# Perioperative Acetaminophen Dosing in Obese Children

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## Abstract

**:**

## 1. Introduction

## 2. Current Acetaminophen Dose Estimation

## 3. Size Model Foibles

_{MAX}, C

_{50}) variability are poorly quantified, but age, particularly in neonates, is important. Size can be standardized to a 70 kg person using allometric theory [29]. Fat is a component of body composition that certainly contributes to PK parameter variability [30], but has been poorly investigated in children [23].

## 4. Physiological Models

## 5. The Target Effect

_{MAX}or Hill equation [42,43]:

_{MAX}, is the maximum drug effect (5.17 on a visual analogue scale 0–10), C

_{50}is the concentration eliciting half of E

_{MAX}(9.97 mg/L), and the Hill exponent (Hill or N = 1) describes the steepness of the concentration–response curve [44]. This relationship is displayed graphically in Figure 1 and can be used to predict the target concentration known to be associated with a target effect. A target effect of 2.6 pain unit reduction (VAS 0–10) is associated with a target concentration of 10 mg/L. This acetaminophen target concentration of 10 mg/L is similar for both neonates and children [44,45]. Acetaminophen is a mild analgesic with a maximum effect of only 5.17 pain units. Children with an initial pain score of 10 pain units will still require remedication at this target concentration because their pain score will remain high at a VAS of 7.4 units. However, pain in those with an initial score of 6 pain units will be better managed.

## 6. Dose Calculation Using the Target Concentration

## 7. Dosing Concepts in the Child

#### 7.1. The Association between Size and Dose

_{STD}) is that for a person of standard weight (WT

_{STD}e.g., 70 kg). This equation demonstrates dosing commonly known as dosing per kilogram. However, it is widely known that maintenance doses expressed as mg/kg, as in Equation (4), are too small in children when compared to adults; this linear approach is not a suitable general method for drug dosing in children [53]. The maintenance dose should be based on clearance (Equation (3)), but clearance has a nonlinear, not linear relationship with size.

#### 7.2. Allometry

_{STD}):

_{MATURATION}) that uses age as an independent variable.

#### 7.3. Fat Mass

#### 7.3.1. Lean Body Mass

#### 7.3.2. Normal Fat Mass

_{CL}) might suggest organ dysfunction. Obesity is associated with organ dysfunction in the morbidly obese. Dexmedetomidine was noted to have a negative value for Ffat

_{CL}in morbidly obese adults [73]. Although we might anticipate that Ffat increases with lipid solubility when used for volume of distribution, this has not yet been demonstrated.

## 8. Application of NFM Principles for Acetaminophen Dosing in Children

#### 8.1. Loading Dose

_{VOL}= 1. Simulated plasma concentrations attained after a loading dose of acetaminophen of 30 mg/kg in a 6-year-old, 20 kg child (FFM 16.4 kg, BMI 15.12 kg/m

^{2}) are shown in Figure 2. Effect compartment concentrations of 10 mg/L are achieved at 25 min and decrease below this concentration at 3.5 h. The loading dose (30 mg/kg) is the same for obese and lean children. Clearance, however, determines the duration of time that concentrations remain above 10 mg/L. Clearance increases with weight when expressed per kilogram, and so the duration of concentration above 10 mg/L in a 6-year-old, 40 kg child (FFM 24.7 kg, BMI 30.25 kg/m

^{2}) is longer (Figure 2). However, while concentrations might be estimated to be below 10 mg/L at 4 h 25 min in the lean child, the impact of adding Ffat = 0.82 to the simulation is minimal. Simulation using TBW (Ffat = 1) with allometry reveals a time below 10 mg/L at 4 h 15 min, a small analgesic difference because the concentration–response curve is shallow at that concentration (Figure 1). The impact of separating out fat mass for loading dose estimation is minimal. Total body weight is the better scaler for an acetaminophen loading dose.

#### 8.2. Maintenance/Infusion Dose

^{2}; weight 50 kg, FFM 33 kg, BMI 25.5 kg/m

^{2}; and weight 70 kg, FFM 39 kg, BMI 35.7 kg/m

^{2}(Figure 4)) given a loading dose of 30 mg/kg and a maintenance dose of 15 mg/kg 6-hourly. While clearance increase is nonlinear and predicted concentrations increase with size, these higher concentrations are unlikely to contribute a meaningful improvement to analgesia. Similarly, the use of NFM (Ffat

_{CL}= 0.82) instead of TBW (Ffat

_{CL}= 1.0) will have minimal impact on pain scores. This clinical impact is minimal because predicted concentrations are on the flat part of the concentration–response curve, because a clinically important pain score change is more than 1 pain unit (VAS 0–10) [80,81], and because both PK and PD parameter estimates are associated with considerable variability [28].

