CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / O experimento foi realizado com o objetivo de avaliar os efeitos da granulometria do calcÃrio e do uso da luz artificial para poedeiras comerciais no segundo ciclo de postura. Foram utilizadas 240 poedeiras Hisex White com 82 semanas de idade, distribuÃdas em um delineamento inteiramente casualizado, em esquema fatorial 5 x 2, resultando em 10 tratamentos com 4 repetiÃÃes de 6 aves. Os fatores estudados foram 5 granulometrias obtidas pelo aumento da proporÃÃo de calcÃrio grosso (0, 25, 50, 75 e 100%) em relaÃÃo ao fino e 2 tipos de iluminaÃÃo, com e sem luz artificial. A granulometria do calcÃrio e a luz nÃo influenciaram o desempenho e qualidade dos ovos. Entretanto, observaram-se mudanÃas no horÃrio de alimentaÃÃo das aves ao longo do dia em resposta ao programa de luz. No tocante a qualidade Ãssea, observou-se que a densidade e matÃria mineral da tÃbia nÃo foram influenciadas pelos tratamentos, entretanto, houve efeito quadrÃtico da granulometria do calcÃrio sobre a deformidade e a resistÃncia Ãssea, obtendo-se pontos de mÃxima inclusÃo de 63% e 59% de calcÃrio grosso, respectivamente. Conclui-se que, embora o programa de luz possa modificar o comportamento da ingestÃo de raÃÃo ao longo do dia, o uso de luz artificial e a granulometria do calcÃrio nÃo influÃncia o desempenho e a qualidade dos ovos de poedeiras no segundo ciclo de produÃÃo, criadas a uma latitude 3Â43â02â sul e 38Â32â35â de longitude oeste. Entretanto, o uso de calcÃrio com maior granulometria se justifica para manter a qualidade Ãssea dessas aves. / The experiment was conducted to evaluate the effects of particle size of limestone and the use of artificial light for laying hens in the second laying cycle. It was used 240 Hisex White laying hens with 82 weeks of age in a completely randomized design in a 5 x 2 factorial arrangement, resulting in 10 treatments with 4 replicates of 6 birds. The variables were the five particle sizes obtained by increasing the proportion of thick limestone (0, 25, 50, 75 and 100%) compared thin limestone and two types of lighting, with and without artificial light. The particle size of limestone and the light did not affect the performance and egg quality. However, there were changes in the schedule of the birds feeding throughout the day in response to the lighting program. With respect to bone quality, it was observed that the density and mineral content of the tibia were not affected by the treatments, however, there was a quadratic effect of particle size of limestone on the deformity and bone strength, obtaining maximum inclusion points with 63% 59% of thick limestone, respectively. It is concluded that, although the lighting program may modify the behavior of intake throughout the day, the use of artificial light and the particle size of limestone does not influence the performance and egg quality of laying hens in the second production cycle, created at latitude 3Â43â02â South and 38Â32â35â west longitude. However, the use of limestone with higher granulate size is justified to maintain bone quality of these birds.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Com o objetivo de avaliar os efeitos dos nÃveis de fibra em detergente neutro (14,5; 16,5; 18,5% de FDN) na raÃÃo de crescimento (7 a 17 semanas de idade) sobre a qualidade Ãssea de poedeiras leves e semipesadas, 840 frangas foram distribuÃdas em um delineamento experimental inteiramente casualizado em esquema fatorial dois x trÃs (duas linhagens x trÃs nÃveis de FDN) com quatro repetiÃÃes de 35 aves. Durante essa fase, semanalmente, as aves e a raÃÃo foram pesadas e, na 17 semana, foram selecionadas duas aves por parcela para serem sacrificadas e retirada das coxas e sobrecoxas, que apÃs desossadas forneceram os ossos, fÃmur e tÃbia, para mensuraÃÃo do comprimento, peso, Ãndice de Seedor, resistÃncia e deformidade. Ao final da fase de crescimento, as aves foram transferidas para o galpÃo de postura, mantendo-se o mesmo delineamento experimental, sendo cada parcela experimental composta por 14 aves, totalizando 336 aves. Para avaliar a qualidade Ãssea das poedeiras, foi realizado o abate de uma ave por parcela na 35 semana de idade, sendo adotado os procedimentos da fase anterior. Conforme a anÃlise dos dados nÃo houve interaÃÃo significativa entre os fatores nÃvel de FDN e linhagem para todas as variÃveis avaliadas nas diferentes fases. O nÃvel de FDN da raÃÃo nÃo influenciou significativamente o crescimento, a qualidade e a composiÃÃo dos ossos, ao final da fase de crescimento e na fase de postura, bem como, a qualidade da casca dos ovos produzidos. Quanto ao efeito da linhagem, as aves semipesadas apresentaram fÃmures e tÃbias maiores e mais pesados, com maior Ãndice de Seedor e menor deformidade, teor de cinzas e proteÃna que as aves leves. Entretanto, a resistÃncia nÃo variou significativamente entre as linhagens. As aves leves apresentaram