Thermoregulation in premature infants: A mathematical model

Author’s Accepted Manuscript Thermoregulation in mathematical model

premature

infants:

a

Carina Barbosa Pereira, Konrad Heimann, Michael Czaplik, Vladimir Blazek, Boudewijn Venema, Steffen Leonhardt www.elsevier.com/locate/jtherbio

PII: DOI: Reference:

S0306-4565(16)30028-6 http://dx.doi.org/10.1016/j.jtherbio.2016.06.021 TB1778

To appear in: Journal of Thermal Biology Received date: 31 January 2016 Revised date: 29 April 2016 Accepted date: 29 June 2016 Cite this article as: Carina Barbosa Pereira, Konrad Heimann, Michael Czaplik, Vladimir Blazek, Boudewijn Venema and Steffen Leonhardt, Thermoregulation in premature infants: a mathematical model, Journal of Thermal Biology, http://dx.doi.org/10.1016/j.jtherbio.2016.06.021 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Thermoregulation in premature infants: a mathematical model Carina Barbosa Pereira1*, Konrad Heimann2, Michael Czaplik3, Vladimir Blazek1,4, Boudewijn Venema1, Steffen Leonhardt1 1

Chair for Medical Information Technology, Helmholtz-Institute for Biomedical Engineering, RWTH

Aachen University, Aachen, Germany 2

Department of Neonatology, University Children's Hospital, University Hospital RWTH Aachen,

Germany 3

Department of Anesthesiology, University Hospital RWTH Aachen, Aachen, Germany

4

Czech Institute of Informatics, Robotics and Cybernetics (CIIRC), CTU Prague, Prague, Czech Republic

Corresponding author. Chair for Medical Information Technology, Helmholtz-Institute for Biomedical Engineering, RWTH, Aachen University, Pauwelsstrasse 20, D-52074 Aachen, Germany, Phone: +49 241 80 – 23202. [email protected]

Abstract PURPOSE: In 2010, approximately 14.9 million babies (11.1%) were born preterm. Because preterm infants suffer from an immature thermoregulatory system they have difficulty maintaining their core body temperature at a constant level. Therefore, it is essential to maintain their temperature at, ideally, around 37 °C. For this, mathematical models can provide detailed insight into heat transfer processes and body-environment interactions for clinical applications. METHODS: A new multi-node mathematical model of the thermoregulatory system of newborn infants is presented. It comprises seven compartments, one spherical and six cylindrical, which represent the head, thorax, abdomen, arms and legs, respectively. The model is customizable, i.e. it meets individual characteristics of the neonate (e.g. gestational age, postnatal age, weight and length) which play an important role in heat transfer mechanisms. The model was validated during thermal neutrality and in a transient thermal environment. RESULTS:

During thermal neutrality the model accurately predicted skin and core temperatures. The difference in mean core temperature between measurements and simulations averaged 0.25 ± 0.21 °C and that of skin temperature averaged 0.36 ± 0.36 °C. During transient thermal conditions, our approach simulated the thermoregulatory dynamics/responses. Here, for all infants, the mean absolute error between core temperatures averaged 0.12 ± 0.11 °C and that of skin temperatures hovered around 0.30 °C. CONCLUSIONS: The mathematical model appears able to predict core and skin temperatures during thermal neutrality and in case of a transient thermal conditions.

Keywords: Thermoregulation; Physiological processes; Premature infants; Bioheat model; Computer simulation 1. Introduction In 2010, approximately 11.1% (uncertainty range 9.1-13.4%) of all live births were preterm (≤ 37 weeks of gestation). This estimate corresponds to 14.9 (range 12.3-18.1) million babies worldwide (Blencowe et al., 2012). According to Blencowe et al. (2012), 10.4% [95% confidence interval (CI) 10.3-10.5%] were very preterm (28 to < 32 weeks), 5.2% (95% CI 5.1-5.3) extremely preterm (≤ 28 weeks) and the remaining 84.3% (95% CI 84.1-84.5) were moderate or late preterm (32 to < 37 weeks). In contrast to full-term babies, premature and very low birth weight (VLBW) babies (< 1,500 g) have an incompletely developed thermoregulatory system, making them highly vulnerable to changes in environmental temperature. Therefore, it is important to maintain their body temperature within a small target range (Abbas et al., 2011; Bissinger and Annibale, 2010; Lemons et al., 2001; Wrobel et al., 2010). According to clinical standards, the skin temperature of these babies should be maintained at 35.5-37.5 °C, with a core temperature of around 37 °C (36.8-37.5 ˚C) (Chen et al., 2012; Heimann et al., 2013; Meyer and Bold, 2007). However, the maintenance of body temperature is a complex process that involves lipolysis and gluconeogenesis: the more energy used to keep a constant body temperature, the less energy is available for other processes such as growth,

brain development and lung maturation (Abbas et al., 2011; Bissinger and Annibale, 2010). In addition, very immature infants are extremely vulnerable to heat loss since they have: a thin subcutaneous fat layer and reduced insulation capacity; a reduced amount of brown adipose tissue; high levels of evaporative losses; increased surface area to body weight ratio; and an underdeveloped autonomic control of the skin vasculature in the first days of life (Cramer et al., 2005; Elzouki et al., 2011; Knobel et al., 2011). Therefore, to reduce the mortality rate of premature/VLBW infants and improve clinical outcome, it is essential to avoid hypo- and hyperthermia by keeping an optimum environmental temperature (Asakura, 2004; Bissinger and Annibale, 2010; Chen et al., 2012; Elzouki et al., 2011; Ginalski et al., 2008; Wrobel et al., 2010). Detailed knowledge on heat transfer processes and body-environment interactions [e.g. related to room temperature, humidity and airflow in neonatal intensive care units) can be achieved by using adapted distributed models. These systematic tools can be used to plan and optimize warming therapies and hyperthermia processes, and also provide more detailed knowledge on pathophysiology related to heat transfer and influences of external factors. The models allow the simulation and prediction of clinical situations without involving real patients in experimental trials. Mathematical modeling of the human thermoregulatory system dates from the 1930s (Burton, 1934). From simple human heat balance equations (Aschoff and Wever, 1958; Burton, 1934), several two-node models were developed (Azer and Hsu, 1977; Gagge and Fobelets, 1985), followed later by more sophisticated models composed of several/multi segments (Fiala et al., 1999; Huizenga et al., 2001; Stolwijk and Hardy, 1966; Stolwijk et al., 1971; Werner and Webb, 1993; Wissler, 1964; Yi et al., 2004). In contrast to the two-node models, the multi-node models simulate a more detailed human body (thermoregulatory system) and more accurately predict global and local physiological responses. Stolwijk et al. (Stolwijk and Hardy, 1966; Stolwijk et al., 1971) developed a pioneering thermoregulation model (multi-node model) based on a man with a body weight of 74.1 kg and a body surface area of 1.89 m2: the model is composed of six compartments representing head, trunk, arms, hands, legs and feet. This novel approach inspired others who further refined, improved and developed it (Fiala et al., 1999; Huizenga et al., 2001; Wissler, 1964). More recently, Fiala et al. (1999) proposed a sophisticated multi-layer model consisting of 15 spherical or cylindrical body elements (head, face, neck, shoulders, arms, hands, thorax, abdomen, legs and feet). Each body element is composed of several annular concentric layers which represent different tissue types (e.g. brain, lung, bone, viscera, muscle, fat and skin). Despite their accuracy, these models can only be used to study heat transfer processes in human adults. However, infants (particularly preterm/VLBW infants) present with significant physiological and anatomical differences. To date, only a few groups have

