this was a cross - sectional study of obese ( bmi , > 95th percentile for age and sex ) pubertal adolescents recruited from an obesity clinic in the children s hospital of philadelphia . exclusion criteria included having previously diagnosed diabetes or sleep disorders , genetic syndromes affecting glucose tolerance or sleep , or major organ system illness , or taking medications affecting insulin or glucose metabolism . the protocol was approved by the children s hospital of philadelphia institutional review board ; informed consent was obtained from the parents or guardians , and assent was obtained from the participants . demographic data and medical history were obtained from guardians and participants . physical examination , including pubertal ( tanner ) staging , was performed by a study investigator . weight was measured using a digital scale ( scaletronix , white plains , ny ) . height was measured using a wall - mounted stadiometer ( holtain inc . , crymych , u.k . ) . bmi was calculated as weight ( kilograms ) divided by height ( meters ) squared . bmi percentiles and z scores were assessed using age- and sex - specific reference data ( 13 ) . after a 12-h overnight fast , an oral glucose tolerance test ( ogtt ) was performed : subjects ingested oral glucose solution ( 1.75 g / kg , maximum 75 g ) , and blood samples for glucose and insulin were obtained at 10 , 0 , 10 , 30 , 60 , 90 , 12 , 150 , and 180 min . hemoglobin a1c ( hba1c ) was also measured . the following morning , after an overnight fast , subjects underwent a frequently sampled intravenous glucose tolerance test ( fsigt ) : infusion of 0.25 g / kg of 25% dextrose intravenously over 30 s , infusion of regular human insulin ( 0.015 units / kg i.v . ) over 5 min at t = 20 min , and drawing of blood samples for glucose and insulin at t = 5 , 2 , 4 , 8 , 19 , 22 , 30 , 40 , 50 , 70 , 100 , and 180 min . plasma glucose levels were measured by the glucose dehydrogenase method ( hemocue analyzer ; hemocue inc . , cypress , ca ) . plasma insulin levels were measured by radioimmunoassay ( linco , st . charles , mo ) . the minmod millenium software program ( 14 ) homeostasis model assessment of ir ( homa - ir ) is a validated measure of insulin sensitivity ( 15):insulinogenic index ( igi ) is a measure of insulin secretion that has been validated in children against the hyperglycemic clamp ( 16):whole - body insulin sensitivity index ( wbisi ) is an insulin sensitivity measure that has been validated in obese children and adolescents ( 15 ) : homeostasis model assessment of ir ( homa - ir ) is a validated measure of insulin sensitivity ( 15 ) : insulinogenic index ( igi ) is a measure of insulin secretion that has been validated in children against the hyperglycemic clamp ( 16 ) : whole - body insulin sensitivity index ( wbisi ) is an insulin sensitivity measure that has been validated in obese children and adolescents ( 15 ) : higher wbisi levels indicate greater insulin sensitivity . acute insulin response to glucose ( airg ) is a parameter of early pancreatic response to glucose , calculated as the mean incremental plasma insulin concentration over baseline in the first 8 min of the fsigt ( 14).sensitivity to insulin ( si ) is a parameter calculated from serial insulin and glucose values during the fsigt ( 14 ) . acute insulin response to glucose ( airg ) is a parameter of early pancreatic response to glucose , calculated as the mean incremental plasma insulin concentration over baseline in the first 8 min of the fsigt ( 14 ) . sensitivity to insulin ( si ) is a parameter calculated from serial insulin and glucose values during the fsigt ( 14 ) . signals were recorded on a computerized system ( rembrandt ; rescare , buffalo , ny ) . the following parameters were recorded : electroencephalogram ( c3/a2 , c4/a1 , o1/a2 , and o2/a1 ) ; right and left electro - oculograms ; submental electromyogram ; tibial electromyogram ; electrocardiogram ; chest and abdominal wall motion by inductance plethysmography ; oronasal pressure / airflow ( nasal pressure cannula with oral thermistor bead ; pro - tech , woodinville , wa ) ; end - tidal pco2 , measured at the nose by infrared capnometry ( nellcor n-1000 ) ; arterial oxygen saturation ( sao2 ) by pulse oximetry , and oximeter pulse waveform . studies were reviewed by a single