# Considerations for Intravenous Anesthesia Dose in Obese Children: Understanding PKPD

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Pharmacokinetic Concepts to Determine Dose

## 3. Dosing Concepts in the Child

#### 3.1. The Association between Weight and Dose

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

_{STD}e.g., 70 kg). However, maintenance doses expressed as mg/kg, as in Equation (3), are commonly observed to be too small in children when compared to adults. For example, propofol infusion rates to maintain a target concentration of 3 mg/L are higher in children than adults [25]. These observations query linear assumptions about dose and weight and point to why the linear approach is not a suitable general method for drug dosing in children [6].

#### 3.2. Use of PKPD to Determine Dose

_{MAX}or Hill equation [27], Figure 1) is used to predict the target concentration known to be associated with a desired target effect. Population pharmacokinetic (PK) and pharmacodynamic (PD) parameter estimates, as well as covariate information, are used to predict time concentration and concentration effect values in a specific patient.

#### 3.2.1. The Target Concentration

#### 3.2.2. Dose Calculation Using Compartment Models

## 4. Allometry

_{STD}):

_{AGE}) during that period. Propofol clearance in obese adults [51] and non-obese adults and in children [15,52,53,54,55] and in obese children [56] is best described using allometry with TBW as the size descriptor rather than FFM, LBM or IBM. Allometry computation is relatively easy for practitioners and can be managed on an application of a cellular phone. The only variable required is weight and knowledge of a standardized clearance in an adult; height is not a required variable.

## 5. Size Scalers for the Obese Child

#### 5.1. Size Scaling and Obesity in Anaesthesia

#### 5.2. Body Mass Index

#### 5.3. Lean Body Mass

#### 5.4. Fat-Free Mass

_{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}[58].

#### 5.5. Ideal Body Weight

## 6. A Universal Size Scaler

#### 6.1. Normal Fat Mass

#### 6.2. Limitations of NFM for IV Dosing

## 7. Application of NFM Principles for TCI to the Obese and Non-Obese Child

#### 7.1. Maintenance/Infusion Dose

#### 7.2. The Dose–Clearance Mismatch Explained

^{2}) compared to the lean child (6 years 20 kg, BMI 15.12 kg/m

^{2}). The steady state concentration, dictated by clearance, is achieved at the same time but there are differences between concentrations and consequent effect (Figure 3). This is because clearance, expressed as per kilogram, is lower in the obese child. Dose, expressed as per kilogram, also requires a similar reduction. Dose reduction, per kilogram, will be similar to the nonlinear changes in clearance (Figure 2). Use of NFM without allometry would result in a dose that is too large because the curvilinear nature of clearance changes with size are unaccounted for. The use of NFM with allometry, irrespective of the value for Ffat, is a better option, since knowing the Ffat of each different drug allows adaptation of the scaler according to the drug’s physical properties.

#### 7.3. Loading Dose

#### 7.3.1. Loading Dose Using a One-Compartment Model

#### 7.3.2. Loading Dose for an Obese Child

#### 7.3.3. The Volume of Distribution at Maximum Effect

_{PEAK}) is dependent on clearance and the effect site equilibration half-time for a one compartment model, but intercompartment clearances also have influence on T

_{PEAK}in multicompartment models. At a submaximal dose, T

_{PEAK}is independent of dose because maximum effect is not reached. At supramaximal doses, maximal effect will occur earlier than T

_{PEAK}and persist for a longer duration because of the shape of the pharmacodynamic (PD) sigmoidal concentration–response relationship; the achieved concentration is on the upper flat part of the curve (Emax). The T

_{PEAK}concept has been used to calculate optimal initial bolus dose [109]. The volume of distribution (Vpe) at the time of peak effect site concentration (C

_{PEAK}) is calculated and used (Equation (12)):

_{PEAK}delayed compared to the child not obese, plasma concentrations higher with lower BIS scores.

#### 7.3.4. Consideration of Adverse Effects

_{1/2}keo) has been estimated as 3–6 min for sedation effect [37,113] and 9.9 min for centrally mediated vasodilation [111]. Rapid administration of dexmedetomidine 0.9 µg/kg in a 6-year-old (50 kg, BMI 37.81 kg/m

^{2}) child achieved acceptable sedation but at the cost of rapid pulse rate falls and blood pressure rises. When infusion time is over 20 min, a larger dose (1.1 µg/kg) is required for the same level of sedation (BIS 73), but cardiovascular changes are less fluctuant (Figure 5).