melhores medidas de qualidade da casca. As raÃÃes destinadas à alimentaÃÃo das frangas na fase crescimento podem conter atà 18,5% de FDN sem que ocorram problemas no desenvolvimento e na qualidade Ãssea das poedeiras. / Our objective was to evaluate the effects of levels of neutral detergent fiber (14.5, 16.5, 18.5% NDF) in the growing ration (7 to 17 week of age) on bone quality of light and semi-heavy birds, this way 840 birds were distributed in a completely randomized with a factorial design 2 x 3 (two lines x three levels of NDF) with four replicates of 35 birds. During this phase, weekly, feed the birds were weighed, and at 17 weeks, two birds were selected per plot to be sacrificed and to remove thighs and drumsticks, which after remove the bones supplied femur and tibia for measuring length, weight, index Seedor, resistance and deformity. At the end of the growth phase the birds were transferred to the laying house, keeping the same experimental design, each plot consisted of 14 birds, totaling 336 birds. To evaluate the bone quality of laying hens, a bird was killed of per plot at 35 weeks of age, and adopted the procedures of the previous phase. As the data analysis no significant interaction between the factors NDF level and lineage for all variables at different stages. The NDF level of the diet did not significantly influence the growth, bones composition and quality in growing and laying phases. Regarding the effect of lineage, semi-heavy birds showed larger and heavier femurs and tibia, with higher Seedor index and lower deformity, ash and proteins than light birds. Howerver, resistance did not vary significantly among lineages. Light birds had better measures of shell quality. The rations used for feeding of pullets in the growing phase may contain up to 18.5% NDF without problems occur in development and bone quality of laying hens.

No description available.

Osteoporosis which is frequently referred to as a pediatric disease with geriatric consequences (Golden, 2000) can result from a lack of optimal bone accrual during the development (NIH Consensus Development Panel on Osteoporosis Prevention, Diagnosis, and Therapy, 2001). Pubertal timing is a key factor that contributes to optimal bone accrual and strength (Bonjour et al., 1994; 21 Warren et al., 2002). Bone mass doubles during the onset of puberty and young adulthood (Katzman et al., 1991) with more than 90% of peak bone mass being accrued at the end of second decade of life (Schneider & Wade, 2000). The rate of periosteal expansion is elevated during the pubertal period (Specker et al., 1987; Bradney et al., 2000) and this expansion parallels longitudinal growth (Parfitt, 1994). Irrespective of other changes, periosteal expansion lowers fracture risk by improving the strength of long bones by increasing the moment of inertia (Orwoll, 2003). Therefore, a delay in puberty may actually increase the time available for periosteal development and positively affect bone strength. Previous animal studies have shown decreases in strength, endocortical bone formation and increases in periosteal bone formation with delayed puberty. Clinical studies report negative effects of delayed puberty on bone mass accrual suggesting that delayed puberty is a multifactorial problem affecting bone strength development. The purpose of this study was to determine the effect of delayed puberty on mechanical strength and endocortical bone marrow cells in two models: female rats treated with gonadatropin releasing hormone antagonists (GnRH-a) and energy restriction (30%). Thirty-two female Sprague Dawley rats (21 to 22 days-of-age) were received from (Charles Rivers Laboratories, Wilmington, MA, USA) and housed individually at the Temple University Central Animal Facility (Temple University Weiss Hall). Animals were randomly assigned to one of three groups; control (n=10), GnRH-a (n=10) and energy restriction (ER) (n=12). The GnRH-a group was injected with gonadotropin releasing antagonist injections (GnRH-a) (Antide, Bachem, Torrance, Ca. USA) at a dose of 2.5 mg/kg/BW. The ER group received a 30% energy restricted diet (0pen Source diet (D07100606)(Research Diets, New Brunswick, NJ). All animals were sacrificed on Day 51. One way analysis of variance testing (ANOVA) with a significance level of 0.05 was used to assess group differences. Following the two protocols the uterine weight in the GnRH-a group was 80.6% lower than control; no change in the ER group. Ovarian weight was significantly lower in the GnRH-a group (83.3%) and in the ER group (33.3%) as compared to controls. A 22.7% lower muscle weight was found in the ER group but was equal to control and GnRH-a when normalized by body weight (BW). The retro-peritoneal fat pad weight was significantly decreased by 64.95% in the ER group as compared to controls. Energy restriction did not result in any deficit in bone strength when normalized by body weight however the