Introduction

Energy transfer, temperature regulation, and human response to cold and heat exposure have been intensively investigated. It had been questioned why the human body needs new food daily as a source of energy input and how the energy is manipulated. Energy input would be transformed into two components, i.e. the storage and the loss. The energy that is released from the body includes the heat loss (H_loss) and the work performed by the body [1]. The body consumes energy for maintaining its homeostasis. In the resting state, more than 75% of the energy expenditure is transformed into heat and is the so-called heat production (H_prod). Heat released by the metabolic process warms up the body tissue and increases the core and the skin temperature. At rest, almost all H_prod is released via dry H_loss in which radiative heat loss, convective and conductive heat loss, respiratory heat loss, and evaporative heat loss account for 54–60%, 25%, 14%, and 7% of total H_prod, respectively [2]. During exercise, when the body temperature (BT) increases up to a particular threshold, it alerts the preoptic/anterior hypothalamus to initiate heat dissipation by stimulating cutaneous vasodilation and sweating. At a given H_prod, individual responses of the skin blood flow and the evaporation differ at BT threshold [3]. In particular, the heat stress circumstance occurs when H_prod is not completely released, and the heat-storage content (heat load, H_load): (Eq1) produces an increase in body core temperature. In terms of BT, heat capacity (HC) is an important factor that determines the magnitude of temperature change in the body at a given H_load. The investigation of HC dates back to the eighteenth century with experiments on the HC of animals performed by Crawford (cited by Kakitsuba) [4]. The most commonly used value of the average specific HC (S_pHC), the HC per mass, of the human body was proposed as 0.83 kcal·kg^-1·°C^-1by Sentor in the nineteenth century (cited by Kakitsuba) [4]. The value of 0.83 kcal·kg^-1·°C^-1 has been widely used until the present despite the criticisms that the value overestimates the actual HC in estimating the heat-storage content [2, 5]. It has been revealed that S_pHC of body components are not identical and the HC equation using S_pHC for particular body components was more precise [4–9]. Based on S_pHC (1.88 kcal·kg^-1·°C^-1for fat and 3.72 kcal·kg^-1·°C^-1for fat-free mass), as cited by Minard [6], Webb developed an equation and reported a S_pHC as 0.837 and 0.669 kcal·kg^-1·°C^-1 for those who have a fat proportion of 12 and 50% of fat, respectively [7]. Using the same approach, Blaxter provided slightly different values for the same calculation as 0.765 and 0.652 kcal·kg^-1·°C^-1 [8]. Using a two-compartment model (fat and fat-free mass), Havenith created an equation for HC in which the S_pHC for fat tissue was 2.51 kj·kg^-1·°C^-1(0.60 kcal·kg^-1·°C^-1) and the S_pHC for fat-free mass was 3.65 kj·kg^-1·°C^-1 (0.872 kcal·kg^-1·°C^-1) [10, 11], whereas a four-element model proposed S_pHC for water, fat, protein, and mineral tissues as 1, 0.507, 0.299, and 0.201 kcal·kg^-1·°C^-1, respectively [2]. Although the HC equation based on body-composition-specific HC can predict the heat storage more precisely than an average S_pHC for the whole body, body composition analysis is not available for general population. H_load and H_loss should be equal so as to maintain the constant BT. H_loss depends on the body surface area (BSA) and the temperature gradient from the body to the environment [12, 13]. H_load increases the BT depending on the HC of the body. Therefore, BSA and HC may be correlated to each other. Our study attempted to compare the previously known HC estimating equations in order to investigate the relationship between HC and the anthropometric variables, including weight and BSA, to derive a predictive equation for HC with anthropometry data for the first time.

Materials and Methods

Measurements

Standing height and weight were assessed using a digital scale. BSA was calculated using the DuBois and DuBois EF formula [16]. Body components including body-fat mass, protein mass, mineral mass, and total body water were measured by multi-frequency bioelectrical impedance analysis (BIA) using the InBody 720 body composition analyzer (Inbody, Seoul, Korea).

HC was estimated using four equations including HC_Eq1 which was based on the widely used average S_pHC (0.83 kcal·kg^-1·°C^-1) and body weight (BW) [2], HC_Eq2 which was based on Webb’s equation [7], HC_Eq3 which was based on Havenith’s equation [10, 11], and HC_Eq4 which was based on a four-component model [2].