explored this field, including: Simbruner (1983a), Bussmann et al. (1998), Breuß et al. (2002), Ying et al. (2004) and, more recently Fraguela et al. (2015). We present a new multi-node model of the thermoregulatory system of newborn infants. The whole body (composed of seven compartments) aims to model the heat-transfer processes occurring in the tissues and at the body surface. Section 2 describes the mathematical model. For validation, the measurements of Hammarlund et al. (1983) were used. Furthermore, a small clinical study in moderate preterm infants was performed. Section 3 describes the experimental protocol. The results are presented in Section 4 , discussed in Section 5, and Section 6 presents the conclusions and offers some future perspectives.

2. Mathematical Model The model proposed is schematically presented in Figure 1; it was inspired by Stolwijk et al. (1971), Fiala et al. (1999), Bussmann et al. (1998) and Werner and Buse (1988). The model consists of two main systems: 1) the controlled system (also called the plant or passive system) and 2) the controller (controlling system or active system). The first (passive) system models the physical body of a neonate and the heat-transfer processes occurring in the tissues and at the body surface. It is composed of one spherical and six cylindrical segments (compartments) which correspond to head, thorax, abdomen, arms and legs, respectively. These body compartments are composed of annular concentric layers that represent various tissues such as brain, bone, fat, lung, muscle, skin and viscera. The head consists of four layers: brain, bone, fat and skin; the thorax and abdomen are composed of five elements (thorax: lung, bone, muscle, fat and skin; abdomen: viscera, bone, muscle, fat and skin); and the upper and lower limbs are composed of four tissues (bone, muscle, fat and skin). Figure 2 shows the body segments and the respective layers. In addition, the model comprises a central blood compartment, which represents large arteries and veins; it exchanges heat by convection (blood flow) with all other compartments. The second (active) system aims to describe/predict the regulatory mechanisms. Adults have several regulatory responses to thermal stress, including vasomotion, sweating, shivering thermogenesis (involuntary muscle movement/contraction), nonshivering thermogenesis, and voluntary muscle movement. Neonates have only a few of these responses. Nonshivering thermogenesis [oxidation of brown adipose tissue (BAT)] is the main, rapid mechanism of heat production in newborn infants in response to cold stress. This is triggered by the hypothalamus via the sympathetic nervous system (SNS). Vasomotion is another important regulatory response in neonates that allows to control peripheral blood flow through vasodilation (widening of blood

vessels) or vasoconstriction (narrowing of blood vessels). Thus, in case of cold stress, peripheral vasoconstriction may occur to reduce heat loss. The model was implemented in the modeling and simulation environment Dymola® (Dymola 2015 FD01, Dassault Systèmes AB, Lund, Sweden) which is based on the open Modelica® modeling language.

2.1 Heat transport within the tissue Mathematical modeling of the human thermoregulatory system started with efforts to formulate the heat balance. The widely known bioheat differential equation was formulated by Pennes (1948) and mathematically describes one-dimensional, steady-state heat transfer mechanisms taking place in living tissues according to

  c  = k ,!!!!"! + !!!# 0+ ρ!"!#  **



$%& ()*&+%

- 

/  * 1)23456)2

M 7 8%&9):6(;

+ K !!!!!!!"!!!!!!!# ρ9: c9: w9:,> (T9:,& − T ), B:))3 C%&62+

(1)

where x represents the tissue type (e.g. brain, bone, fat, lung, muscle, skin or viscera) and bl blood, ρ is the density (kg m-3), c stands for heat capacitance (J kg-1 K-1), T denotes the tissue temperature (K) and t is the time (s). In addition, k represents tissue conductivity (W m-1 K-1), r denotes the radius (m), ω is a geometry factor (dimensionless) [ω=1 corresponds to polar coordinates (compartments: abdomen, thorax, arms and legs) and ω=2 stands for the spherical coordinates (compartment: head)]. Finally, M defines the heat production by metabolism (W m-3), K is a countercurrent factor (dimensionless), wbl,0x is the blood perfusion in thermal neutrality (s-1) and Tbl.a denotes the temperature of the arterial blood (K). In brief, this formulation proposed by Pennes (1948) considers a radial and conductive heat flow transport from warmer to colder tissues (e.g. bone to skin) (Figure 1b), as well as the contributions of the convective heat transported through the cardiovascular system and metabolic heat production. Note that whereas basal metabolism is the major source of heat in premature newborns, blood circulation is the main process of heat distribution. The combination of those effects influences and determines heat storage in the tissue layers (Figure 3). The bio-heat balance equation was applied to the tissue layers of all segments by using the corresponding material constants (ρ, c, k), basal blood perfusion rate (wbl,0) and basal heat production (M). Table 1 presents the thermophysical and physiological properties/parameters used in the passive system of our model. 2.1.1 Heat conduction This model considers temperature variations in the radial direction only, as given by Eq. (1); the total amount of heat transferred in the angular and axial direction is insignificant compared with the heat transported radially. Therefore, the angular and axial heat flows are neglected and not incorporated in the heat conduction term. The local heat flow density qDD (rE, t) (heat flow per unit area, per unit

time in the direction of decreasing temperature gradient – W m-2) in a homogeneous, isotropic solid is given by Fourier’s law:

qDD (rE, t) = −k∇T(rE, t),

(2)

where ∇T(rE, t) stands for the temperature gradient in K and the negative sign refers to the heat

transfer from higher to lower temperatures. As emphasized, the heat transport was considered onedimensional (r-direction - radial). Thus, Fourier’s law can be simplified as given by Eq. (3): 3 Q̇ = −kA . 3*

Here, Q̇ (W) represents the heat flow rate in the r direction and A (m2) the area of the tissue.

(3)

In cylinders, heat conduction is dependent on the (a) internal ri (m) and external re (m) radius of the

segments, (b) its length l (m), and the temperature difference between the inner Ti (K) and outer Te (K) wall as given by

 N Q̇ = 2kπl :2(*L ⁄*O ), O

where,

:2(*O ⁄*L ) RSU:

L

(4)

represents the thermal resistance.

In spherical structures, the heat transport is dependent only on the internal and external radius of the segment,

and

( N )* * Q̇ = 4kπ L O L O,

*O N*L WSU*L *O

*O N*L

(5)

stands for the thermal resistance.