sleep board - certified investigator ( l.j.b . ) , who had no knowledge of subjects metabolic status . sleep architecture ( n1 , n2 , n3 , and rem sleep stages ) and respiratory disturbances ( including the apnea - hypopnea index [ ahi ] , arousal index , and lowest oxyhemoglobin saturation [ lowest sao2 ] ) were scored using standard pediatric criteria ( 17 ) . histograms and one - sample kolmogorov - smirnov tests were used to assess normality of distribution of continuous variables . pearson or spearman correlations were used to examine associations between sleep architecture or osa measures and parameters of glucose homeostasis and insulin secretion and sensitivity . hierarchical linear regression procedures were used to evaluate the aforementioned relationships while controlling for potential confounding variables ( e.g. , degree of obesity and osa ) . assumptions of linearity were tested by examining plots of the standardized residuals as a function of standardized predicted values . where curve estimation procedures uncovered curvilinear relationships , polynomial regressions were conducted . analysis of covariance ( ancova ) models were used to examine differences in the outcome variables between sexes and among different pubertal stages , controlling for covariates . as we tested three underlying hypotheses relating to the relationship between sleep architecture and insulin secretion and sensitivity and overall glycemia , we used an adjusted p value of < 0.017 ( 0.05/3 ) for statistical significance . demographic data and medical history were obtained from guardians and participants . physical examination , including pubertal ( tanner ) staging , was performed by a study investigator . weight was measured using a digital scale ( scaletronix , white plains , ny ) . height was measured using a wall - mounted stadiometer ( holtain inc . , crymych , u.k . ) . bmi was calculated as weight ( kilograms ) divided by height ( meters ) squared . bmi percentiles and z scores were assessed using age- and sex - specific reference data ( 13 ) . after a 12-h overnight fast , an oral glucose tolerance test ( ogtt ) was performed : subjects ingested oral glucose solution ( 1.75 g / kg , maximum 75 g ) , and blood samples for glucose and insulin were obtained at 10 , 0 , 10 , 30 , 60 , 90 , 12 , 150 , and 180 min . after an overnight fast , subjects underwent a frequently sampled intravenous glucose tolerance test ( fsigt ) : infusion of 0.25 g / kg of 25% dextrose intravenously over 30 s , infusion of regular human insulin ( 0.015 units / kg i.v . ) over 5 min at t = 20 min , and drawing of blood samples for glucose and insulin at t = 5 , 2 , 4 , 8 , 19 , 22 , 30 , 40 , 50 , 70 , 100 , and 180 min . plasma glucose levels were measured by the glucose dehydrogenase method ( hemocue analyzer ; hemocue inc . , cypress , ca ) . homeostasis model assessment of ir ( homa - ir ) is a validated measure of insulin sensitivity ( 15):insulinogenic index ( igi ) is a measure of insulin secretion that has been validated in children against the hyperglycemic clamp ( 16):whole - body insulin sensitivity index ( wbisi ) is an insulin sensitivity measure that has been validated in obese children and adolescents ( 15 ) : homeostasis model assessment of ir ( homa - ir ) is a validated measure of insulin sensitivity ( 15 ) : insulinogenic index ( igi ) is a measure of insulin secretion that has been validated in children against the hyperglycemic clamp ( 16 ) : whole - body insulin sensitivity index ( wbisi ) is an insulin sensitivity measure that has been validated in obese children and adolescents ( 15 ) : higher wbisi levels indicate greater insulin sensitivity . acute insulin response to glucose ( airg ) is a parameter of early pancreatic response to glucose , calculated as the mean incremental plasma insulin concentration over baseline in the first 8 min of the fsigt ( 14).sensitivity to insulin ( si ) is a parameter calculated from serial insulin and glucose values during the fsigt ( 14 ) . acute insulin response to glucose ( airg ) is a parameter of early pancreatic response to glucose , calculated as the mean incremental plasma insulin concentration over baseline in the first 8 min of the fsigt ( 14 ) . sensitivity to insulin ( si ) is a parameter calculated from serial insulin and glucose values during the