2025 年 32 巻 2 号 p. 188-197
Aim: Increased arterial stiffness impairs the functional and structural properties of arteries, which in turn elevates blood pressure (BP). The aim of this study was to test whether indices obtained from the second derivative of the finger photoplethysmogram (SDPTG), a marker of arterial stiffness, predict future development of hypertension in middle-aged men.
Methods: The SDPTG was measured in 902 men without hypertension (mean age 44±6 years) at an annual medical checkup. The development of hypertension was monitored for a maximum of 4 years. Two indices of arterial stiffness were calculated from the SDPTG waveforms: b/a, an index of large elastic arterial stiffness, and d/a, an index of systemic arterial stiffness, including the structural and functional properties of small and muscular arteries and peripheral circulation. A Cox proportional hazards model was used to examine whether the b/a and d/a ratios were independent predictors of future development of hypertension.
Results: During the follow-up period, 124 individuals developed hypertension, defined as a systolic/diastolic BP ≥ 140/90 mm Hg or the use of antihypertensive medications. The hazard ratio for the development of hypertension significantly increased in the lowest quartile of the d/a ratio (2.84, 95% confidence interval: 1.58–5.13, p<0.001) compared with the highest quartile, after adjusting for multiple potential confounders. In contrast, the b/a ratio did not show significant hazard ratios for the development of hypertension.
Conclusions: The d/a ratio, calculated from the SDPTG waveforms, predicted the risk of future development of hypertension in this study population.
Hypertension is a leading contributor to premature death globally1). To reduce the risks of morbidity and mortality from cardiovascular and other hypertension-related diseases, it is important not only to lower blood pressure (BP) in patients with hypertension but also to prevent its development in those without hypertension.
Elevated BP causes vascular damage and accelerates arterial stiffening2). Conversely, increased arterial stiffness leads to the deterioration of arterial properties, such as endothelial dysfunction and early return of reflected pulse waves from the periphery, which in turn worsens BP regulation2). Therefore, in individuals without hypertension, increased arterial stiffness may be a risk factor for the development of hypertension. The second derivative of the finger photoplethysmogram (SDPTG) has been used as a non-invasive and convenient method for pulse wave analysis in various clinical, occupational, and epidemiological settings3-18). The SDPTG is obtained from double differentiation of the finger photoplethysmogram (PTG), and indices calculated from the SDPTG represent the structural and functional properties of both the central and peripheral arteries15, 19). Several previous studies, including ours, have suggested that the SDPTG indices are associated with BP8-10, 13, 17, 18), other cardiovascular risk factors5, 8-10, 13, 16, 17, 20) and the estimated risk of coronary heart disease8). In addition, the SDPTG index has been reported to predict cardiovascular mortality in a Japanese cohort study21).
Previous studies have shown that the arterial stiffness indices obtained using tonometric or oscillometric methods can predict the risk of developing hypertension22-27). However, no data exists regarding the longitudinal association between the SDPTG indices and the risk of developing hypertension.
The aim of this study was to test whether the SDPTG indices can predict future development of hypertension in a middle-aged male population.
This study was conducted at a precision equipment manufacturing company in Kanagawa, Japan. A total of 1,093 male workers aged between 35–63 years who underwent medical checkup (including SDPTG measurement) in 2005 (baseline examination) were recruited for this study. Among them, individuals with hypertension (n=186), history or presence of cardiovascular disease (n=3), and incomplete recording of the SDPTG (n=2) were excluded. Finally, 902 individuals without hypertension participated in this study. The study protocol was approved by the Institutional Ethics Committee of the Nippon Medical School, Tokyo, Japan (date of approval: 5th October, 2005). All the participants provided written informed consent.
Baseline ExaminationAll participants underwent anthropometric and BP measurements as well as blood tests. All measurements were conducted between 9 AM and 11 AM in a temperature-controlled room, maintained at 22±2℃.
Brachial systolic and diastolic BP were measured by well-trained staff members using a mercury sphygmomanometer with an optimal cuff size selected for the participants’ arm circumference. BP measurements were taken on the right arm of a seated participant after at least 5 minutes of rest. The first and fifth Korotkoff sounds were recorded to determine the systolic and diastolic BP, respectively. BP was measured twice with a 1-minute interval between measurements. The recording that provided a lower BP category, according to the guidelines for the management of hypertension28, 29), was used for the analysis. If the BP category was the same between the measurements, the recording that showed a lower systolic BP was used. Hypertension was defined as systolic BP ≥ 140 mm Hg, diastolic BP ≥ 90 mm Hg, or current use of antihypertensive medications.