(HC_Eq1)(HC_Eq2)(HC_Eq3)(HC_Eq4)

Results

The training set included 282 men and 318 women, whereas the test set was composed of 138 men and 164 women. There was no difference in the demographic data, body composition characteristics or HC among the training and test sets (Table 1). Fig 1 shows the correlations between each HC equation. In general, the HC equations were well-correlated to each other. Equations based on two components (HC_Eq2 and HC_Eq3) and four components (HC_Eq4) were strongly correlated (r = 0.996 to 0.999, mean difference = 1.64 to 4.62 kcal·°C^-1), whereas equations using the average S_pHC for the whole body overestimated HC compared to the other equations (r = 0.974 to 0.990, mean difference = 1.66 to 6.28 kcal·°C^-1). The difference among HCs estimated by equations based on body composition data was lowest between HC_Eq4 and HC_Eq2. Because HC_Eq4 originated from more precise body composition analysis, further analysis regarding the relationship between HC and the anthropometric indices was performed using HC_Eq4.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 1. Correlation between the heat capacity (HC) values estimated by four equations.

HC_Eq1, heat capacity calculated based on the widely used average specific heat capacity (0.83 kcal·kg^-1·°C^-1) and body weight; HC_Eq2, heat capacity calculated based on Minard’s equation; HC_Eq3, heat capacity calculated based on Havenith’s equation; and HC_Eq4, heat capacity calculated based on four components model. r, correlation coefficient; Diff, mean and 95% confident interval of difference between the two HC values (x—y).

https://doi.org/10.1371/journal.pone.0141498.g001

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Demographic, body composition, and heat capacity by gender in the training and test sets.

https://doi.org/10.1371/journal.pone.0141498.t001

The relationship between BW versus HC_Eq4 and BSA versus HC_Eq4 could be described by a linear regression model (HC_Eq4 versus BW, r = 0.986, 0.988, and 0.986 for the total, men, and women, respectively; HC_Eq4 versus BSA, r = 0.985, 0.974, and 0.955 for the total, men, and women, respectively). In Fig 2, the correlation coefficients between HC_Eq4 and weight were high, however, there was a clear gender difference. The gender difference was attenuated between HC_Eq4 and BSA. This pattern was also found in the same analysis for HC_Eq2 and HC_Eq3 (S1 Fig). Table 2 shows the results of the multivariate regression analysis. In the case of model 1 adjusted according to age, gender, and BW, all of the factors were significantly associated. In the case of model 2 adjusted according to age, gender, and BSA, all of the factors were also significantly associated for predicting HC, however, the gender differences were clearly attenuated and the coefficient for female was decreased from -2.96 to -0.36. In the case of model 3 adjusted with age, gender, BW, and BSA, age was not associated with HC whereas gender, BW, and BSA, were significantly associated. Interestingly, although BSA and BW was strongly correlated (r = 0.97), they contributed independently in predicting HC. After adjusting for BW and BSA, women on the average had lower HC than men by 1.96 kcal·°C^-1 (95%CI, 1.76 to 2.16 kcal·°C^-1). Three factors, including gender, BW, and BSA, explained more than 99% of the variation of HC estimated by HC_Eq4 among individuals (Table 2). The predictive model for HC with anthropometry data of the 600 study patients was HC (kcal ⋅ °C⁻¹) = 14.29 × BSA (m²) + 0.46 × BW (kg) − 1.96 (if women) − 6.06.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. Relationship between heat capacity (HC) estimated using the equation based on the four-component model (HC_Eq4) and weight (a) and body surface area (b) for men (black dots) and for women (grey dots).

https://doi.org/10.1371/journal.pone.0141498.g002

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 2. Multivariate regression analysis for predicting HC_Eq4.

https://doi.org/10.1371/journal.pone.0141498.t002

As for the analysis of concordance on the test set, the predictive model for HC with anthropometry data showed extremely highly satisfactory values (r = 0.996; ICC = 0.996). The predictive model also had a low standard error of measurement (SEM = 0.77 kcal·°C^-1) with the limits of agreement varying approximately±1.5 kcal·°C^-1 (Fig 3). The final predictive model for HC with anthropometry data from all of the study patients was HC (kcal ⋅ °C⁻¹) = 14.482 × BSA (m²) + 0.456 × BW (kg) − 1.996(if women) − 6.064 (r = 0.996, S1 Table.)

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. Bland Altman plot with marginal histograms for the agreement between the predictive model and HC_Eq4 in the test set.

