader and Heck [An, OBLA, and mDmax as indicators of endurance performance, running velocities at each concept were compared with the participant’s performance (average velocity (m·s−1)) over various distances . One participant did not provide performance data, so only data from nine participants were included in correlation analysis.First, the participants performed a 30 s isokinetic sprint test on a cycle ergometer with subsequent measurements of whole-blood lactate concentration for the determination of VLaon OBLA;  mmol∙L−1mol∙L−1) . The cLTand Heck , and sub−1 body mass. After an additional passive rest for 5 min, a 30 s sprint test was performed on a cycle ergometer adjusted to an isokinetic mode set to a cadence of 120 rpm [max was calculated using the following equation [peak (mmol L−1) is the peak post-exercise lactate concentration, Larest (mmol L−1) is the resting lactate concentration, texerc (s) is the duration of exercise, and talac (s) is the period at the beginning of exercise in which no lactate formation is assumed. According to Heck et al. [talac was set to 5.5 s for all participants.The participants first performed a 10 min standardized warm-up at 1.5 W kg 120 rpm ,26. Partequation :VLamax   and breath-by-breath expired gases  were continuously measured throughout the test. The VO2max corresponded to the highest value measured (moving average of 30 s) during the test.The graded exercise test was performed on a treadmill , which started at 2.4 m s−1 [Blood lactate concentrations during the incremental tests were plotted against running velocity and then fitted by a third-order polynomial function. Running velocity at OBLA was set as the point at which blood lactate concentration reached 4 mmol∙L−1 .An, the oxidative and glycolytic energy production depending on exercise intensity must initially be known, which can be expressed as the activity of oxidative phosphorylation (VO2ss) and glycolysis (VLass), respectively [To determine cLTectively . The theectively ,22.2ss and VLass. Since there is no simple and practical procedure for measuring free ADP concentration, the ADP-dependent equations in the previous study were transposed into VO2ss-dependent equations [2ss” represents the steady-state oxygen consumption at a constant work rate [2ss in relation to exercise intensity based on the assumption of a linear relationship between oxygen demand (VO2) and workload. Thereby, a constant value for VO2 per 1 W (Ks4 = 11.7 mL O2 W−1) was used for all participants based on the data of previous cycling experiments [2 in running is more affected by an athlete’s exercise economy  than in cycling. Running economy was shown to be influenced by several physiological and biomechanical factors [Ks4 (mL kg−1·min−1 per 1 m∙s−1 running velocity) individually, by plotting VO2 during incremental tests against running velocity. The Ks4 corresponded to the slope of linear regression (y = mx + b) between VO2 and running speed .−1) is the running velocity, VO2rest (mL kg−1 min−1) is the resting oxygen uptake, and Ks4 is the constant value of the relationship between oxygen demand and the running velocity .After determining the individual 2ss (from resting level to VO2max), it is possible to calculate VLass (lactate formation) as a function of VO2ss, as demonstrated in the following equation:max (mmol L−1·s−1) is the maximal glycolytic rate, VO2max (mL kg−1 min−1) is the maximal oxygen uptake, VO2ss (mL kg−1 min−1) is the steady-state oxygen consumption, and Ks1 and Ks2 are the 50% activity rate constant of oxidative phosphorylation (0.0631) and glycolysis (1.331), respectively [By knowing VOectively .oxmax) which depends on VO2ss can also be calculated based on the experimentally estimated value of lactate equivalent , lactate distribution volume [oxmax (mmol L−1 min−1) is the maximal lactate elimination rate as a function of the steady-state oxygen consumption  [Furthermore, the maximal lactate elimination rate  .2 and 0.4 L H2O per kg body weight, respectively. Thus, simulating the simultaneous lactate formation and elimination depending on the metabolic rate or running speed can be carried out based on the individual VO2max and VLamax value, as well as body weight. cLTAn is defined as the running velocity at which the lactate formation is exactly equal to elimination .According to Hauser et al. , lactateAn concepts were determined using one-way repeated measure ANOVA with Bonferroni correction for post hoc tests. Statistical differences were considered to be significant for p ≤ 0.05. To estimate the practical relevance, effect sizes  were calculated for the main effect. According to Cohen [ηp² ≥ 0.01 indicates small effects, ≥0.059 medium effects, and ≥0.138 large effects. To display the concordance between the LTAn concepts, Bland–Altman plots were constructed. Furthermore, the intra-class correlation coefficients (ICC) were calculated based on a single-measure