A self-report questionnaire was used to collect data regarding the participants’ parental history of hypertension and lifestyle factors, including smoking status, exercise habits, and alcohol intake. Smoking status was categorized as current or non-smoking. Current smoking was defined as regular cigarette consumption (at least once daily) at the time of the study. Regular exercise was defined as continuous exercise for at least 15 minutes on ≥ 3 days per week for at least 1 year. Weekly alcohol intake was calculated by combining the amount of alcohol consumed per day and frequency per week. Excessive alcohol intake was defined as an alcohol intake ≥ 300 g/week, based on the results of a large-scale Japanese cohort study30).
The participants’ heights and weights were measured without shoes and with light indoor clothing to determine their body mass index, which was calculated as body weight (kg) divided by the square of the height (m2). Obesity was defined as a body mass index ≥ 25 kg/m2.
Blood samples were collected from the antecubital vein after overnight fasting. Standard enzymatic methods were used to measure serum total cholesterol, triglyceride, creatinine, and plasma glucose levels. Serum high-density lipoprotein cholesterol (HDL-C) levels were measured using the direct method. Serum low-density lipoprotein cholesterol (LDL-C) levels were calculated using Friedewald’s formula31) in 893 participants with serum triglyceride levels <400 mg/dl. Serum C-reactive protein levels were measured using a latex turbidimetric immunoassay. Dyslipidemia was defined as an LDL-C level ≥ 140 mg/dl, a triglyceride level ≥ 150 mg/dl, an HDL-C level <40 mg/dl, or current use of antidyslipidemic medications. Impaired fasting glucose/diabetes mellitus was defined as a fasting plasma glucose level ≥ 110 mg/dl or current use of glucose-lowering medications. Estimated glomerular filtration rate was calculated according to an equation presented by the Japanese Society of Nephrology32).
SDPTG MeasurementThe SDPTG was recorded in the sitting position using an SDP-100 instrument (Fukuda Denshi, Tokyo, Japan), with the participant having rested for at least 5 minutes. A transducer was placed on the cuticle of the forefinger of the left hand, at the same height as the participant’s heart. The signal of the blood volume changes in the peripheral circulation, which indicated PTG, was sent to the SDP-100. The PTG measurement methodology has been described in detail elsewhere33). Multiple waveforms of the PTG were obtained during the 5-s of recordings and averaged. Double differentiation of the PTG (i.e., the SDPTG) was then performed automatically using the device.
A representative waveform of the PTG and SDPTG is shown in Fig.1. The SDPTG consists of four waves in systole (‘a,’ ‘b,’ ‘c,’ and ‘d’ waves) and one wave in diastole (‘e’ wave). The ratio of the height of the ‘b’ and ‘d’ waves to that of the ‘a’ wave (b/a and d/a) was calculated. Acceptable reproducibility of these indices has been reported previously34, 35). A higher b/a ratio represents increased stiffness of large elastic arteries, while a lower d/a ratio represents increased systemic arterial stiffness, including impaired structural and functional properties of small and muscular arteries and peripheral circulation15).

The SDPTG comprises five consecutively named waves: ‘a,’ ‘b’, ‘c’, ‘d,’ and ‘e’. The b/a and the d/a were defined as the ratio of the height of ‘b’ and ‘d’ waves to that of ‘a’ wave, respectively.
The outcome of this study was the development of hypertension. BP and initiation of antihypertensive medications were followed up for a maximum of four years via annual medical checkup data, and the development of hypertension was determined using this information. Participants were censored when they lost to follow-up or when they completed the 4-year follow-up period without developing hypertension.