## 8. Practical Considerations

^{2}), grade 2 (BMI > 35 kg/m

^{2}) and grade 3 (BMI > 40 kg/m

^{2}), child obesity is graded depending on the percentile above the median for that particular age group; overweight (>85th percentile), obese (>95th percentile) and severely obese (120% of 95th percentile or >35 kg/m

^{2}). A crude but practical method to determine a size scaler that uses readily measured variables (total body weight and height) might be a calculated weight for the pump that comprises:

- (A)
- Overweight: use total body weight less 5%
- (B)
- Obese: use total body weight less 10%
- (C)
- Severely obese: use total body weight less 20%

## 9. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Principles behind the target concentration strategy are shown diagrammatically. The upper panel shows a concentration response for a drug with sedative properties. The shape of this response is determined using the E

_{MAX}equation. Light sedation is associated with a bispectral index (BIS) of 73. This target effect is associated with a target concentration of 3.7 µg/L. Pharmacokinetic knowledge (lower panel) is then used to achieve this target concentration in the effect compartment (Ce). A 2-compartment pharmacokinetic model is shown in this example. Concentration in the central compartment (Cp) is linked to that in the effect compartment by a rate constant (k1e = keo at steady-state).

**Figure 2.**Clearance relative to a person of 70 kg total body mass (TBM) is shown using different size metrics. Children younger than 1 year of age (approx. 10 kg) are not shown because maturation is incomplete in that cohort. Metrics are standardized to a male with typical height for age and weight from 10 to 200 kg. A nonlinear relationship exists between weight and clearance for most body size metrics. The use of the linear per kilogram model, based on TBM, increasingly overestimates clearance in adults of weight greater than 70 kg. The use of BSA (weight with an exponent of 2/3) and allometry using an exponent of 3/4 are similar at lower masses but diverge when TBM is greater than 100 kg. Note that the James formula [57] (purple line) fails in adults of short stature with increasing total body weight [58,59].

**Figure 3.**Propofol time concentration and concentration effect profiles after infusion (10 mg/kg/h) in a 6-year-old male child of 20 kg, height 115 cm and a 6-year-old child of 50 kg, height 115 cm. Effect is measured by bispectral index (BIS). Concentrations are higher in the 50 kg child because clearance is less than that in the 20 kg child.

**Figure 4.**Estimation of volume of distribution at the time of peak effect (Vpe) in a 6 year old child of 20 kg and of 50 kg given dexmedetomidine 1 µg/kg [109]. Simulation performed using dexmedetomidine pharmacokinetic parameters derived by Morse and colleagues [87]. Dexmedetomidine clearance was best scaled using FFM and NFM (FfatV = 0.29) for volume of distribution.

**Figure 5.**Simulation of hemodynamic adverse effects when dexamethasone is given intravenously to a 6-year-old child (20 kg). Drug in the upper panel was administered as a rapid bolus 0. 9 µg/kg. The lower panel shows hemodynamic changes after a larger loading dose of 1.1 µg/kg delivered as an infusion over 20 min. A similar level of sedation (BIS 73) is achieved at 20 min but the slow infusion is without the dramatic changes in heart rate and mean arterial blood pressure observed after rapid infusion.

**Table 1.**Factor of fat (Ffat) estimates for pharmacokinetic parameters of clearance and volume of distribution for glomerular filtration rate (GFR) and selected drugs that have been investigated.

Ffat Clearance | Ffat Volume | Source | |
---|---|---|---|

GFR | 0.22 | - | Neonates to adults, n = 928 [86] |

Acetaminophen | 0.816 | 1 | Adults 18–49 y, 49–116 kg, n = 116 [87] |

Busulfan | 0.509 | 0.203 | 0.1–66 years, n = 1610 [88] |

Dexmedetomidine | 0 | 0.293 | Neonates to adults, n = 202 [87] |

Dexmedetomidine | 0 ** | 0 | Adults Obese n = 20, age 18–54 y, Weight 94–152 kg, BMI 36–52 kg·m ^{−2}Lean n = 20, age 18–60 y, Weight 59–97 kg, BMI 23–30 kg·m ^{−2})[89] |