two-way mixed-effects model. For evaluating the degree of agreement between cLTAn vs. OBLA or mDmax, the “absolute agreement” type of analysis ) was chosen. For the comparison of each LTAn concept vs. 3000 m, 5000 m, or 10,000 m, we chose the “consistency” type of analysis ). According to Koo and Li [For statistical analysis of the data, the software IBM SPSS version 24  was used. Descriptive statistics of the data are presented as means ± standard deviation (±SD). The normal distribution and the variance homogeneity were verified using the Shapiro–Wilk test and Mauchly test of sphericity, respectively. Statistically relevant differences between the three LTto Cohen , a ηp² ≥o and Li , the dego and Li .An concept are presented in Individual values of maximal metabolic performance tests and individual running velocities at each LTAn concepts with a large effect . Post hoc analysis using Bonferroni correction revealed that running velocity at OBLA was significantly higher compared to cLTAn and mDmax (p < 0.01). No significant difference was found between running velocity at cLTAn and mDmax (p = 0.49). The cLTAn indicated a high correlation with OBLA  and mDmax . Between OBLA and mDmax, there was a very high correlation .Repeated measures ANOVA showed a significant difference between LTAn was −0.13 ± 0.43 m∙s−1 and −0.32 ± 0.39 m∙s−1 compared to mDmax and OBLA, respectively. The intraclass correlation coefficient comparing cLTAn with mDmax showed a good agreement (ICC = 0.87), whereas a moderate agreement was shown between cLTAn and OBLA (ICC = 0.74).According to the Bland–Altman Plots , the mea−1, 5.37 ± 0.26 m s−1, and 5.03 ± 0.26 m s−1, respectively. cLTAn and mDmax indicated moderate to high correlations with running performance over all distances observed , whereby OBLA had the poorest correlations  compared to other concepts in most cases (An (ICC = 0.75–0.86) and mDmax (ICC = 0.82–0.88) with running performance over all distances observed, whereas OBLA showed only moderate concordance (ICC = 0.68–0.80) in most cases.The mean running velocities over the distances of 3000 m, 5000 m, and 10,000 m were 5.65 ± 0.29 m sst cases a. The inst cases b also reAn in running by adapting the mathematical model for metabolic simulation previously described by Mader and Heck [An demonstrated moderate to good concordance with the established concepts in determining the running velocity at LTAn. Although cLTAn provided lower running velocity compared to mDmax and OBLA, the correlation of cLTAn with the endurance running performance was similar compared to mDmax and even better compared to OBLA.The purpose of this study was to determine cLTand Heck  and Hausand Heck . cLTAn dr = 0.66–0.92) between various LTAn concepts and performance in endurance running competitions and therefore justified the practical application of those concepts in sports diagnostics. Even though cLTAn did not indicate significantly superior results, its good concordance (ICC = 0.75–0.86) with mDmax and OBLA, as well as comparable correlations (r = 0.61–0.76) with competition performance, can support its applicability as a valid indicator to assess an athlete’s endurance performance.One of the relevant criteria for the practical application of a laboratory test parameter is its relationship with competitive performance. A comprehensive review by Faude et al.  demonstrAn) incorporates the influence of individual VO2max, VLamax, and Ks4 on LTAn, as well as their combined effects [Ks4 values are dependent on individual exercise economy, expressed by the relationship between energy demand and running velocity [2max, running economy has been shown to be a crucial indicator of distance running performance [2max: 80.3 vs. 80.1 mL kg−1∙min−1, VLamax: 0.33 vs. 0.31 mmol L−1 s−1); however, participant 3 displayed a much higher speed at LTAn regardless of the used LTAn concept (Ks4 (13.2 vs. 14.2 mL kg−1 min−1 per 1 m s−1). A recent training study used the metabolic simulation-model-detected training-induced changes in single performance capacities . The authors reported specific explanations of changes in endurance performance (MLSS) [The metabolic simulation model  , which hAn concepts, cLTAn systematically provides lower running velocities in our study . However, the mean time to exhaustion of our test protocol was ~38 min, which is significantly longer than the “optimal” test duration for assessing VO2max, as suggested by previous studies [2max, achieved with the same graded exercise test protocol as in our study, was significantly lower (on average 2 mL min−1 kg−1) than assessed by incremental tests with shorter test duration (ranged from 7–11 min). Hauser [2max  leads to a 44% increase in calculated MLSS in cycling. Indeed, cLTAn is increased by ~0.2 m s−1 when the participant’s VO2max is increased by 2 mL min−1 kg−1 , and thus the difference between running speed at cLTAn and the other LTAn is