Statistical AnalysisAll statistical tests were performed using the Stata software (version 15.0; StataCorp, College Station, Texas, USA). Continuous variables with and without skewed distribution are presented as median (interquartile range) and mean±SD, respectively. Categorical data are presented as numbers (percentages). Continuous variables were compared using unpaired t-test or the Mann–Whitney U test. Categorical data were compared using the chi-square test. Pearson’s moment correlation coefficient was used to evaluate the simple correlation between the SDPTG indices and baseline BP. To examine the risk of developing hypertension associated with the b/a or d/a ratios, unadjusted, age-adjusted, and multi-adjusted Cox proportional hazards models were used to calculate the hazard ratio (HR) and corresponding 95% confidence interval (CI). The b/a and d/a ratios were divided into quartiles and used for the analyses. Because the d/a ratio has been reported to be negatively associated with increased arterial stiffness15), the highest quartile of the d/a ratio was set as a reference. The covariates used in the multi-adjusted Cox analysis were age, body mass index, C-reactive protein level, pulse rate, dyslipidemia, impaired fasting glucose/diabetes mellitus, estimated glomerular filtration rate, current smoking, regular exercise, weekly alcohol intake, family history of hypertension, and baseline systolic and diastolic BP. The violation of the proportional hazard assumption for the b/a and d/a ratios was not shown according to the Schoenfeld residuals (p=0.64 and p=0.39, respectively). Finally, to determine the effect of lifestyle-related factors on the association between the SDPTG indices and the risk of developing hypertension, a subgroup analysis with interaction of the subgroups×the SDPTG indices was performed. All statistical tests were 2-sided, and p<0.05 was considered statistically significant.
As presented in Table 1, the mean age at baseline was 43.5±6.1 years. The mean systolic and diastolic BPs were 116.7±10.4 mm Hg and 74.3±7.6 mm Hg, respectively, and approximately half of participants had optimal BP. Approximately 45% had dyslipidemia, and only 4.4% had impaired fasting glucose/diabetes mellitus.
| Variables | Overall | Development of hypertension | p value* | |
|---|---|---|---|---|
| (–) | (+) | |||
| Number of subjects | 902 | 778 | 124 | |
| Age, years | 43.5±6.1 | 43.3±6.1 | 45.0±5.6 | 0.002 |
| Body mass index, kg/m2 | 23.1±2.7 | 22.8±2.6 | 24.4±3.1 | <0.001 |
| Obesity, n (%) | 196 (21.7) | 152 (19.5) | 44 (35.5) | <0.001 |
| Systolic BP, mm Hg | 116.7±10.4 | 115.3±10.1 | 125.3±7.8 | <0.001 |
| Diastolic BP, mmHg | 74.3±7.6 | 73.5±7.4 | 79.4±6.6 | <0.001 |
| BP category | ||||
| Optimal, n (%) | 435 (48.2) | 420 (54.0) | 15 (12.1) | <0.001 |
| Normal, n (%) | 275 (30.5) | 232 (29.8) | 43 (34.7) | |
| High normal, n (%) | 192 (21.3) | 126 (16.2) | 66 (53.2) | |
| Pulse rate, bpm | 68.8±9.3 | 71.9±9.3 | 68.3±9.2 | <0.001 |
| Total cholesterol, mg/dl | 199.4±31.7 | 206.6±31.7 | 206.6±30.6 | 0.006 |
| LDL cholesterol, mg/dl (n = 893) | 131.0±33.0 | 130.1±32.6 | 136.9±3.0 | 0.035 |
| HDL cholesterol, mg/dl | 56.3±13.4 | 56.2±13.4 | 57.2±13.1 | 0.41 |
| Triglycerides, mg/dl (IQR) | 90 (63, 130) | 89 (61, 127) | 105.5 (71.5, 142) | 0.039 |
| Dyslipidemia, n (%) | 415 (46.0) | 350 (45.0) | 65 (52.4) | 0.12 |
| Fasting plasma glucose, mg/dl | 91.0±11.4 | 90.6±11.4 | 93.2±11.4 | 0.019 |
| IFG/diabetes, n (%) | 40 (4.4) | 31 (4.0) | 9 (7.3) | 0.10 |
| Serum creatinine, mg/dl | 0.82±0.13 | 0.82±0.13 | 0.82±0.16 | 0.83 |
| Estimated GFR, ml/min/1.73m2 | 84.2±14.4 | 84.2±13.6 | 84.3±18.4 | 0.94 |
| C-reactive protein, mg/l (IQR) | 0.3 (0.2, 0.6) | 0.3 (0.2, 0.6) | 0.4 (0.2, 0.75) | 0.008 |
| Current smoking, n (%) | 265 (29.4) | 233 (30.0) | 32 (25.8) | 0.35 |
| Weekly alcohol intake, g/week (IQR) | 57.5 | 57.5 | 103.5 | 0.050 |
| (11.5, 149.5) | (11.5, 149.5) | (23, 207) | ||
| Excessive alcohol intake, n (%) | 67 (7.4) | 56 (7.2) | 11 (8.9) | 0.51 |
| Regular exercise, n (%) | 197 (21.8) | 170 (21.9) | 27 (21.8) | 0.99 |
| Family history of hypertension, n (%) | 205 (22.7) | 170 (21.9) | 35 (28.2) | 0.12 |
| b/a | -0.64±0.11 | -0.64±0.11 | -0.62±0.11 | 0.11 |
| d/a | -0.25±0.11 | -0.24±0.11 | -0.30±0.11 | <0.001 |
BP, blood pressure; bpm, beats per minute; LDL, low-density lipoprotein; HDL, high-density lipoprotein; IQR, interquartile range; IFG, impaired fasting glucose; GFR, glomerular filtration rate. *Comparison between the groups with and without developing hypertension. Chi-square test for categorical variables, Mann–Whitney U test for triglycerides, C-reactive protein, and weekly alcohol intake, and unpaired t-test for other continuous variables.