GnRH-a group had a 26.2% lower bone strength compared to control. Histomorphometric changes were not significantly different between groups, but the ratio for periosteal versus endocortical bone formation rates for the control group was 1.38, GnRH-a was significantly higher with a ratio of 5.54 and for ER was 3.02 indicating that periosteal BFR are almost twice endocortical BFR in the experimental groups. There was a significant decrease in the trabecular percent bone volume (BV/TV) of the lumbar vertebra in the GnRH-a group (20.2%) compared to control. However BV/TV was significantly higher in the ER (18.4%) compared to the control group. Proliferation was suppressed to 59.6% of control in the GnRH-a group but only 85.5% of control in the ER group. The alkaline phosphatase activity was 31.2% lower in the GnRH-a group and 63.9% lower in the ER group. The relative quantification (RQ) of RUNX2 gene expression was lowest in control followed by GnRH-a and highest in ER group although no statistical significance was observed between any groups. Thus our data infers that 30% energy restriction does not negatively impact bone health. Thirty percent food restriction with no deficits in micronutrients or hormone suppression may just suppress growth as indicated by the maintenance of bone strength per body weight and equivalent muscle mass per body weight in the ER group compared to control. The GnRH-a injections resulted in decreased bone strength and trabecular bone volume. Female Athlete Triad or Anorexia Nervosa are the two clinical conditions hypothesized to result from a combination of ER and estrogen deficient environment. Studies replacing estrogen in hypothalamic amenorrhea or IGF-1 in anorexia alone have failed to improve bone mineral density (BMD), but a combination of IGF-1 and estrogen has been successful in improving BMD. This suggests that estrogen dependant and independent mechanisms work in combination to protect bone. Our study investigated both mechanisms separately and indicates that ER at 30% may be protective for bone health. Since estrogen deficiency may be the extreme end of the spectrum affecting trabecular bone, treatment therapies may have to be based on age, magnitude and severity of energy restriction and presence or absence of menstrual status. / Kinesiology

The purpose of this investigation was to determine the effects of post pubertal caloric restriction on bone architecture, strength, and medullary adipose quantity. A randomized control comparison design was utilized and the study was conducted in a laboratory setting. All procedures were approved by the Institutional Animal Care and Use Committee (IACUC) at Temple University (protocol number 3396). Female Sprague Dawley rats (23days-of-age, n=120) were randomly assigned into seven groups, baseline (BL) (n=18), control (C) (n=17), caloric restriction (FR) (n=17), control recovery (RC) (n=17), caloric restriction recovery (RFR) (n=17), control ovariectomy (COVX) (n=17) and food restricted ovariectomy (FROVX) (n=17). On day 65, a 6 week 30% caloric restriction protocol was administered. Following food restriction, a subset of the control and food restricted groups were sacrificed (n=34) and the remaining animals (n=68) control recovery (RC) and food restricted recovery (RFR) groups had a 10 week recovery with ad lib food. Recovery groups, RC and RFR: were sacrificed after the 10 week recovery period at 183 days of age (n=34). The remaining animals were ovariectomized (OVX) and grouped into control ovariectomy (COVX) and food restricted ovariectomy (FROVX). Six weeks post OVX the animals were sacrificed at 270 days of age. After sacrifice blood was taken by cardiac puncture, bones were harvested, cleaned of soft tissue, fixed and prepared for analysis. Anthropometric measurements were taken including retroperitineal and gonadal fat pad weights as well as adrenal glands, ovaries, uteri, and tricep surae muscle group weights. Main Outcome Measures: The outcome variables for this study were bone mechanical competence, trabecular and cortical bone mass and architecture, marrow adipocyte number as well as serum markers of bone formation and resorption. Insulin - like growth factor - 1 (IGF-1) and C- terminal telopeptide (CTX) was measured to determine bone formation and resorption. Statistical Analysis: One-way Analysis of Variance (ANOVA) was performed to determine differences between all groups. Tukey's honestly significant difference (HSD) post hoc analysis was conducted to determine differences between groups. Student's t - tests were used to detect differences between age groups (acute, recovery, post-OVX) A p value was set at less than or equal to 0.05 for all statistical tests. All statistical analysis was performed using (GraphPad Prism version 5.00 for Windows, GraphPad Software, San Diego California USA). Variables were normalized with a linear regression-based correction using body weight. All