## 9. Consideration of Adverse Effects

#### 9.1. Hepatotoxicity

#### 9.1.1. Loading Dose

#### 9.1.2. Maintenance Dose

#### 9.2. Concentration or Dose

#### 9.3. The Acetaminophen–NSAID Interaction

_{MAX}5 to 6, VAS 0–10) remained the same as that for either agent alone, but that analgesic effect was sustained at 4 to 8 h after combination dosing [92,93,94]. The dose for this combination therapy is often also dictated by regulatory authorities, e.g., 4.5 mg/kg ibuprofen (maximum dose 300 mg) and 15 mg/kg paracetamol (max dose 1000 mg) [95]. The dose of ibuprofen is lower than that commonly prescribed alone [96]. Ibuprofen has a similar FAT fraction for clearance (fFat

_{CL}= 0.86) to acetaminophen, but with a lower FAT fraction for volume (fFat

_{VOL}= 0.72) [72]. However, because the ibuprofen dose is small, the dose for the mixture could be calculated based on calculations for acetaminophen alone.

_{MAX}is the maximum FFM for any given height (HT, m) and WHS

_{50}is the TBW value when FFM is half of WHS

_{MAX}. For men, WHS

_{MAX}is 42.92 kg·m

^{−2}and WHS

_{50}is 30.93 kg·m

^{−2}, and for women, WHS

_{MAX}is 37.99 kg·m

^{−2}and WHS

_{50}is 35.98 kg·m

^{−2}[98]. Computation of FFM in children has been simplified by the availability of online calculators (e.g., [99]).

## 10. Conclusions

_{CL}= 0.82) and because some consider the estimation of this parameter to have low precision [100], then TBW is a reasonable proxy if used with allometric scaling.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**A diaphragmatic representation of the target concentration strategy. The upper panel shows the concentration–response for acetaminophen and analgesia. This response is described mathematically using the E

_{MAX}equation. The target effect of 2.6 pain unit reduction (VAS 0–10) is associated with a target concentration of 10 mg/L. A 2-compartment pharmacokinetic model (lower panel) is used to calculate a dose that achieves this target concentration in the effect compartment (Ce). Concentration in the central compartment (Cp) is linked to that in the effect compartment by a rate constant (k1e = keo at steady-state conditions). This equilibration rate constant (keo, determining rate from effect compartment to outside) is often expressed as the equilibration half-time (T

_{1/2}keo).

**Figure 2.**Simulated time–concentration profiles are shown for a loading dose of acetaminophen of 30 mg/kg in a 6-year-old, 20 kg child (FFM 16.4 kg, BMI 15.12 kg/m

^{2}). Effect compartment concentrations of 10 mg/L are achieved at 25 min and decrease below this concentration at 3.5 h. While the loading dose (30 mg/kg) is the same for obese and lean children, clearance determines the duration of time that concentrations are above 10 mg/L. The duration of concentration above 10 mg/L in a 6-year-old, 40 kg child (FFM 24.7 kg, BMI 30.25 kg/m

^{2}) is longer.

**Figure 3.**Changes in clearance are demonstrated as total body mass (expressed as weight) increases. The size metrics (body surface area, fat-free mass, linear total body weight, total body weight with allometry, and fat-free mass with allometry) are shown relative to a person with 70 kg total body mass. Children younger than 1 year of age (approx. 10 kg) are not shown because maturation is incomplete in that cohort. There is a nonlinear relationship between weight and clearance for most body size metrics, demonstrated with a curvilinear shape. The per kilogram model is shown as a straight line and increasingly overestimates clearance in adults of weight greater than 70 kg.

**Figure 4.**Simulated time–concentration profiles are shown for a loading dose of acetaminophen of 30 mg/kg in a 10-year-old, 30 kg child (FFM 24 kg, BMI 15.3 kg/m

^{2}). Effect compartment concentrations for that child and obese children (weight 50 kg, FFM 33 kg, BMI 25.5 kg/m

^{2}and weight 70 kg, FFM 39 kg, BMI 35.7 kg/m

^{2}) are shown after regular maintenance dosing of 15 mg/kg 6-hourly. Concentration increases as weight increases because clearance has a nonlinear relationship with weight.

**Figure 5.**Simulation to demonstrate that an obese teenager (125 kg) administered a loading dose of acetaminophen of 2000 mg with a maintenance dosing of 1000 mg 6-hourly will not reach the target concentration of 10 mg/L at steady-state conditions. There will be a mean pain score decrease of 2 (VAS 0–10) and while this is a meaningful pain decrease, it is a small decrease and will require supplementation from other analgesic drugs.

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**MDPI and ACS Style**

Anderson, B.J.; Cortinez, L.I. Perioperative Acetaminophen Dosing in Obese Children. *Children* **2023**, *10*, 625.
https://doi.org/10.3390/children10040625

**AMA Style**

Anderson BJ, Cortinez LI. Perioperative Acetaminophen Dosing in Obese Children. *Children*. 2023; 10(4):625.
https://doi.org/10.3390/children10040625

**Chicago/Turabian Style**

Anderson, Brian Joseph, and Luis Ignacio Cortinez. 2023. "Perioperative Acetaminophen Dosing in Obese Children" *Children* 10, no. 4: 625.
https://doi.org/10.3390/children10040625