The correlations of the b/a and d/a ratios with baseline BP are shown in Fig.2. The d/a ratio showed a significant but weak correlation with both systolic and diastolic BP (r=-0.21, p<0.001 and r=-0.19, p<0.001, respectively). The b/a ratio showed a statistically significant but clinically meaningless correlation with systolic BP (r=0.08, p=0.012).

Scatter plots showing the correlation of the b/a or d/a ratio with systolic and diastolic blood pressures
During a total follow-up of 3,226 person-years, 124 individuals developed hypertension (112 showed systolic/diastolic BP ≥ 140/90 mm Hg and 12 initiated antihypertensive medications), and 698 were censored at the completion of the 4-year follow-up, whereas the remaining 80 were censored before the completion of the 4-year follow-up. The rate of developing hypertension per 1,000 person-years was 38.4 (95% CI 32.2–45.8). Compared with participants who did not develop hypertension, those who did were older and had a higher prevalence of obesity, higher systolic and diastolic BP, lower pulse rate, higher LDL-C levels, and higher serum C-reactive protein levels at baseline (Table 1). There were no significant differences in the prevalence of dyslipidemia, prevalence of impaired fasting glucose/diabetes mellitus, and estimated glomerular filtration rate between the groups. Similar findings were observed regarding current smoking, excessive alcohol intake, regular exercise, and family history of hypertension. The d/a ratio was significantly lower in participants who developed hypertension (-0.30±0.11) than in those did not develop hypertension (-0.24±0.11, p<0.001). In contrast, the b/a ratio did not differ significantly between the groups (-0.62±0.11 and -0.64±0.11, respectively, p=0.11).
Table 2 shows the HRs for the development of hypertension associated with the quartiles of the b/a and d/a ratios. For the d/a ratio, the HR for the development of hypertension gradually increased with decreasing quartiles in the unadjusted, age-adjusted, and multi-adjusted models (p<0.001 for trend in all models). The lowest quartile of the d/a ratio showed a significantly increased HR for the development of hypertension, relative to the highest quartile, in the unadjusted, age-adjusted, and multi-adjusted (HR 2.84, 95% CI 1.58–5.13, p<0.001) models. In the multi-adjusted model, predictors of hypertension occurrence other than the d/a ratio were body mass index, pulse rate, and baseline systolic BP (data not shown). For the b/a ratio, the HR for the development of hypertension gradually increased with increasing quartiles in the unadjusted model, but it did not reach statistical significance (p=0.074 for trend). However, there were no significant HR trends for increase in the quartiles of the b/a ratio in the age-adjusted or multi-adjusted model. Moreover, no significant HR for the development of hypertension was observed in any quartile of the b/a ratio compared with the lowest quartile in any model.