fsigt ( 14 ) . homeostasis model assessment of ir ( homa - ir ) is a validated measure of insulin sensitivity ( 15):insulinogenic index ( igi ) is a measure of insulin secretion that has been validated in children against the hyperglycemic clamp ( 16):whole - body insulin sensitivity index ( wbisi ) is an insulin sensitivity measure that has been validated in obese children and adolescents ( 15 ) : homeostasis model assessment of ir ( homa - ir ) is a validated measure of insulin sensitivity ( 15 ) : insulinogenic index ( igi ) is a measure of insulin secretion that has been validated in children against the hyperglycemic clamp ( 16 ) : whole - body insulin sensitivity index ( wbisi ) is an insulin sensitivity measure that has been validated in obese children and adolescents ( 15 ) : higher wbisi levels indicate greater insulin sensitivity . acute insulin response to glucose ( airg ) is a parameter of early pancreatic response to glucose , calculated as the mean incremental plasma insulin concentration over baseline in the first 8 min of the fsigt ( 14).sensitivity to insulin ( si ) is a parameter calculated from serial insulin and glucose values during the fsigt ( 14 ) . acute insulin response to glucose ( airg ) is a parameter of early pancreatic response to glucose , calculated as the mean incremental plasma insulin concentration over baseline in the first 8 min of the fsigt ( 14 ) . sensitivity to insulin ( si ) is a parameter calculated from serial insulin and glucose values during the fsigt ( 14 ) . signals were recorded on a computerized system ( rembrandt ; rescare , buffalo , ny ) . the following parameters were recorded : electroencephalogram ( c3/a2 , c4/a1 , o1/a2 , and o2/a1 ) ; right and left electro - oculograms ; submental electromyogram ; tibial electromyogram ; electrocardiogram ; chest and abdominal wall motion by inductance plethysmography ; oronasal pressure / airflow ( nasal pressure cannula with oral thermistor bead ; pro - tech , woodinville , wa ) ; end - tidal pco2 , measured at the nose by infrared capnometry ( nellcor n-1000 ) ; arterial oxygen saturation ( sao2 ) by pulse oximetry , and oximeter pulse waveform . studies were reviewed by a single sleep board - certified investigator ( l.j.b . ) , who had no knowledge of subjects metabolic status . sleep architecture ( n1 , n2 , n3 , and rem sleep stages ) and respiratory disturbances ( including the apnea - hypopnea index [ ahi ] , arousal index , and lowest oxyhemoglobin saturation [ lowest sao2 ] ) were scored using standard pediatric criteria ( 17 ) . histograms and one - sample kolmogorov - smirnov tests were used to assess normality of distribution of continuous variables . pearson or spearman correlations were used to examine associations between sleep architecture or osa measures and parameters of glucose homeostasis and insulin secretion and sensitivity . hierarchical linear regression procedures were used to evaluate the aforementioned relationships while controlling for potential confounding variables ( e.g. , degree of obesity and osa ) . assumptions of linearity were tested by examining plots of the standardized residuals as a function of standardized predicted values . where curve estimation procedures uncovered curvilinear relationships , polynomial regressions were conducted . analysis of covariance ( ancova ) models were used to examine differences in the outcome variables between sexes and among different pubertal stages , controlling for covariates . as we tested three underlying hypotheses relating to the relationship between sleep architecture and insulin secretion and sensitivity and overall glycemia , we used an adjusted p value of < 0.017 ( 0.05/3 ) for statistical significance . seventy obese adolescents were screened for participation ; seven cancelled prior to the study date and one did not undergo psg , leaving 62 participants for analysis . insulin and glucose values , calculated indices , and psg results are presented in table 2 . subject characteristics glucose tolerance testing and psg results sleep architecture ( durations are given in minutes ; percentages are denoted as % ) . % tst in n = percentage of total sleep time spent in a given sleep stage ( e.g. , % tst in n1=% total sleep time in n1 ) . total sleep time ( tst ) was significantly or near - significantly associated