2.1.2 Metabolism The brain is the major contributor to heat production in preterm neonates. In the first year of life the metabolic rate of this organ corresponds to more than half of the basal metabolic rate (BMR) (approximately 0.6) (Holliday, 1986; Okken and Koch, 2012). Other organs (such as heart, kidneys, liver, lung and muscles) also play an important role in heat production. Therefore, in this model, we assumed that 23%, 11% and 6% of the BMR are produced in the viscera, lung and muscles, respectively. This assumption is based on the work of Bussmann et al. (1998), Holliday (1986), and Simbruner (1983a). The total BMR (W) is governed by the equation BMR = Z

(1.7 + 0.1 ∙ PA) ∙ W, PA < 10 . d2.7 + 0.01 ∙ (PA − 9)f ∙ W, PA ≥ 10

(6)

This is dependent on both the postnatal age (PA) in days and on the weight W of the neonate (kg). The BMR of each individual tissue (BMRx,0) can be extrapolated from the total BMR. For example, BMR B*&62,> = 0.6 ∙ BMR.

Control of body temperature is achieved via negative feedback; this is a complex system that aims for an equilibrium between heat loss and gain. The temperature-regulating center is located in the preoptic area, i.e. the anterior portion of the hypothalamus. In case of thermal stress, the hypothalamic structures, which trigger the thermoregulatory response, are activated by neuronal thermal inputs coming from the core and cutaneous thermoreceptors (via afferent pathway). The afferent signals are further weighted and integrated in the hypothalamus, which responds by, e.g., increasing the oxidation of BAT (via efferent pathway). These thermoregulatory processes are illustrated in Figure 4. To model the afferent inputs, the approach proposed by Bussmann et al. (1998) was applied. The afferent signal (also afferent temperature) Taff (K) is governed by the following weight function ijmm = ∑so∑udps,u ∙ is,u fv,

(7)

where, Ts,x (K) is the temperature in a layer x of a determined segment/compartment s, and gs,x is a weighting factor. A deviation ΔTaff (K) of the afferent temperature Taff (K) from the setpoint (target value) Tsetpoint (K) can be calculated according to xijmm = ijmm − isyz{|}~z .

(8)

Hence, a ΔTaff < 0 corresponds to a decrease in body and/or ambient temperature(s), whereas ΔTaff > 0 corresponds to an increase of this/these parameter(s). BAT usually accumulates in regions such as neck, axillae, back, mediastinum, and abdomen (Carter and Schucany, 2008). As a result, the thermoregulatory heat production by nonshivering thermogenesis was limited to the core layers of the torso. The response to a cold stress ΔM (additional heat produced by nonshivering thermogenesis) in the thorax and abdomen is given by x€ = ‚ƒ„…† ∙ ‡ˆ

0, xijmm ≥ 0

‡ˆ‰ŠŠ

‹‰ŒŽ

, xi‘juŽ < xijmm < 0,

ƒ„…† , xijmm ≤ xi‘juŽ

(9)

where, maxM and ΔTmaxM are parameters of the model. Thus, if the afferent temperature is higher than the Tsetpoint (ΔTaff ≥ 0) due to an increase of ambient or internal temperatures, there is no heat production. If ΔTaff is negative and decreases successively, a linear increase in heat production by nonshivering thermogenesis can be seen as a response to cold temperatures. Saturation (maxM = 1) is reached at xi‘juŽ = -1. In contrast to the other core layers, heat production in the core of the thorax and abdomen (Mx) is given by the term €u = “€”u,> (1 + x€) ∙ 2‡ˆ‰ŠŠ ⁄•>.

(10)

This is dependent on the basal value BMRx,0 and on the additional heat produced ΔM (e.g. in the

BAT). The factor 2‡ˆ‰ŠŠ ⁄•> defines the Van’t Hoff Q10 effect with a sensitivity coefficient of 2; this

reflects the dependence of biochemical reaction on temperature. This Van’t Hoff Q10 effect is also noticeable in other layers (brain, arms and legs). Their metabolic rate is defined according to, €u = “€”u,> ∙ 2‡ˆ‰ŠŠ ⁄•>.

(11)

2.1.3 Blood perfusion

Vasomotion is another basic regulatory response in neonates, responsible for adjustment of blood flow in the skin (Δwbl,skin). Thus, wblskin (blood perfusion in the skin) is governed by the equation –—˜™š›œ = –—˜,>™š›œ ∙ d1 + x–—˜,sž}~ f,

(12)

and wbl,0skin is the skin’s basal blood perfusion. In thermal neutrality, body tissues are supplied with blood at basal perfusion rates. However, in non-neutral conditions (cold and hot stress) the skin’s blood flow varies according to Δwbl,skin, which is given by x–—˜,sž}~ =

ƒ„…£¤ , xijmm ≥ xi‘ju,£¤ ⎧ ‡ˆ‰ŠŠ ⎪ƒ„…£¤ ∙ , xi‘ju,£¤ > xijmm ≥ 0 ‡ˆ‹‰Œ,¥¦ ‡ˆ‰ŠŠ

⎨ ƒ¨©£¤ ∙ , 0 > xijmm > xi‘}~,£¤ ‡ˆ‹›œ,¥¦ ⎪ ƒ¨©£¤ , xijmm ≤ xi‘}~,£¤ ⎩

.

(13)

Here, minBF and maxBF stand for the minimal and maximal value for the decrease and increase of the blood flow, respectively. ΔTmin,BF and ΔTmax,BF are parameters that represent deviations from the setpoint (negative and positive deviations). On the one hand, if ΔTaff is ≥ 0 and increases successively in response to heat, a proportional increase in blood perfusion is observed. Saturation (upper limit/plateau of the effector response) is reached at ΔTmax,BF (0.3 K). This mechanism corresponds to an effector response to an increase in body temperature. On the other hand, if ΔTaff is ≤ 0 and diminishes in response to cold, a proportional decrease in blood perfusion is seen. The maximal response activity (saturation) is reached at ΔTmin,BF (-0.3 K). The previous mechanism corresponds to an effector response to a decrease in body temperature. During cold stress (ΔTaff < 0), vasoconstriction occurs, reducing heat loss through the skin. In hot environments (heat stress, ΔTaff > 0), vasodilation occurs and the increased blood perfusion promotes heat loss through the skin. 2.1.4 Geometric and Anatomic model This model aims to describe the thermoregulation processes in neonates. Since the total body surface area (BSA) plays an important role in the heat transference processes, it was used as an input parameter for our mathematical model. Various studies have aimed to formulate a suitable equation that can accurately estimate BSA for high-risk infants (Ahn, 2010; Boyd, 1935; Du Bois and Du Bois, 1916; Meban, 1983; Mosteller, 1987; Sharkey et al., 2001). In the present model, the approach proposed by Meban (1983)

“ª« = (6.4954 ∙ (­ ∙ 1000)>.®¯R ∙ °>.±R> )⁄10000,

(14)

was used. Here, BSA (m2) stands for body surface area, W corresponds to the neonate’s weight in kg

Body Compartments

Layer

¸

¹

º

BMRx,0

»¼½,¾¿

À

and L (cm) is the crown-heel length. Meban analyzed 79 dead human fetuses (11-42 weeks) weighing 8-4080 g. According to him the expression showed an excellent relationship between the body surface and the variables body weight and crown-heel length (correlation coefficient reached 0.979). To calculate the area of each body segment (head Ahead, arm Aarm, leg Aleg, thorax Athorax and abdomen Aabdomen) the work of Simbruner (1983) was taken into consideration. This is based on both the BSA and neonate’s weight according to

«²yj³ = (0.248 − 0.0153 ∙ ­) ∙ “ª«,

«j¶‘ = (0.062 + 0.00497 ∙ ­) ∙ “ª«,

«:y· = (0.134 + 0.00165 ∙ ­) ∙ “ª«,

«z²|¶ju = (0.129 + 0.00072 ∙ ­) ∙ “ª«,

«j—³|‘y~ = (0.230 + 0.00128 ∙ ­) ∙ “ª«.