| b/a | Quartile of b/a | p for trend | |||
| Lowest | Second | Third | Highest | ||
| Range | -1.02 ~ -0.72 | -0.71 ~ -0.64 | -0.63 ~ -0.57 | -0.56 ~ -0.25 | |
| No. of case/at risk | 30/232 | 27/245 | 28/203 | 39/222 | |
| Unadjusted | |||||
| Hazard ratio | 1.00 | 0.83 | 1.06 | 1.45 | 0.074 |
| 95% CI | Reference | 0.49–1.40 | 0.63–1.77 | 0.90–2.33 | |
| p value | - | 0.48 | 0.83 | 0.13 | |
| Age-adjusted | |||||
| Hazard ratio | 1.00 | 0.75 | 0.90 | 1.10 | 0.52 |
| 95% CI | Reference | 0.45–1.27 | 0.53–1.53 | 0.66–1.83 | |
| p value | - | 0.29 | 0.71 | 0.72 | |
| Multi-adjusted* | |||||
| Hazard ratio | 1.00 | 0.88 | 1.04 | 1.30 | 0.28 |
| 95% CI | Reference | 0.51–1.51 | 0.60–1.79 | 0.75–2.25 | |
| p value | - | 0.41 | 0.84 | 0.41 | |
| d/a | Quartile of d/a | p for trend | |||
| Highest | Third | Second | Lowest | ||
| Range | 0.04 ~ -0.17 | -0.18 ~ -0.23 | -0.24 ~ -0.31 | -0.32 ~ -0.71 | |
| No. of case/at risk | 18/225 | 22/216 | 29/229 | 55/232 | |
| Unadjusted | |||||
| Hazard ratio | 1.00 | 1.28 | 1.62 | 3.38 | <0.001 |
| 95% CI | Reference | 0.69–2.39 | 0.90–2.92 | 1.99–5.76 | |
| p value | - | 0.44 | 0.11 | <0.001 | |
| Age-adjusted | |||||
| Hazard ratio | 1.00 | 1.24 | 1.50 | 2.94 | <0.001 |
| 95% CI | Reference | 0.67–2.32 | 0.83–2.73 | 1.67–5.18 | |
| p value | - | 0.50 | 0.18 | <0.001 | |
| Multi-adjusted* | |||||
| Hazard ratio | 1.00 | 1.56 | 1.62 | 2.84 | <0.001 |
| 95% CI | Reference | 0.83–2.94 | 0.88–2.96 | 1.58–5.13 | |
| p value | - | 0.17 | 0.12 | <0.001 | |
CI, confidence interval. *Adjusted for age, body mass index, C-reactive protein, pulse rate, dyslipidemia, impaired fasting glucose/diabetes mellitus, estimated glomerular filtration rate, current smoking, regular exercise, weekly alcohol intake, family history of hypertension, and baseline systolic and diastolic blood pressure.
Since significant increases in the risk of hypertension were observed only in the quartiles of the d/a ratio, subgroup analyses by lifestyle-related factors were conducted only in the d/a group. As shown in Fig.3, increased risk of hypertension in the lowest quartile of the d/a ratio, compared with that in the highest quartile, remained consistent in all subgroups. There was no significant interaction of the subgroups×quartile of the d/a ratio for the risk of developing hypertension.

Error bars indicate 95% CI. *Adjusted for age, body mass index, C-reactive protein, pulse rate, dyslipidemia, impaired fasting glucose/diabetes mellitus, estimated glomerular filtration rate, current smoking (except when this is a subgroup factor), regular exercise (except when this is a subgroup factor), weekly alcohol intake, family history of hypertension, and baseline systolic and diastolic blood pressure.
The novel and most important finding of this study was that the lowest quartile of the d/a ratio was associated with an approximately three-fold greater risk of developing hypertension, compared with the highest quartile, in a working-age male population. Our study also showed that the risk of developing hypertension gradually increased with decreasing d/a quartiles. In contrast, no significant association was observed between the b/a ratio and the risk of developing hypertension. These findings suggest that increased stiffness of the systemic arterial tree, including small and muscular arteries, rather than large elastic arteries, is associated with a future BP increase, leading to an increased risk of developing hypertension in this study population. Subgroup analyses by lifestyle-related factors showed that the risk of developing hypertension in the lowest quartile of the d/a ratio remained consistent in all subgroups with no statistical significance of the interaction. Therefore, the d/a ratio may be useful for estimating the risk of future developing hypertension, irrespective of individual lifestyle variations.