with both short- and long - term measures of glucose homeostasis ( table 3 ) . curve estimation modeling and regression statistics showed that these relationships were u shaped ( quadratic ) ( fig . c ) . there was no association between any measure of osa and measures of glucose homeostasis ( supplementary table 1 ) . glu 1 h , glucose level 1 h after oral glucose ingestion on ogtt ; glu 2 h , glucose level 2 h after oral glucose ingestion on ogtt . numbers in boldface indicate significant association , and numbers in italics indicate near - significant association ( p value between 0.017 and 0.05 ) . spearman correlation analysis . sleep duration and glucose homeostasis measures . b : association between 2-h glucose level on ogtt and total sleep duration ( minutes ) that evening . in all three panels , the u - shaped relationships suggest that a sleep duration of 420510 min ( 78.5 h ) is associated with optimal glucose homeostasis . on regression analysis , individual sleep stages , pubertal stage , and sex were not significant predictors of any glucose homeostasis measure ; bmi z score was a significant contributor , and tanner stage was a marginal contributor , to the overall 2-h glucose model only ( not to the overall fasting glucose or hba1c models ) . for the overall regression models mentioned above , adjusted r and p values were as follows : 0.201 ( p = 0.002 ) for fasting glucose , 0.442 ( p < 0.0005 ) for 2-h glucose , and 0.200 ( p = 0.002 ) for hba1c . n3 sleep , both total duration and the percentage of total sleep time in n3 ( % tst in n3 ) , correlated significantly or with marginal significance ( p value between 0.017 and 0.05 ) with several insulin secretory measures ( table 4 ) in bivariate analysis . curve estimation modeling uncovered a cubic relationship between n3 and airg ( r = 0.286 ; p = 0.001 ) , with inflection points at approximately 65 and 98 min . osa measures did not associate significantly with any measure of insulin secretion ( supplementary table 2 ) . a marginally significant negative association was seen between pubertal stage and both n3 duration ( r = 0.282 ; p = 0.028 ) and % tst in n3 ( r = 0.252 ; p = 0.050 ) , but there was no association between pubertal stage and any of the insulin secretory measures examined , or between sex and insulin secretory measures . correlation of sleep architecture with measures of insulin secretion and sensitivity sleep architecture ( durations are given in minutes ; percentages are denoted as % ) . % tst in n = percentage of total sleep time spent in a given sleep stage . numbers in boldface indicate significant association , and numbers in italics indicate near - significant association ( p value between 0.017 and 0.05 ) . other sleep stages , tst , osa measures , and sex were not significant predictors of insulin secretory measures in the final regression model . bmi z score contributed significantly to the airg final model but not to the igi model , and pubertal stage contributed significantly to the final igi model but not the airg model . adjusted r and p values for the overall models were 0.161 ( p = 0.002 ) for igi and 0.383 ( p < 0.0005 ) for airg . correlation analysis showed a marginally significant negative association between n2 sleep and several insulin sensitivity measures ( table 4 ) . a marginally significant negative correlation was seen between ahi and si ( r = 0.338 ; p = 0.025 ; see supplementary table 3 ) . however , on regression analysis , no strong associations were seen between sleep architecture or osa and ogtt - derived insulin sensitivity measures . we found a marginal relationship between n2 duration and homa - ir ( overall r = 0.088 ; p = 0.040 ) , and although the relationship between % tst in n2 and si was stronger , bmi z score ( i.e. , degree of obesity ) was the strongest predictor in that model ( overall model r = 0.400 ; p < 0.0005 ) . seventy obese adolescents were screened for participation ; seven cancelled prior to the study date and one did not undergo psg , leaving 62 participants for analysis . insulin and glucose values , calculated indices , and psg results are presented in table 2 . subject characteristics glucose tolerance testing and psg results sleep architecture ( durations are given in minutes ; percentages are denoted as % ) . % tst in n = percentage of total