(15)

(16)

(17)

(18)

(19)

As defined in Eq. (16) to Eq. (19), this method considers that the surface of the arms, legs and trunk (thorax and abdomen) increases with the total BSA. In contrast, the surface of the head decreases with increasing body size [Eq. (15)]. Those areas are used to calculate the radii used to compute the thermal resistances [Eq. (4) and Eq. (5)].

2.2 Heat exchange with the Environment At the body surface, heat is exchanged by convection, evaporation, radiation, and conduction (e.g. with a mattress). Therefore, the bioheat equation of the skin includes four additional terms to represent those processes. A detailed description of each heat transport mechanism is presented and the convective and radiative heat transfer coefficients are given in

Head

Thorax

Abdomen

Arms

Legs

Brain Bone Fat Skin Lung Bone Muscle Fat Skin Viscera Bone Muscle Fat Skin Bone Muscle Fat Skin Bone Muscle Fat Skin

W m-1 K-1 0.49 0.40 0.16 0.47 0.28 0.40 0.42 0.16 0.47 0.53 0.40 0.42 0.16 0.47 0.40 0.42 0.16 0.47 0.40 0.42 0.16 0.47

kg m-3 1080 1500 850 1085 550 1357 1085 850 1085 1000 1357 1085 850 1085 1357 1085 850 1085 1357 1085 850 1085 1069

J kg-1 K-1 3850 1591 2300 3680 3718 1700 3768 2300 3680 3697 1700 3768 2300 3680 1700 3768 2300 3680 1700 3768 2300 3680 3650

0.60 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.00 0.23 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.00 0.00 0.03 0.00 0.00

m3 s-1 m-3 3.3 x 10-3 0 0 1.25 x 10-3 7.0 x 10-3 0 4.0 x 10-3 0 1.25 x 10-3 7.0 x 10-3 0 -3 4.0 x 10 0 1.25 x 10-3 0 1.25 x 10-3 0 -3 1.25 x 10 0 1.25 x 10-3 0 1.25 x 10-3

1 1 1 0.9 1 1 1 1 0.9 1 1 1 1 0.9 1 1 1 0.9 1 1 1 0.9

Á is the thermal conductivity,  defines the tissue density, à stands for the specific heat, “€”u,> corresponds to the basal metabolism, –—˜,>Œ is basal blood perfusion rate or blood perfusion in thermal neutrality, and Ä is the countercurrent factor.

Blood

Table 2. Convection The convective heat exchange qc between the skin of the neonate (with temperature Tskin) and the incubator air (with temperature Tair) was modeled according to ÅÆ = ℎÆ ∙ «sž}~,j ∙ (isž}~ − ij}¶ ).

(20)

Here, hc (W m-2 K-1) and Askin,a denote the convection coefficient and area of the skin of a determined segment in contact with the air. 2.2.1 Evaporation Evaporation of water is one of the main modes of heat loss. Insensible water loss is a sum of two elements: evaporation from the skin qev and water loss from the respiratory system. The former can be described by the following equation ÅyÈ = ÉyÈ ∙ «sž}~,j ∙ iÊ­°,

(21)

where, eev is the specific enthalpy of the vaporization of water (0.65 W h g-1) and TEWL (g m-2 h-1) represents the transepidermal water loss. Hammarlund et al. determined TEWL in newborns under controlled environmental conditions. They found an exponential relationship between TEWL and

gestational age (GA) at different PAs (from birth to 4 weeks after birth) (Figure 5) (Hammarlund et al., 1983). According to Ultman (1987), this mathematical relationship can be described by iÊ­° = Ë ∙ ,Ìs∗ − •>> ∙ Ìj∗ 0, ¶Î

(22)

where, d represents a diffusion coefficient (g h-1 m-2 kPa-1), rH is the relative humidity, Ìs∗ and Ìj∗

stand for the partial pressure of water vapor at body surface temperature and at air temperature, respectively. The diffusion coefficient is dependent on the skin temperature of the newborn as given by

Ë = Ë> ∙ É

Ï.••ÏN

-ÐÑРҙš›œ

.

(23)

The coefficient d0 is governed by the following equation d> = 1.5 ∙ ,1 +

R∙³Ô N± 0, RÕÖ×

(24)

where d1 (Bussmann et al., 1998; Ultman, 1987) is given by ˕ = Ø

1.3, Ù« > 35 . 24000 ∙ É N>.Rڕ∙Û× , Ù« ≤ 35

(25)

The respiratory water loss (RWL) can be computed according to the equation proposed by Ultman (1987)

”­° = − ,0.411 + 0.000968 ∙ (ij}¶ − 273.15) −

Ü.W∙¶Î∙{‰∗ 0∙ •>•±±N¶Î∙{‰∗

­.

(26)

This is dependent on the air temperature Tair, relative humidity rH, partial pressure of water vapor at

air temperature Ìj∗ and on the weight of the neonates W. 2.2.2 Radiation

Radiation corresponds to the heat transfer by long-wave radiation qr as defined by Ŷ = ℎ¶ ∙ «sž}~,j ∙ (isž}~ − i†Ýˆ ),

(27)

where, TMRT (K) is mean radiant temperature (MRT) and hr (W m-2 K-1) stands for the radiative heatexchange coefficient. 2.2.3 Conduction The conductive heat exchange between the neonate and the mattress (qcond) also needs to be considered. This can be described by

ÅÆ|~³ = Á‘ ∙ «sž}~,‘ ∙ (isž}~ − i‘ ),

(28)

where, km (W m-2 K) stands for the heat transfer coefficient, Tm is the temperature of the mattress, and Askin,m denotes the area of the skin of a determined segment in contact with the mattress.

2.3 Validation of the mathematical model To validate the mathematical model, the work of Hammarlund et al. (1983) was used. In their study, measurements in 19 newborns [10 males and 9 females, GA 39.58 ± 0.61 weeks (mean ± SD), weight 3.56 ± 0.51 kg, length 0.51 ± 0.02 cm] were performed directly after birth. Their aim was to examine the relationship between ambient humidity and insensible water loss. The infants were placed in an incubator and the relative humidity was varied from 20-65%, with increments of 5%. Moreover, the ambient temperature (incubator temperature) was maintained as constant as possible. During the measurements (lasting 2.4 ± 0.8 h) rectal and skin temperature at the trunk were determined. To validate our mathematical model, we compared the temperatures experimentally obtained by Hammarlund et al. (1983) with those estimated in our simulations. In addition, an experimental feasibility study was conducted in the department of Neonatology of the University Hospital RWTH Aachen. The aim was to analyze the performance of our model during transient thermal conditions using the following experimental protocol.