Bias, mean of differences between the two HC equations, the predictive model and HC_Eq4; Upper LoA, upper level of limits of agreement = mean of differences + 1.96 standard deviation; Lower LoA, lower level of limits of agreement = mean of differences—1.96 standard deviation; r, Pearson correlation coefficients; ICC, Intraclass correlation coefficient; SEM, standard error of measurement.

https://doi.org/10.1371/journal.pone.0141498.g003

Discussion

Although HC plays an important role in the process of heat balancing, very few studies pay attention on investigating an accurate and simple tool for calculating HC. In previous studies, HC has been popularly calculated by multiplying BW to the average S_pHC, 0.83 kcal·kg^-1·°C^-1. However, it has been revealed that the equation using the average S_pHC overestimated the actual human body HC [4–9]. In concordance with that, in the present study the HC equation using the average S_pHC provided a higher value compared with those using body composition data, particularly with that using the four components model. We also found that gender interacted more strongly in the relationship between HC and weight, but unsteadily in the relationship between HC and BSA. In addition, BSA contributed to HC as an independent factor in addition to weight. The model that includes both BW and BSA appears to be better than that containing each variable alone. The model composed of weight, BSA, and gender appeared to be extremely well fitted for predicting HC without any information regarding body composition. With the 99% variation of HC which could be explained by the model with gender, weight, and BSA, we are able to correctly estimate HC without using complicated body component measurement. The validation analysis showed that the predictive model was reliable and sufficient to be applied for estimating HC. Anthropometry-based calculation of HC is a very useful feature in many other fields, including sports science, architectural engineering, environment physiology, etc.

Our study is the first to date to attempt to investigate the relationship between BSA and HC. Heat load increases the BT depending on HC. Heat loss depends on the temperature gradient between the BT and the ambient temperature and BSA. Both heat load and heat loss should be the same for the maintenance of BT. Therefore, if the ratio of the change of BT and the temperature gradient is relatively constant, the HC and BSA should be linearly correlated with each other. Our results very strongly demonstrate this possibility. The relationship between weight and HC was highly correlated in our results, however, there were clear gender differences. Interestingly, the gender differences were greatly attenuated in the relationship between BSA and HC. These results suggest the possibility that the human body during its development adaptively matches HC and BSA to each other in order to regulate the BT.

The relationship of BW, BSA, and HC may shed some light on the heat flow in the body. During prolonged physical exercise, BW may be remarkably reduced due to dehydration while the BSA remains constant [17]. That consequently induces the reduction of HC, increases the temperature load, and enhances the heat-related damage. All of our study participants were healthy and without any known disease. The linear relationships between HC and BSA were observed in a healthy population in which all of the participants were considered as normal in their thermoregulation response and in their capacity to balance the heat flow. We assume that the balance between HC and BSA may be skewed in unhealthy status patients and which might be related to a thermoregulation disorder. This could be a potential study hypothesis in future studies.

Our findings should be interpreted in the context of their strength and limitations. The present study enrolled a relatively high number of participants with a wide age range. However, because validation analysis was performed on the estimated HC values, the predictive model should be confirmed with measured values. Furthermore, because there were fewer patients aged in their 60s and no patient was 70 or older, the findings should be cautiously applied in the elderly population. It has been widely accepted that multi-frequency BIA is valid tool to estimate body composition, particularly in predicting lean mass, fat mass, and total body water [18–22]. Evidence also revealed that multi-frequency BIA is a useful approach for body somatic protein store [23] and body bone mineral content estimation [24]. In addition, because proportion of protein and mineral mass is relatively low in contribution to BW, potential bias of these body components measurement in predicting body HC seems to be not crucial. Since the body fat content strongly affects the HC, the bias from our new equation may be caused by the fat content. We found the fat mass or the % fat mass correlated with the difference in predictive model HC and HC_Eq4, however, the estimation bias was relatively low and less than ± 1 kcal·°C^-1 per 10 kg fat mass or per 10% fat mass (S2 Fig). Therefore the new equation can be applied within our data range of fat mass or % fat mass and should be employed with care for those who have extremely low or high fat mass.

In conclusion, our results suggest that gender, BSA, and weight are the independent factors for calculating HC. For the first time, a predictive equation based on anthropometry data was developed and this equation could be useful in estimating HC in the general population without body composition measurements.

Supporting Information

Acknowledgments

This work was supported by the Bio & Medical Technology Development Program of the National Research Foundation (NRF) funded by the Ministry of Science, ICT & Future Planning (Fund receiver Chae Hun Leem, No. 2012–0009829, No. 2015M3A9B6028310 and No. 2014M3A9D7034366).