reduced (data not presented). To solve the underestimation of VO2max, further work should use a VO2max verification bout [2max and the individual Ks4 at the same time, as two core parameters of the metabolic simulation model.Despite the moderate to good agreement with other LTur study . This di studies ,38,39. S studies  reported. Hauser  showed tion bout ,42 or a ion bout . Such prAn and other LTAn concepts could be the run-nonspecific test procedure for the assessment of VLamax and its influence on cLTAn. The cycling sprint test is an established anaerobic test for nearly all sports disciplines. Thus, we determined the participant’s VLamax using an isokinetic cycle sprint [max, is dependent on the exercise modality used in tests [max determination exists. Just recently, Quittmann et al. [max and sprint performance parameters using a running sprint test. However, this study used fixed distances, rather than a fixed time for the sprint test, which might influence VLamax determination. Whether and how VLamax estimation and cLTAn determination would be affected by applying a running-specific anaerobic test procedure remain to be clarified.Another potential contributing factor to the difference between cLTe sprint ,23,36,44n et al.  attempte2ss contributes as a core parameter to the calculation of both the lactate formation and elimination rate at any given running velocity, it is necessary to determine VO2ss (from resting level to VO2max) as precisely as possible. For the determination of VO2ss, the relationship between oxygen demand and running velocity (Ks4) plays an important role [Ks4 value considering the inter-individual variation in the running economy. Typically, it is assumed that there is a linear relationship between VO2 and workload. This has been supported by several investigations indicating a nearly invariant oxygen cost of transport  over a range of running speeds (2.0–4.0 m s−1) [An intensity and not till exhaustion. Daniels and Daniels [2max [An intensity, differ between athletes, and how they affect the LTAn, is unclear. With respect to the previous model in cycling [Ks4 from a linear fit to calculate VO2ss in our study. However, there is abundant space for further progress in analyzing the relationship between metabolic rate and running velocity and its influence on cLTAn determination. For instance, a curvilinear fit suggested by Batliner et al. [An intensity, which might consequently lead to an improved performance prediction of cLTAn.Since VOant role . In contant role , we indi0 m s−1) ,47. Howe Daniels  suggestels [2max . These f cycling , we, ther et al.  might be2max, VLamax, and Ks4), which are also relevant quality criteria for the application of the cLTAn. However, previous research in cycling already demonstrated a very high reliability for both VO2max and VLamax, as well as the calculated MLSS from these two parameters [In addition to the above methodological limitations, it is important to note that our data did not address the basic variability and reproducibility of each physiological measure (VOrameters . FurtherAn) provides an insight into the complex interplay of single metabolic systems and their influence on endurance performance. This allows a differentiated interpretation of the athlete’s performance, which could be useful for establishing training interventions targeting and eliminating specific weaknesses in the physiological profile of an athlete.The present study suggests that the mathematical model for metabolic simulation could be applied to assess an athlete’s endurance performance in running by considering multiple physiological parameters. Considering multiple physiological measures, the metabolic simulation model  revealed a moderate to good agreement with other established concepts. However, the velocity at cLTAn was lower with regard to the other LTAn concepts. With regard to the compared LTAn concepts, comparable and partially better correlations between cLTan and the endurance performance of sub-elite middle- and long-distance runners were found.The metabolic simulation model considers different metabolic parameters to evaluate an athlete’s performance profile. In determining running velocity at LT