3. Experimental Protocol

To validate the mathematical model during transient thermal conditions, a study was performed at the RWTH Aachen Unive Aachen (EK032/09) and parental consent was obtained. Both infants had a stable condition;

Table 3 presents their characteristics. The experiments had three phases. In the first phase, core and skin temperatures of the newborns were measured while they were inside the incubator (circa 1 h); skin temperature measurements were performed every 15 min. Core temperature was measured at time points 0 and 60 min. Then, infants were removed from the incubator for Kangaroo care (also known as skin-to-skin care) for about 1 h and skin temperature measurements were performed every 20 min. Rectal temperature was assessed at time point 120 min. In the final phase, the infants were replaced in the incubator. Skin and core temperature measurements were again performed (every 15 min for 1 h, and at time point 180 min, respectively). Figure 6 presents all measurement time points. The core/rectal temperature was measured with a standard clinical thermometer. Skin temperature was measured using a long wave infrared camera VarioCAM® HD head 820S/30 mm (InfraTec GmbH, Dresden, Germany). Room temperature and relative humidity were acquired with the HOBO® U12-012 data

logger (Onset Computer Corporation, Bourne, Massachusetts, USA). As described in section 4, our model is also dependent on the temperature and relative humidity of the incubator. Standardly, incubators present sensors that automatically assess these properties without the need for additional measurement devices.

4. Results The work of Hammarlund et al. (1983) was used to validate our model during stable environmental conditions. Table 4 compares the empirical data (rectal/core temperature and skin temperature) for all 19 subjects obtained by the latter group with the model simulations. The average difference in mean core temperature between Hammarlund et al. (1983) and the mathematical model was 0.25 ± 0.21°C, and that of skin temperature was 0.36 ± 0.36 °C. Furthermore, to verify the outcome of the model during transient thermal conditions, a study was performed with two preterm babies as previously mentioned. Figure 7 presents a comparison between core temperatures for model predictions (dashed and solid lines) and experimental measurements (circles and squares): the dashed green line/circles represent infant S1, the solid blue line/squares represent the newborn preterm S2. For infant S1, the mean absolute error between core temperatures [rectal temperature (measurements) and temperature of the internal layer of the abdomen (viscera) (simulation)] was 0.04 ± 0.04 °C and that for infant S2 was 0.19 ± 0.19 °C. Figure 8 compares the skin temperatures (measured using a thermal camera and simulated using the current mathematical model) for each body segment (head, thorax, abdomen, arms and legs) and the infants: green lines are the results for infant S1 and blue lines for infant S2. The temperatures measured with the thermal camera are illustrated with markers (circles for S1, squares for S2). Table 5 complements Figure 8 in presenting the mean absolute errors between the measurements and simulations. As shown, similar results were obtained for both infants and compartments (hovering around 0.30 °C). The only exception was the skin temperature of the legs: the mean absolute error was 0.18 ± 0.14 °C and 0.67 ± 0.43 °C for infants S1 and S2, respectively.

5. Discussion Perinatal and neonatal research remains controversial with regard to ethical considerations, as children are extremely vulnerable research subjects (Behrman et al., 2007; Laventhal et al., 2012). Therefore, pediatric research has to consider ethical challenges, including: balancing risks and benefits, parental informed consent and assent, and clinical equipoise (Laventhal et al., 2012). Few studies have examined heat transfer processes in infants and preterm neonates and studies on the influence of thermal transients are often lacking due to ethical reasons. Nevertheless, such studies

are needed since thermoregulation in preterm neonates is not as developed as that in full-term newborns. Currently available thermoregulatory models of adults are related to a ‘standard’ person, with predefined body characteristics including, e.g., body weight, fat-to-body mass ratio, and skin surface area. In contrast, our mathematical approach is customizable, since it incorporates individual characteristic of neonates such as GA, PA, weight and length. These features are essential because evaporation losses are highly dependent on the area of the skin, and on the GA and PA (Figure 5). In addition, the remaining heat processes (in tissues and at the body surface) are influenced by the area of the tissue layers which can be derived from the BSA and, hence, from the body weight and length of the newborn. To validate our model during thermal neutrality, the work of Hammarlund et al. (1983) was used. This group performed measurements in a relatively homogeneous group of newborns, with a GA averaging 39.58 ± 0.61 weeks (section 2.3). Table 4 compares these latter empirical results with those obtained in our simulations. Similar environmental conditions were reproduced, i.e. the same ambient temperature and relative humidity, including its variations (from 20-65%, with increments of 5%). The two parameters measured, i.e. rectal temperature (core temperature) and skin temperature of the trunk, were compared with the calculated core temperature of the abdomen (layer viscera) and its skin temperature. Table 4 shows that similar results were obtained with the real measurements and simulations. The mean core temperature difference averaged 0.25 ± 0.21 °C and the mean skin temperature difference averaged 0.36 ± 0.36 °C. The standard deviation (SD) of the results is (in nearly all cases) identical in magnitude to the absolute magnitude of the value. As mentioned, the study population had a similar weight, length, GA and PA [PA 1 ± 0.00 days (mean ± SD), GA 39.58 ± 0.61 weeks, weight 3.56 ± 0.51 kg, length 0.51 ± 0.02 cm]. The environmental conditions (ambient temperature and relative humidity) were also similar. In the measurements performed by Hammarlund et al. (1983), the SDs were also similar to ours ( SD Tcore = 0.13 and

SDTskin = 0.19 ); however, small fluctuations were visible, possibly due to varying environmental temperatures. In contrast to our simulations in which the environmental temperature was kept constant, small temperature variations were found during the measurements. Our model demonstrated its ability to correctly estimate core temperature and skin temperature in thermal neutrality in full-term newborns. Unfortunately, we were unable to find studies similar to that of Hammarlund et al. (1983) dealing with preterm infants; therefore, our validation was performed on full-term infants with regard to body temperature in thermal neutrality. In addition to thermal neutrality, it is important to verify the outcome of our model in case of transient thermal conditions, e.g. a drop in environmental temperature. For this, a small pilot study was performed at the department of Neonatology of the University Hospital RWTH Aachen with two