variables with an R2 level greater than 0 were normalized to avoid choosing an arbitrary R2 value as a cut-off for normalization. Results: Body weight was 18% lower than control animals following caloric restriction. Weight loss was due to fat mass predominately; muscle mass was maintained relative to body weight. Bone length and growth rates were diminished however no differences were found following refeeding. No differences were found in bone strength at any time point. However relative to body weight peak moment and stiffness were significantly higher following caloric restriction. Cortical bones mass and cross sectional moment of inertia were enhanced in the femoral diaphysis with bone mass greater post OVX in the calorically restricted group (FR-OVX). No significant differences were found in ash percent in the femur was found between any groups at any time point however vertebral bone mineral density in acute FR and post OVX time points in FROVX was significantly greater indicating an enhanced bone quality in the restricted. No change in trabecular quantity or quality were observed in the distal femur between groups however vertebral trabecular architecture was enhanced in number and thickness in acute FR and post OVX time points in FROVX. No significant difference in number of marrow adipocytes were found at any time point. Serum CTX decreased significantly in acute in FR and increased at recovery in RFR and post OVX in FROVX. Serum IGF - 1 decreased in the acute FR with IGF - 1 significantly greater after recovery in RFR. Conclusions: Evidence was found to suggest that moderate caloric restriction (nutrient replete) post puberty was positive for bone. Bone quantity was increased with relative cortical area and bone area relative to body weight increased in the FR group. Significant increases in FROVX bone quantity post OVX suggests that bone mass gains during caloric restriction attenuated cortical bone loss at maturity post OVX. Bone quality increases in cross sectional moment of inertia relative to body weight may have accounted for the transient increase in FR bone strength in the femur. Decreases in acute CTX and IGF- 1 levels indicates that bone formation and resorption were decreased during development that may have been the mechanism for bone loss attenuated post OVX in calorically restricted. Growth rate slowing during caloric restriction may have decreased the rate of formation and resorption during a crucial time of peak bone mass accrual and bone modeling. This decrease in one modeling may have been mechanism that preserved bone quantity during acute caloric restriction. Increases in femur quality in polar moment of inertia coupled with a decrease in bone length changed the shape of the bone making it more robust. A shorter bone with a thicker cortex with no change in mineral content may have been the mechanism in the transient increase in bone strength in the femur. Quality changes in mineral density in vertebrae acting as a mineral storage back up as a last resort if quantity and quality changes were not sufficient in maintain bone strength. Moderate caloric restriction transiently increased strength, by increasing bone mass relative to body, altering bone geometry and increased vertebral mineral density. / Kinesiology

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Thesis (DMed)--Stellenbosch University, 2008. / The comparative study presented in this dissertation specifically aimed to assess fracture risk in black (Xhosa) and white South African women by evaluating known determinants of bone strength as well as the propensity to falls. We thus compared the prevalence of clinical (historic) risk factors for osteoporosis, measured and compared vertebral and femoral bone mineral density (BMD) employing dual energy X-ray absorptiometry (DEXA), ultrasound variables using the Sahara sonometer, serum parathyroid hormone (PTH) and 25-OH Vitamin D, mineral homeostasis and modern biochemical markers of bone turnover, bone geometry and the propensity to falls. Finally, we determined the prevalence of vertebral fractures in these black and white South African females. 1. Significant ethnic differences were noted in the presence and frequency of historical clinical and lifestyle risk factors for osteoporosis. Blacks were heavier and shorter, they consumed less calcium, were more inactive, preferred depot-medroxyprogesterone acetate as contraceptive agent and were of higher parity. Whites smoked more, preferred oral oestrogen containing contraceptive tablets and were more likely to have a positive family history of osteoporosis. Hormone therapy was used almost exclusively by postmenopausal whites. Inter-ethnic differences in weight, physical activity and high parity was most marked in the older subjects. 