This view provides an information-theoretic interpretation of T cell activation that explains a range of experimental observations. Based on this analysis, we propose that effective T cell therapeutics may be enhanced by optimizing the inherent stochasticity of TCR-pMHC binding dynamics.Adaptive immune responses depend on interactions between T cell receptors (TCRs) and peptide major histocompatibility complex (pMHC) ligands located on the surface of T cells and antigen presenting cells (APCs), respectively. As TCRs and pMHCs are often only present at low copy numbers their interactions are inherently stochastic, yet the role of stochastic fluctuations on T cell function is unclear. Here, we introduce a minimal stochastic model of T cell activation that accounts for serial TCR-pMHC engagement, reversible TCR conformational change and TCR aggregation. Analysis of this model indicates that it is not the strength of binding between the T cell and the APC cell  T cell Each TCR has a short intracellular domain that, alone, does not have the capacity to initiate signalling . ConsequThree or four main mechanisms have been proposed to initiate signalling events following pMHC-TCR binding ,6,14–18,It is likely that not one mechanism alone is responsible for the initiation of signalling events . For exaIndeed, there is increasing evidence that T cell activation can be induced by as few as approximately 1–10 pMHC ligands ,36,40–42per se, but rather by the information conveyed to the T cell by the encounter, as assessed by the entropy rate of the TCR-pMHC binding dynamics. We validate this hypothesis against a range of experimental studies, including a number of dose–response datasets, before discussing the implications for T cell based therapeutics.Here, we develop a minimal stochastic model of the TCR-pMHC binding dynamics that includes serial TCR-pMHC engagement, reversible TCR conformational change and TCR aggregation. We show that, collectively, these three mechanisms are both necessary and sufficient for the T cell to convert stochastic fluctuations in the TCR-pMHC binding dynamics into a well-defined signal. Based on this analysis, we propose that the T cell response to an APC is not determined by the strength of TCR-pMHC binding . 2. 2.1To start, we will introduce some information-theoretic notions in the context of a simple model of TCR-pMHC binding, before discussing how they apply to a more realistic model of T cell activation.L denotes the pMHC ligand, R denotes the TCR, B denotes the TCR-pMHC complex, koff is the rate of unbinding, kon/ν is the rate of binding he Although we have focused on the T cell response, the simplicity of our model means that an information-theoretic perspective of receptor–ligand binding could have application to a wide range of other therapeutics. For instance, experimental evidence for binding-induced conformational change that subsequently induces aggregation and clustering not only exists for the TCR  but has . 4. 4.1Bmax and Umax denote the smaller and larger, respectively, of the total number of pMHC ligands, Lmax, and total number of TCRs, Rmax, given byIn the context of the reactions of equation , let BmaBmax is also the maximum number of TCR-pMHC complexes. The stationary probability distribution of the TCR-pMHC complex number, p(B), is given byKd is given by equation . Combining Kd ∈  and kon/ν ∈  s−1. Lmax ∈ . We extended the upper limit of Lmax by an order of magnitude because many dose–response studies consider a wider range of doses . Finally 10–100 –21,33,34. 4.3RI, binding with a pMHC ligand, L, to form a TCR-pMHC complex, B. Equation , , 2.7),  and 2.92.9 modelequation . Furtherequation  models td was calculated via repeated stochastic simulations of the reactions given in equations (RI(0) = Rmax = 10 and RA(0) = B(0) = S(0) = 0. The unbinding rate, koff, was fixed at 1/s and the binding rate, kon/ν, was varied between 10−4/s and 10−1/s to give the values of Kd shown in the legend as calculated via equation (S(t) > 104 or t > 104 s and then the signalling rate was calculated as The mean signalling rate shown in figure 3quations –2.10) a ad was cequation . Each st® functions that provide robust computational calculations for the key equations have been made available at https://github.com/josephrobertegan/fluctuations.The deterministic solutions of equations –2.10) a a2.10) a. 4.4The assay was performed as previously detailed ,107. In T cells were cultured at 37°C, 6/ml in Opti-MEM serum-free medium containing mRNA for the 1G4 TCRα, TCRβ and CD3ζ chains at 2 μg/106 cells and electroporated at 300 V, 2 ms in an ECM 830 Square Wave Electroporation System (BTX).T cells were resuspended at 25 × 106/ml in 12-well plates with 1 ml of differentiation medium containing 50 ng ml−1 interleukin 4  and 100 ng ml−1 granulocyte–monocyte colony-stimulating factor  for 24 h. For maturation, the following cytokines were added for an additional 24 h: 1 μM prostaglandin E2 , 10 ng ml−1 interleukin 1β , 50 ng ml−1 tumour necrosis factor α  and 20 ng ml−1 interferon γ .Monocytes were enriched using a RosetteSep kit (Stemcell Technologies) and cultured at 1 − 2 × 10. 4.5Monocyte-derived dendritic cells (moDCs) were pulsed with a titration of different variants of the NYE-ESO157–165 as in . Loading. 4.6c.Human interleukin 2 (IL-2) Ready-SET Go! ELISA kit (eBioscience/Invitrogen) and Nunc MaxiSorp 96-well plates (Thermo Fisher) were used according to the manufacturer’s instructions to test appropriately diluted (commonly fourfold) T cell supernatant for secretion of IL-2. The mean of three independent experiments is shown in figure 4