preterm newborns. Figure 7 shows the variation in rectal temperature and the core temperature dynamics for both infants estimated with our approach. As expected, there was a decrease in temperature followed by an increase; also, a high level of agreement was achieved between the measurements and simulations. The absolute error between core temperatures averaged 0.04 ± 0.04 °C and 0.19 ± 0.19 °C for infant 1 and infant 2, respectively. Figure 8 presents the measured and estimated skin temperatures. Once more a small decrease, followed by an increase in temperature was perceived. For all body compartments there was excellent agreement between the measured and the simulated temperatures. This is further corroborated by the results presented in Table 5. The mean absolute error of almost all compartments hovered around 0.30 °C. The only exception was the skin temperature of the legs, with a mean absolute error of 0.18 ± 0.14 °C and 0. 67 ± 0.43 °C for infant S1 and S2, respectively. In this context, it should be noted that during Kangarooing care the skin-to-skin contact between mother and infant was taken into account. Equally important is the fact that, in both validations, only healthy infants were included. Other research groups also studied heat exchange processes and energy balance in newborns. Bussmann et al. (1998) and Breuß et al. (2002) presented very similar approaches. The former group developed a compartment model to describe the thermoregulatory system, and the latter introduced a finite volume approach. Both models are composed of six compartments: head, trunk, arms, and legs. The head consists of 4 layers (core, bone, fat and skin) and the other compartments have only 3 layers (core, fat and skin). As far as we know, the above-mentioned authors did not compare their simulations with clinical data. Ying et al. (2004) proposed a simple model, composed of 3 body segments (head, trunk and legs) to study the influence of clothing on the thermoregulation processes. To validate their approach, the experimental study of Bolton et al. (1996) was taken into account. The results showed a good agreement between skin temperatures for trunk and legs. In 2015, Fraguela et al. presented an algorithm to control the temperature of the incubator based on the infant’s temperature. The heat exchange and the energy balance in the newborn was described with a single compartment model consisting of two layers, core (representing tissues, bones and internal organs) and surface (representing fat and skin). However, the authors did not compare their simulations with clinical data (Fraguela et al., 2015). In contrast to the previous approaches, our model includes more compartments and layers, allowing to simulate a more detailed human body (section 2). Therefore, more accurate global and local physiological responses can be predicted. In addition, the model was successfully validated during both thermal neutrality and transient thermal conditions.

6. Conclusion

As premature babies suffer from an incompletely developed thermoregulatory system, maintenance of an optimal thermal environment (ideally between 36.8 and 37.5 °C) is indispensable for their survival and growth. Mathematical models can help to provide detailed knowledge on heat transfer processes and body-environment interactions. We have proposed a multi-node model of the thermoregulatory system of newborn infants. A first successful validation of our approach in thermal neutrality was made by comparing our simulations with the empirical results obtained by Hammarlund et al. (1983). Their study was performed in a homogenous group of newborn infants, with a GA of approximately 39 weeks (full-term infants), directly after birth. Since this approach can also be extended to premature infants (moderate preterm, very preterm and extremely preterm infants), we aim to validate our model with data of other experimental groups. Besides thermal neutrality, thermal transient thermal conditions were also taken into consideration. Our small pilot study showed a good agreement between model and measured data, as well as the model’s ability to simulate thermoregulatory dynamics/responses. Because only two infants were involved, future studies should include more infants. In conclusion, it appears that our mathematical approach is able to predict body temperatures (core and skin temperature) during thermal neutrality and even in a transient thermal conditions. It can be a useful tool for physicians in the aim to achieve a better understanding of the heat transfer processes and body-environment interactions that occur in preterm infants.

Acknowledgments C. B. Pereira wishes to acknowledge FCT (Foundation for Science and Technology in Portugal) for her PhD grant SFRH / BD / 84357 / 2012.

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Biographies

Carina Pereira was born in Braga, Portugal, on November 6, 1988. She received the M.Sc. degree in Biomedical Engineering from the University of Minho, Braga, Portugal, in 2011. Currently, she is working toward the doctor degree at the Philips Chair for Medical Information Technology, RWTH Aachen University, Aachen, Germany. Her research interests include infrared thermography, imaging and biosignal processing as well as feedback control in medicine.

Konrad Heimann was born in Cologne, Germany, in 1969. He received the M.D. degree at the university of Cologne in 1996. After working for one and a half years at the Department of Pediatrics of the University Hospital of Cologne, he was educated in pediatrics at the University Hospital of the RWTH of Aachen. Since 2006, he is a senior physician at the Department of

Neonatology and Pediatric Intensive Care. His main fields of research are non-contact monitoring of vital parameters and thermoregulation in full and preterm infants.

Associate professor Dr. Michael Czaplik is working at the department of anesthesiology, university hospital RWTH Aachen as senior consultant in anesthesiology. As leader of the interdisciplinary section “medical technology” he is in charge of diverse research projects combining medical and technical knowledge and expertise. His main field of research includes innovative monitoring modalities and telemedicine in anesthesiology, intensive care medicine and emergency medicine.

Vladimir Blazek was born in Czechoslovakia, in 1945. He received the Dipl.-Ing. degree in electrical engineering from the Technical University, Brno, Czech Republic, in 1969, the Dr.-Ing. degree from RWTH Aachen University, Aachen, Germany, in 1979, and the Venia Legendi degree from the Czech Technical University, Prague, in 1993. In 1971, he was with the Institute of High Frequency Technology, RWTH Aachen University. Since 2011, he has been with the Philips Chair of Medical Information Technology, RWTH Aachen University. His current research interests include optoelectronics in medicine, biomedical sensors, functional optical imaging techniques, and tissue optics.

Boudewijn Venema was born in Amsterdam, the Netherlands, in 1983. He holds the Dr.-Ing. Degree in Electrical Engineering from RWTH Aachen University, Aachen, Germany. Currently, he is with the Philips Chair of Medical Information Technology, RWTH Aachen University. His research interests include optoelectronics in medicine, the study of photon-tissue interaction with Monte-Carlo and contactless long-term measurement of vital signs using photoplethysmographic and infrared sensor technologies.

Steffen Leonhardt was born in Frankfurt, Germany, in 1961. He received the M.S. degree in computer engineering from the State University of New York at Buffalo, Buffalo, NY, USA, the Dipl.-Ing. degree in electrical engineering and the Dr.-Ing. degree in control engineering from the Technische Universität Darmstadt, Darmstadt, Germany, and the M.D. degree in medicine from Johann Wolfgang Goethe University, Frankfurt, Germany. After 5 years of industrial work experience as a R&D manager with Dräger Medical GmbH, Lübeck, in 2013 he was appointed Full Professor and Head of the Philips Endowed Chair of Medical Information Technology at RWTH Aachen University, Aachen, Germany.

Glossary Acronyms

BAT

Brown adipose tissue

CI

Confidence interval

SD

Standard deviation

SNS

Sympathetic nervous system

VLBW

Very low birth weight

Latin Symbols Area (m2)

 !"

Basal metabolic rate (W)

#

Body Surface Area (m2)

$

Heat capacitance (J kg-1 K-1)

%

Diffusion coefficient (g h-1 m-2 kPa-1)

&

Specific enthalpy of vaporization of water (W h g-1)

'

Weighting factor (dimensionless)

(

Gestational age (weeks)

ℎ*

Convective heat transfer coefficient (W m-2 K-1)

ℎ+

Radiative heat transfer coefficient (W m-2 K-1)

,

Thermal conductivity (W m-1 K-1)

-

Length (m)

.

Crown-heel length (cm)

/

Countercurrent factor (dimensionless)

!

Heat production by metabolism (W m-3)

0∗

Partial pressure of water vapor (kPa)

2

Postnatal age (days)

3 44

Heat flow density (W m-2)

5̇

Heat flowrate (W)

7

Radius (m)

78

Relative humidity (%)

"9.