2. We found that peak spinal BMD was lower, but peak femoral BMD similar or higher (depending on the specific proximal femoral site measured) in black South-African females compared with whites. The lower peak spinal BMD was mainly attributed to lower BMD’s in the subgroup of black females with normal to low body weight, indicating that obesity either protected black females against a low spinal BMD or enhanced optimal attainment of bone mineral. An apparent slower rate of decline in both spinal- and femoral BMD with ageing was noted in the black females compared with whites in this cross-sectional study – an observation which will require confirmation in longitudinal, follow-up studies. This resulted in similar spinal BMD values in postmenopausal blacks and whites, but significantly higher femoral BMD measurements in blacks. The volumetric calculation of bone mineral apparent density (BMAD) at the lumbar spine and femoral neck yielded similar results to that of BMD. Spinal BMAD was similar in blacks and whites and femoral neck BMAD was consistently higher in all the menopausal subgroups studied. Weight significantly correlated with peak- and postmenopausal BMD at all sites in the black and white female cohorts. Greater and better maintained body weight may be partially responsible for slower rates of bone loss observed in black postmenopausal females. Most of the observed ethnic difference in BMD was, in fact, explained by differences in body weight between the two cohorts and not by ethnicity per se. 3. A low body weight and advanced age was identified as by far the most informative individual clinical risk factors for osteopenia in our black and white females, whereas physical inactivity was also identified as an important individual risk factor in blacks only. Risk assessment tools, developed and validated in Asian and European populations, demonstrated poor sensitivity for identification of South African women at increased risk of osteopenia. The osteoporosis risk assessment instrument (ORAI) showed the best results, with sensitivities to identify osteopenic whites at most skeletal sites approaching 80% (78% - 81%). The risk assessment tool scores appear to be inappropriate for our larger sized study cohort, especially our black subjects, thus resulting in incorrect risk stratification and poor test sensitivity. General discriminant analysis identified certain risk factor subsets for combined prediction of osteopenia in blacks and whites. These risk factor subsets were more sensitive to identify osteopenia in blacks at all skeletal sites, compared with the risk assessment tools described in the literature. 4. Higher ultrasonographically measured broadband ultrasound attenuation (BUA) and speed of sound (SOS) values were documented in our elderly blacks compared with whites, even after correction for differences in DEXA determined BMD at the spine and proximal femoral sites. BUA and SOS showed no decline with ageing in blacks, in contrast to an apparent significant deterioration in both parameters in ageing whites. If these quantitative ultrasound (QUS) parameters do measure qualitative properties of bone in our black population, independent of BMD as has been suggested in previous work in Caucasian populations, the higher values documented in elderly blacks imply better preservation of bone quality in ageing blacks compared with whites. The correlation between QUS calcaneal BMD and DEXA measured BMD at the hip and spine was modest at best. QUS calcaneal BMD was therefore unable to predict DEXA measured BMD at clinically important fracture sites in our study population. 5. Bone turnover, as assessed biochemically, was similar in the total pre- and postmenopausal black and white cohorts, but bone turnover rates appeared to differ with ageing between the two racial groups. A lower bone turnover rate was noted in blacks at the time of the menopausal transition and is consistent with the finding of a lower percentage bone loss at femoral sites at this time in blacks compared with whites. Bone turnover only increased in ageing postmenopausal blacks, and this could be ascribed, at least in part, to the observed negative calcium balance and the more pronounced secondary hyperparathyroidism noted in blacks. Deleterious effects of secondary hyperparathyroidism on bone mineral density at the proximal femoral sites were demonstrated in our postmenopausal blacks and contest the idea of an absolute skeletal resistance to the action of PTH in blacks. The increase in bone turnover and the presence of secondary hyperparathyroidism due to a negative calcium balance may thus potentially aggravate bone loss in ageing blacks, especially at proximal femoral sites. 