Ethanol | 1 (Vmax) | 0.39 | Adults, n = 108 [90] |

Gemcitabine | 0 | 0 | Adults, n = 56 [91] |

Heparin | 0 | 1 | Children 0.5–15 y n = 64 [92] |

Ibuprofen | 0.863 | 0.718 | Adults 18–49 y, 49–116 kg, n = 116 [87] |

Lithium | 0 | 0 | Children (n = 61) [93] |

Miltefosine | 0 | 0 | Children and adults [94] |

Oxycodone | 1 | 1 | Neonates to adults, n = 237 [95] |

Oxypurinol | 0 | 0 | Adult patients with gout (n = 92), healthy subjects (n = 12) [96] |

Propofol | 1 | 1 | Adults obese (n = 19, age 40 SD 8.7 y, Weight 106 SD 18 kg, BMI 39.7 SD 4.1 kg·m^{−2}) and 51 non-obese (n = 51) [46] |

Remifentanil (LBM from [57]) | 0 | 0 | Adults 18–60 years, n = 24 Obese 38 SD 8 y, Weight 113 SD 17 kg Lean 38 SD 7 y, Weight 64 SD 10 kg [63] |

Tacrolimus | 0 | 0 | Adult kidney transplant recipients, n = 44 [97] |

Warfarin | 0 | 0 | Adults, n = 264 [98] |

**Table 2.**Dexmedetomidine infusion rate required to achieve a target effect of bispectral index of 73 in a male child of 6 years of age and height of 115 cm. The target concentration was 1 µg/mL. The loading dose was administered over 20 min. Subsequent infusion rates were altered at 20 min and 50 min in order to maintain the target concentration. Simulation for rate determination performed using pharmacokinetic parameters from Morse et al. [87].

20 kg | 30 kg | 40 kg | 50 kg | 20 kg | 30 kg | 40 kg | 50 kg | |
---|---|---|---|---|---|---|---|---|

Duration (min) | Rate: mg/kg/h | Rate mg/h | ||||||

0–20 | 2.9 | 2.58 | 2.27 | 2 | 58.78 | 77.4 | 90.9 | 100 |

20–50 | 1.4 | 1.14 | 1.00 | 0.90 | 28.0 | 34.2 | 40.0 | 45 |

50–150 | 1.1 | 0.89 | 0.78 | 0.69 | 22.4 | 26.9 | 31.0 | 34.4 |

Mass Scaled Using Allometry | ||
---|---|---|

Total Body Weight (kg) | Total Body Mass (kg) | Fat-Free Mass (kg) |

10 | 16.3 | 15.8 |

20 | 27.4 | 28.0 |

30 | 37.1 | 37.8 |

40 | 46.0 | 47.0 |

50 | 54.4 | 55.6 |

60 | 62.4 | 62.8 |

70 | 70.0 | 70.0 |

80 | 77.4 | 76.6 |

90 | 84.5 | 82.8 |

100 | 91.5 | 88.7 |

110 | 98.3 | 94.2 |

120 | 104.9 | 99.5 |

140 | 117.7 | 109.3 |

160 | 130.1 | 118.2 |

180 | 142.1 | 126.5 |

200 | 153.8 | 134.1 |

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**MDPI and ACS Style**

Morse, J.D.; Cortinez, L.I.; Anderson, B.J.
Considerations for Intravenous Anesthesia Dose in Obese Children: Understanding PKPD. *J. Clin. Med.* **2023**, *12*, 1642.
https://doi.org/10.3390/jcm12041642

**AMA Style**

Morse JD, Cortinez LI, Anderson BJ.
Considerations for Intravenous Anesthesia Dose in Obese Children: Understanding PKPD. *Journal of Clinical Medicine*. 2023; 12(4):1642.
https://doi.org/10.3390/jcm12041642

**Chicago/Turabian Style**

Morse, James Denzil, Luis Ignacio Cortinez, and Brian Joseph Anderson.
2023. "Considerations for Intravenous Anesthesia Dose in Obese Children: Understanding PKPD" *Journal of Clinical Medicine* 12, no. 4: 1642.
https://doi.org/10.3390/jcm12041642