Respiratory water loss (g kg h-1)

:

Temperature (K)

;

Time (s)

:<9.

Transepidermal water loss (g m-2 h-1)

=

Volume (m3)

>

Perfusion rate (s-1)

9

Weight (kg)

Non-Latin Symbols ?

Difference

@

Enthalpy of vaporization (W h g-1)

A

Density (kg m-3)

B

Geometry factor used in the bioheat differential equation (dimensionless)

C

Gradient

Subscripts 0

Thermal neutrality

EFF

Afferent

G-

Blood

G-, E

Arterial Blood

$

Convection

$IJ%

Conduction

&

External

&K

Evaporation

L

Internal

M

Mattress

!":

Mean radiant temperature

7

Radiation

N

Segment (head, thorax, abdomen, arm, leg)

N&;0ILJ;

Setpoint/target value

O

Tissue/Layer (brain, bone, fat, lung, muscle, skin or viscera)

Figure 1 – Schematic representation of the plant. (a) Diagram depicting the seven segments (head, thorax, abdomen, arms and legs) that compose the model. The head is defined as a sphere and the other segments are modeled as cylinders. (b) Transversal section of the abdomen (section A-A’). Coordinates r, θ, and z denote the radial, angular, and axial directions, respectively. This model only considers radial heat transport. Figure 2 – Illustration of the body segments and respective layers. The head is composed of four layers, skin, fat, bone and brain; the thorax and abdomen of five elements (thorax: lung, bone,

muscle, fat and skin; abdomen: viscera, bone, muscle, fat and skin); and the legs and arms are composed of four tissues (bone, muscle, fat and skin). Figure 3 – Representation of the (1) radial conductive heat flow transport in the abdomen between adjacent tissue layers (viscera, bone, muscle, fat and skin) (2) convective heat transported through the cardiovascular system, and (3) heat exchange with the environment (convection, radiation, evaporation and conduction). Figure 4 – Graphical representation of the thermoregulatory processes in infants. SNS=sympathetic nervous system. Figure 5 – Relationship between transepidermal water loss and gestational age at different postnatal ages (Hammarlund et al., 1983). Figure 6 – Chronogram representing all measurement time points. Core/rectal temperature was measured with a standard clinical thermometer and skin temperature with a thermal camera. Figure 7 – Comparison between core temperatures for model simulations (solid and dashed lines) and clinical measurements (circles and squares). The dashed green line/circles represent infant S1, and the solid blue line/squares represent infant S2. Background: light gray segments indicate the periods the newborn infants were in the incubator (‘I’ = incubator); dark gray segments indicate the periods the preterm babies were removed from the incubator for Kangaroo care (K = Kangaroo care). Figure 8 – Comparison between skin temperatures for the model simulations (solid/dashed lines) and clinical measurements (circles/squares). The dashed green line/circles represent infant S1 and the solid blue line/squares represent infant S2. Background: light gray segments represent the periods the newborn infants were in the incubator (‘I’ = incubator); dark gray segment represents the period the preterm babies were removed from the incubator for Kangaroo care (‘K’ = Kangaroo care). A comparison was made between all body compartments (head, thorax, abdomen, arms and legs).

Table 1 – Thermophysical and physiological parameters used in the passive system of the proposed mathematical model according to Bussmann et al., (1998) and Fiala et al. (1999) Body Compartments Head

Thorax

Abdomen

Arms

Legs

Layer Brain Bone Fat Skin Lung Bone Muscle Fat Skin Viscera Bone Muscle Fat Skin Bone Muscle Fat Skin Bone Muscle Fat Skin

U W m-1 K-1 0.49 0.40 0.16 0.47 0.28 0.40 0.42 0.16 0.47 0.53 0.40 0.42 0.16 0.47 0.40 0.42 0.16 0.47 0.40 0.42 0.16 0.47

Blood

V kg m-3 1080 1500 850 1085 550 1357 1085 850 1085 1000 1357 1085 850 1085 1357 1085 850 1085 1357 1085 850 1085 1069

W J kg-1 K-1 3850 1591 2300 3680 3718 1700 3768 2300 3680 3697 1700 3768 2300 3680 1700 3768 2300 3680 1700 3768 2300 3680 3650

BMRx,0 0.60 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.00 0.23 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.00 0.00 0.03 0.00 0.00

XYZ,[\ m3 s-1 m-3 3.3 x 10-3 0 0 1.25 x 10-3 7.0 x 10-3 0 4.0 x 10-3 0 -3 1.25 x 10 7.0 x 10-3 0 4.0 x 10-3 0 1.25 x 10-3 0 1.25 x 10-3 0 1.25 x 10-3 0 1.25 x 10-3 0 -3 1.25 x 10

] 1 1 1 0.9 1 1 1 1 0.9 1 1 1 1 0.9 1 1 1 0.9 1 1 1 0.9

, is the thermal conductivity, A defines the tissue density, $ stands for the specific heat, !"P,Q corresponds to the basal metabolism, >RS,QT is basal blood perfusion rate or blood perfusion in thermal neutrality, and / is the countercurrent factor.

Table 2 – Convective hc and radiative hr heat transfer coefficients used in the mathematical model (Bussmann et al., 1998) Sub.

Gender

S1 M S2 M Mean ± SD

Birth weight (Kg) 2.130 2.160 2.145 ± 0.02

Birth height (cm) 44 46 45 ± 1.41

Study weight (Kg) 1.930 2.000 1.965 ± 0.05

Study height (cm) 44 46 45 ± 1.41

GA (weeks)

PA (days)

Feeding method

33 33 33

3 6 4.5 ± 2.12

Orogastric Orogastric

Table 3 – Patient data (Sub. – subjects, SD – standard deviation) Body Compartments Head Thorax Abdomen Arms Legs

Layer Skin Skin Skin Skin Skin

hc hR W m-2 K-1 W m-2 K-1 4 5 3 4 3 4 5 4 5 4

Table 4 – Comparison between the empirical results obtained by Hammarlund et al. (1983) and the results achieved with our model Hammarlund et al. (1983)