6. Shorter, adult black women have a significantly shorter hip axis length (HAL) than whites. This geometric feature has been documented to protect against hip fracture. The approximately one standard deviation (SD) difference in HAL between our blacks and whites may therefore significantly contribute to the lower hip fracture rate previously reported in South African black females compared with whites. Average vertebral size was, however, smaller in black females and fail to explain the apparent lower vertebral fracture risk previously reported in this population. Racial differences in vertebral dimensions (height, width) and/or other qualitative bone properties as suggested by our QUS data may, however, account for different vertebral fracture rates in white and black women – that is, if such a difference in fact exists. 7. The number of women with a history of falls was similar in our black and white cohorts, and in both ethnic groups the risk of falling increased with age. There is a suggestion that the nature of falls in our black and white postmenopausal females may differ, but this will have to be confirmed in a larger study. Fallers in our postmenopausal study population were more likely to have osteoporosis than non-fallers. Postmenopausal blacks in our study demonstrated poorer outcomes regarding neuromuscular function, Vitamin D status and visual contrast testing and were shown to be more inactive with ageing compared with whites. An increased fall tendency amongst the black females could not however be documented in this small study. Quadriceps weakness and slower reaction time indicated an increased fall risk amongst whites, but were unable to distinguish black female fallers from non-fallers. 8. Vertebral fractures occurred in a similar percentage of postmenopausal blacks (11.5%) and whites (8.1%) in our study. Proximal femoral BMD best identified black and white vertebral fracture cases in this study. Quite a number of other risk factors i.e. physical inactivity, alcohol-intake, poorer physical performance test results and a longer HAL were more frequent in the white fracture cases and could therefore serve as markers of increased fracture risk, although not necessarily implicated in the pathophysiology of OP or falls. However, in blacks, only femoral BMD served as risk factor. Similar risk factors for blacks and whites cannot therefore be assumed and is deserving of further study. White fracture cases did not fall more despite lower 25-OH-Vitamin D, poorer physical performance and lower activity levels than non-fracture cases. Calcaneal ultrasonography and biochemical parameters of bone turnover were similar in fracture and non-fracture cases in both ethnic groups. Our study data on vertebral fractures in this cohort of urbanized blacks thus cautions against the belief that blacks are not at risk of sustaining vertebral compression fractures and emphasize the need for further studies to better define fracture prevalence in the different ethnic populations of South Africa. 9. In our study, hormone therapy in postmenopausal white women improved bone strength parameters and reduced fall risk. In hormone treated whites compared with non-hormone users, a higher BMD at the spine and proximal femur as determined by DEXA were documented and all QUS measurements were also significantly higher. The biochemically determined bone turnover rate, as reflected by serum osteocalcin levels, was lower in hormone users. Fall frequency was lower in the older hormone treated women (≥ 60yrs) and greater quadriceps strength and reduced lateral sway was noted. Only one patient amongst the hormone users (2%) had radiological evidence of vertebral fractures compared with four patients (6%) amongst the never-users. As hormone therapy was used almost exclusively by whites in this study population, the impact of hormone therapy on postmenopausal black study subjects could not be assessed.

Patients with Turner syndrome (TS) have increased fracture risk and decreased bone density, patients with severe hemophilia have low bone density. The etiology of these changes hasn't been completely elucidated in any of the two diseases. Our aimes were to assess bone density and geometry at the radius using a new method peripheral quantitative CT densitometry (pQCT) and to describe associations between densitometry parameters and estrogen treatment in TS and laboratory as well as clinical markers of disease severity in haemophilia. Sixty-seven girls with TS (median age 14.3 years, range 6.0-19.4) and 42 boys with haemophilia (median age 12.7 years, range 6.6-19.2) have been measured using peripheral quantitative CT at the radius. The results have been compared to published reference data. Girls with TS had decreased cortical bone density and thinner cortex. These parameters were positively correlated to the length of estrogen treatment. Trabecular bone density was normal in prepubertal girls but it was decreased after puberty. There was no association between trabecular bone density and the estrogen treatment. Boys with haemophilia had decreased trabecular density and low muscle area at the forearm. Densitometry parameters were influenced neither by the clotting factor VIII/IX level nor by the frequency of...

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