sleep time spent in a given sleep stage ( e.g. , % tst in n1=% total sleep time in n1 ) . total sleep time ( tst ) was significantly or near - significantly associated with both short- and long - term measures of glucose homeostasis ( table 3 ) . curve estimation modeling and regression statistics showed that these relationships were u shaped ( quadratic ) ( fig . c ) . there was no association between any measure of osa and measures of glucose homeostasis ( supplementary table 1 ) . glu 1 h , glucose level 1 h after oral glucose ingestion on ogtt ; glu 2 h , glucose level 2 h after oral glucose ingestion on ogtt . numbers in boldface indicate significant association , and numbers in italics indicate near - significant association ( p value between 0.017 and 0.05 ) . spearman correlation analysis . sleep duration and glucose homeostasis measures . a : association between sleep duration and fasting plasma glucose levels on ogtt . b : association between 2-h glucose level on ogtt and total sleep duration ( minutes ) that evening . in all three panels , the u - shaped relationships suggest that a sleep duration of 420510 min ( 78.5 h ) is associated with optimal glucose homeostasis . on regression analysis , tst was the most significant predictor of glucose homeostasis measures . individual sleep stages , pubertal stage , and sex were not significant predictors of any glucose homeostasis measure ; bmi z score was a significant contributor , and tanner stage was a marginal contributor , to the overall 2-h glucose model only ( not to the overall fasting glucose or hba1c models ) . for the overall regression models mentioned above , adjusted r and p values were as follows : 0.201 ( p = 0.002 ) for fasting glucose , 0.442 ( p < 0.0005 ) for 2-h glucose , and 0.200 ( p = 0.002 ) for hba1c . n3 sleep , both total duration and the percentage of total sleep time in n3 ( % tst in n3 ) , correlated significantly or with marginal significance ( p value between 0.017 and 0.05 ) with several insulin secretory measures ( table 4 ) in bivariate analysis . curve estimation modeling uncovered a cubic relationship between n3 and airg ( r = 0.286 ; p = 0.001 ) , with inflection points at approximately 65 and 98 min . osa measures did not associate significantly with any measure of insulin secretion ( supplementary table 2 ) . a marginally significant negative association was seen between pubertal stage and both n3 duration ( r = 0.282 ; p = 0.028 ) and % tst in n3 ( r = 0.252 ; p = 0.050 ) , but there was no association between pubertal stage and any of the insulin secretory measures examined , or between sex and insulin secretory measures . correlation of sleep architecture with measures of insulin secretion and sensitivity sleep architecture ( durations are given in minutes ; percentages are denoted as % ) . % tst in n = percentage of total sleep time spent in a given sleep stage . numbers in boldface indicate significant association , and numbers in italics indicate near - significant association ( p value between 0.017 and 0.05 ) . spearman correlation analysis . other sleep stages , tst , osa measures , and sex were not significant predictors of insulin secretory measures in the final regression model . bmi z score contributed significantly to the airg final model but not to the igi model , and pubertal stage contributed significantly to the final igi model but not the airg model . adjusted r and p values for the overall models were 0.161 ( p = 0.002 ) for igi and 0.383 ( p < 0.0005 ) for airg . correlation analysis showed a marginally significant negative association between n2 sleep and several insulin sensitivity measures ( table 4 ) . a marginally significant negative correlation was seen between ahi and si ( r = 0.338 ; p = 0.025 ; see supplementary table 3 ) . however , on regression analysis , no strong associations were seen between sleep architecture or osa and ogtt - derived insulin sensitivity measures . we found a marginal relationship between n2 duration and homa - ir ( overall r = 0.088 ; p = 0.040 ) , and although the relationship between % tst in n2 and si was stronger , bmi z score ( i.e. , degree of obesity ) was the strongest predictor in that model ( overall model r = 0.400 ; p < 0.0005 ) . in this multiethnic group of obese adolescents , we found strong relationships between sleep , hyperglycemia , and insulin secretion . specifically , we found u - shaped relationships between total sleep duration and measures of both short- and long - term glycemia , and positive or cubic associations between n3 and insulin secretory measures , even after adjusting for potential confounders such as degree of obesity , osa , sex , and pubertal stage . our sleep duration data suggest that glucose metabolism is optimal when 7.58.5 h of sleep is achieved . this is consistent with adult data noting u - shaped associations between self - reported sleep duration and t2 dm risk ( 5 ) . adults with t2 dm have also been reported to have shorter n3 duration than nondiabetic adults ( 18 ) . although one postulated mechanism suggests that n3 loss increases ir ( 19 ) , our results instead demonstrated a relationship between n3 and insulin secretion . this relationship , which appeared to be a function of n3 itself rather than of total sleep duration , suggested that an absolute n3 duration of 1 h may be needed to achieve a stable amount of insulin secretion , and that increasing n3 might greatly improve insulin secretion . our results may help explain the aforementioned association between n3 lack and t2 dm , as a loss in first - phase insulin secretion is both an early marker of t2 dm and part of its pathogenesis ( 20 ) . parasympathetic activity , which is increased in n3 sleep ( 21 ) , stimulates glucose - induced insulin secretion ( 22 ) ; we speculate that increased parasympathetic activity may be responsible for our observed associations . although growth hormone ( gh ) secretion occurs largely during the n3 sleep ( 23 ) , gh is unlikely to be a factor in the associations , as gh increases insulin resistance ( 24 ) rather than insulin secretion . in addition , insulin - like growth factor-1 levels in our subjects did not correlate significantly with either sleep duration or any individual sleep stage , further corroborating that gh secretion is unlikely to explain the observed associations . finally , we found a positive association between n2 sleep and insulin sensitivity , with varying contribution from degree of obesity . although n2 duration was also negatively associated with at least one marker of osa , the ahi , indicating possible confounding , the ahi did not consistently associate with insulin sensitivity measures ; thus , the observed association may represent an intrinsic relationship between n2 sleep and insulin sensitivity . a night in the sleep laboratory does not necessarily reflect sleep at home , a possible limitation of our study . however , in our study , the ogtt preceded the psg . thus , any observed associations between sleep parameters and ogtt - derived measures could not have been short - term effects of a night in the laboratory . the association between tst and hba1c , which reflects long - term glycemia , also supported our findings . also , families completed post - psg surveys asking whether sleep in the laboratory was typical of home sleep . only 32% indicated worse sleep in the laboratory ; these subjects had no significant demographic , anthropometric , or glucose / insulin parameter differences compared with the remaining subjects , and of the sleep parameters , the only difference seen was a lower absolute rem duration in the  poorer sleep  group . our subjects mean tst of 7.1 h was similar to the mean 7.2-h sleep duration reported in the 2006 national sleep foundation adolescent poll ( 2 ) . a recent study showed an association between short sleep on actigraphy and metabolic dysregulation in school - age children ( 25 ) . although home - based actigraphy studies could be useful , actigraphy is less precise and can not discriminate between sleep stages . in conclusion , we found significant relationships between sleep duration and sleep architecture and measures of glucose homeostasis and insulin secretion . to our knowledge , this is the first report of an association between n3 sleep and changes in -cell function and of a u - shaped association between sleep duration and glucose levels in a pediatric population . we speculate that inadequate sleep duration and altered sleep architecture ( relative suppression of n3 sleep ) may play a role in t2 dm development . ensuring adequate sleep might reduce the risk of t2 dm in at - risk obese adolescents .