Mathematical model

Mean temperature difference Tcore Tskin

GA

W

L

Tamb ± SD

Tcore ± SD

Tskin ± SD

Tamb

Tcore ± SD

Tskin ± SD

weeks

kg

mm

°C

°C

°C

°C

°C

°C

39

3.970

0.520

34.2 ± 1.5

36.7 ± 0.4

35.4 ± 0.3

34.2

36.8 ± 0.1

35.4 ± 0.1

0.1

0.0

M

38

3.100

0.490

34.6 ± 0.4

36.9 ± 0.1

36.0 ± 0.1

34.6

36.8 ± 0.1

35.7 ± 0.1

0.1

0.3

F

40

2.830

0.495

34.8 ± 0.2

36.7 ± 0.1

35.7 ± 0.2

34.8

36.8 ± 0.1

35.8 ± 0.1

0.1

0.1

I4

F

40

4.010

0.515

34.5 ± 0.3

36.6 ± 0.1

35.5 ± 0.1

34.5

36.9± 0.1

35.8 ± 0.1

0.3

0.3

I5

M

40

4.430

0.555

34.1 ± 0.2

36.6 ± 0.1

34.5 ± 0.4

34.1

36.9 ± 0.1

35.7 ± 0.1

0.3

1.2

I6

M

40

3.610

0.505

34.2 ± 0.4

36.8 ± 0.1

34.6 ± 0.4

34.2

36.8 ± 0.1

35.6 ± 0.1

0.0

1.0

I7

F

40

3.945

0.520

32.6 ± 0.4

36.1 ± 0.0

34.6 ± 0.3

32.6

36.6 ± 0.1

35.2 ± 0.1

0.5

0.6

I8

F

39

3.570

0.500

33.2 ± 0.3

36.4 ± 0.2

35.2 ± 0.1

33.2

36.7 ± 0.1

35.3 ± 0.1

0.3

0.1

I9

M

40

4.400

0.530

32.5 ± 0.2

36.7 ± 0.1

34.9 ± 0.1

32.5

36.7 ± 0.1

35.3 ± 0.3

0.0

0.4

I10

M

40

3.270

0.500

33.6 ± 0.1

36.2 ± 0.2

35.3 ± 0.2

33.6

36.7 ± 0.1

35.4 ± 0.1

0.5

0.1

I11

M

39

3.500

0.510

32.5 ± 0.4

36.9 ± 0.1

36.2 ± 0.1

32.5

36.5 ± 0.1

35.2 ± 0.1

0.4

1.0

I12

M

40

3.680

0.520

34.3 ± 0.2

36.6 ± 0.1

35.9 ± 0.1

34.3

36.9 ± 0.1

35.7 ± 0.1

0.3

0.2

I13

F

40

2.850

0.470

33.7 ± 0.4

36.5 ± 0.1

35.6 ± 0.3

33.7

36.6 ± 0.1

35.4 ± 0.1

0.1

0.2

I14

F

40

3.150

0.490

33.7 ± 0.3

36.6 ± 0.1

36.0 ± 0.3

33.7

36.7 ± 0.1

35.5 ± 0.1

0.1

0.5

I15

M

40

3.580

0.520

33.8 ± 0.2

36.8 ± 0.1

35.2 ± 0.1

33.8

36.8 ± 0.1

35.5 ± 0.1

0.0

0.3

I16

F

39

3.990

0.520

34.1 ± 0.3

36.3 ± 0.2

35.8 ± 0.2

34.1

36.9 ± 0.1

35.8 ± 0.1

0.6

0.0

I17

M

39

3.810

0.520

34.0 ± 0.2

36.2 ± 0.1

35.5 ± 0.2

34.0

36.9 ± 0.1

35.8 ± 0.1

0.7

0.3

I18

F

39

2.700

0.485

32.5 ± 0.5

36.5 ± 0.1

35.3 ± 0.1

32.5

36.3 ± 0.1

35.2 ± 0.1

0.2

0.1

I19

F

40

3.200

0.500

32.1 ± 0.7

36.5 ± 0.1

35.3 ± 0.1

32.1

36.4 ± 0.1

35.2 ± 0.1

0.1

0.1

Mean 39.6 3.558 0.509 33.6 36.6 35.4 33.6 36.7 SD 0.6 0.507 0.019 0.8 0.2 0.5 0.8 0.2 I – infant, G – gender, GA – gestational age, W – weight, L – length, SD – standard deviation

35.5 0.2

0.25 0.21

0.36 0.36

I

G

I1

M

I2 I3

Tamb – ambient temperature, Tcore – core temperature, Tskin – skin temperature

°C

°C

Table 5 – Mean absolute errors between skin temperature measurements (with infrared thermography) and simulations for all subjects and body compartments

Subject S1 S2 Mean

^_`a,b ± SD °C

^_`a,c ± SD °C

^_`a,de ± SD °C

^_`a,d ± SD °C

^_`a,f ± SD °C

0.39 ± 0.28 °C 0.35 ± 0.42 °C 0.27 ± 0.32 °C 0.30 ± 0.27 °C 0.18 ± 0.14 °C 0.31 ± 0.19 °C 0.35 ± 0.30 °C 0.31 ± 0.32 °C 0.31 ± 0.27 °C 0. 67 ± 0.43 °C 0.35 ± 0.06 °C 0. 35 ± 0.00 °C 0.29 ± 0.03 °C 0.31 ± 0.01 °C 0.43 ± 0.35 °C _ ^ – mean absolute error, sk – skin, h – head, t – thorax, ab – abdomen, a – arms, l – legs

a

A A‘

b

A

è

Äz

Är

z

A‘ r

Head

Skin Fat Bone Brain

Thorax

Abdomen

Fat Skin

Muscle

Muscle Fat

Bone

Skin

Viscera

Lung Bone

Leg

Skin

Fat

Muscle

Bone

Arm

Skin

Fat

Muscle

Bone

Environment

Mattress

Convection, Radiation, and Evaporation

Skin Conduction Fat

Conduction

x=5

Blood Flow Convection

x=4

Blood Flow Convection

Conduction Muscle Conduction Bone

x=3

x=2

Blood Flow Convection

Blood Flow Convection

Conduction Viscera

x=1 Segment - Abdomen

Blood Flow Convection

Central Blood

Control

Afferent pathway

Setpoint

Hypothalamus Vasomotion

1. Brown adipose tissue metabolism

Heat Gain - Nonshivering thermogenesis

Effectors

Core Thermoreceptors

Cutaneous Thermoreceptors

Input

SNS

Efferent pathway

Thermoregulation in Infants

Transepidermal water loss (g/m2h) 0

10

20

30

40

50

60

Gestational age (weeks)

26 28 30 32 34 36 38

28

24

s Po

20

l ag ta tna

16

12

ys) da ( e

8

4

0

0

30

45

60

100

Time (minutes)

80

Core temperature measurements

15

135

150

165

180

Skin temperature measurements

120

Kangarooing Care

Temperature (°C)

36

36.5

37

37.5

38

0

I 20

40

60

80

100

Time (minutes)

K 120 140

160

I 180

S1 - Model S1 - Rectal temperature S2 - Model S2 - Rectal temperature

Temperature (°C)

Temperature (°C)

0

33

35

37

34 0

35

36

I

I

Arms

50 100 150 Time (minutes)

I K

Head

50 100 150 Time (minutes)

I K

Temperature (°C) Temperature (°C)

37

0

33

35

37

0

34

36

38

I

I Legs

50 100 150 Time (minutes)

I K

Thorax

50 100 150 Time (minutes)

I K

Temperature (°C) 0

34

36

38

I

S1 - Model S1 - IRT S2 - Model S2 - IRT

Abdomen

50 100 150 Time (minutes)

I K

Highlights ·

A new multi-node model of the thermoregulatory system of newborn infants is proposed.

·

The model is customizable, i.e. it meets individual characteristics of the neonates.

·

The model was able to accurately predict skin and core temperatures during thermal neutrality.

·

This mathematical approach was capable of simulating thermoregulatory dynamics during thermal transients