Several epidemiological studies have been conducted to evaluate the predictive value of arterial stiffness for future development of hypertension22-27). Among these studies, most indices representing muscular, small, or systemic arterial stiffness predicted future development of hypertension23-26). These observations are in line with those of the present study in which the d/a ratio was significantly associated with the risk of developing hypertension. On the other hand, the present study did not show a significant association between the b/a ratio and the risk of developing hypertension, although previous studies showed the predictive ability of indices representing large elastic arterial stiffness (i.e., the aorta or carotid artery) for the development of hypertension22, 27). It has been reported that large elastic arterial stiffness correlates quadratically with age, with the increase being particularly pronounced after the age of 50–60 years36, 37). Therefore, one possible explanation for the discrepant results may be the difference in the participants’ age between the studies; the mean age was 56–60 years in previous studies22, 27) and 44 years in the present study.
The correlation coefficients of the d/a ratio with systolic and diastolic BPs in our study were -0.21 and -0.19, respectively. These results suggest that a substantial clinical relationship was not shown between the d/a ratio and baseline BP, as only 4.4% (=-0.21^2) and 3.6% (=-0.19^2) of systolic and diastolic BP, respectively, could be explained by the d/a ratio. Furthermore, the association between the d/a ratio and the risk of developing hypertension remained significant after adjusting for covariates that showed significant differences between the groups with and without developing hypertension, such as baseline systolic and diastolic BP, age, body mass index, pulse rate, lipid and glycemic profiles, and C-reactive protein levels, which are also known risk factors for hypertension38-49). Taken together, our study indicates that the d/a ratio did not show a substantial clinical relationship with baseline BP, but had a significant predictive ability for the development of hypertension, independent of known risk factors for hypertension.
As in previous research using tonometric and oscillometric methods22-27), our current study showed that increased arterial stiffness evaluated with the SDPTG was associated with the risk of developing hypertension. The SDPTG has also been reported not only to be associated with the estimated risk of coronary heart disease8) but also to predict cardiovascular mortality21). The strengths of the SDPTG measurement are that it is less time-consuming and easier to perform than conventional measurements using tonometric or oscillometric methods, such as carotid-femoral or brachial-ankle pulse wave velocity and cardio-ankle vascular index. Indeed, application of the SDPTG in epidemiological settings has been recommended because of its simplicity and easy accessibility50). This suggests that the SDPTG may be a more useful modality for identifying individuals at an increased risk of developing hypertension and subsequent cardiovascular disease in high-throughput settings, such as routine health screening. Taken together, our results provide further evidence for the clinical utility of SDPTG in the field of cardiovascular preventive medicine.
This study had several limitations. First, the study population comprised only middle-age Japanese men. Therefore, it is unknown whether our results can be extrapolated to women, older adults, or other ethnic groups. Second, sodium intake was not assessed in this study, although excessive sodium intake is well known to raise BP and thus increase the risk of developing hypertension. In this respect, it is also not possible to fully control for other residual confounding factors, as this is a cohort study. Third, a weakness of SDPTG measurement is the difficulty in obtaining plethysmograph waveforms in individuals with impaired capillary blood flow in the fingertip. Tonometric or oscillometric measurements may be superior to finger plethysmographic measurements for those individuals. Fourth, because it is difficult to know exactly when hypertension developed, we defined the date of hypertension development as the date of the annual health examination in which hypertension was diagnosed, which may have adversely affected the reliability of our results. However, this limitation is unavoidable in cohort studies that use annual health examination results as the study outcome. Finally, the follow-up duration in our study was shorter than that in previous studies on the longitudinal association between arterial stiffness and the risk of developing hypertension22, 25-27). The predictive value of the b/a ratio might have been observed if the follow-up period was longer and the participants were older. Further long-term follow-up studies with larger, multi-racial and wider age populations are expected to be conducted to examine the predictive value of the SDPTG indices for the development of hypertension.
This study revealed a significant association between the d/a ratio, an index obtained from SDPTG waveforms, and the risk of developing hypertension in middle-aged Japanese males. This finding suggests that increased stiffness of the systemic arterial tree, including small and muscular arteries, is involved in future BP increase and the subsequent development of hypertension. From a clinical perspective, d/a measurement may be useful in cardiovascular preventive medicine to identify individuals at an increased risk of developing hypertension.
We would like to thank Editage (www.editage.jp) for English language editing.
The authors declare no conflicts of interest.
This study did not receive any specific grants from funding agencies in the public, commercial, or not-for-profit sectors.