## Introduction

BlueBerry is a web software with a graphical user interface that has a goal of providing a standard Moment analysis module on the Internet. Since this is a web-based software, we are trying to make it available on various environments (e.g., operating systems and devices). This document will be updated as the software updated.

Please leave your comments below this page or send an email directly to the developers if there is any concern about BlueBerry. Comments are always welcome. The software will be continuously improved. The updates would be shared with the history of changes. We hope this software, released with good intentions, is helpful. However, there is no warranty for the results that this software produce and the software itself.

This page is printable. This guide is based on the BlueBerry 2021.07.25 update.

## Requirements

This section introduces the client environment for use. We are trying to support all possible features of the software in the environment below. However, there may be some limitations especially in mobile environments.

The support environment below may be changed in the future.

- Operating systems: Microsoft Windows 10, Microsoft Windows 11 (Insider Preview), Apple iOS (latest version)
- Web browsers: Mozilla FireFox (latest version), Naver Whale (latest version), Microsoft Edge (latest version), Apple iOS Sarfari (lateset version)

## How to use

### Access

You can access BlueBerry on https://nca.simcube.org/blueberry. If the address is changed, the old URL would be automatically redirected to the new address.

### Enter data

Click the Add Data button at the top of the list page.

You can input new data on the following page: https://nca.simcube.org/blueberry/nca . Data entry pages may be changed when new analysis methods are added to Blueberry.

### Browse data

Select an item you want to see on the list page (https://nca.simcube.org/blueberry). There will be the result of NCA (e.g., half-life, clearance, and volume of distribution), graphs, etc. analyzed through moment analysis.

The structure of the address is *https://nca.simcube.org/blueberry/data:[data number]@[data creator ID]*. Data can be accessed only by the creator of the data or by those authorized to be shared. The data sharing function is not availabile, yet.

We are developing a data sharing function, and when the sharing function is applied, we plan to make it available to attach data on your posts so that you can share your opinions. Access rights to data are reserved by the data creator or those designated by the data creator. Through future development, we plan to allow authors to specify permissions for specific groups.

### Edit data

Entered data can be corrected. You can edit the entered data by clicking the "Edit" button at the bottom of the view page. Automatically calculated values cannot be modified.

The structure of the data editing page address is *https://nca.simcube.org/blueberry/nca/data:[data number]@[data creator ID]*. The right to modify the data is held by the data creator or the person designated by the data creator.

## Analysis of data

The entered data is automatically analyzed according to the information entered by the data creator.

### Unit conversion

If the units entered for dose do not match the units entered for concentrations, the prefix is interpreted as follows to match the two units.

**International unit prefix (SI Prefix)**

SI Prefix |
Scientific Notation |

Y | 10^{24} |

Z | 10^{21} |

E | 10^{18} |

P | 10^{15} |

T | 10^{12} |

G | 10^{9} |

M | 10^{6} |

k | 10^{3} |

h | 10^{2} |

1 | 10^{0} |

d | 10^{-1} |

c | 10^{-2} |

m | 10^{-3} |

u | 10^{-6} |

μ | 10^{-6} |

n | 10^{-9} |

p | 10^{-12} |

f | 10^{-15} |

a | 10^{-18} |

z | 10^{-21} |

y | 10^{-24} |

### Calculation of PK parameters

PK parameters are calculated based on the input data. The formula for each parameter is as follows. The number of significant figures for parameters are 4. These significant figures are rounded up and displayed at the very end of the calculation process, and the most accurate mathematical constants that can be obtained in a 64-bit system were used for the calculation. However, since we did not receive information about the significant digits of the number entered, it does not mean information about the actual significant digits. Please consider the significant digits that are meaningful for your data.

#### Dose

Outputs the dose entered by the user. When used for calculation, it is used after unit conversion. If entered in mol-based unit, it can be calculated after converting to gram using the molecular weight.

#### C_{0}

It means the concentration at the time zero (0). Blueberry will estimate the concentration at the time zero for a single dose, and at the time of the last administration for repeated doses. If there are other inputs from the user, an estimate is obtained according to the following rules:

- Extravenous route, or intravenously infusion
- In the case of repeated doses, the time will be counted from the time of the last dose.
- If there is input concentration at the time zero, the value will be incorporated. At this time, in order to reflect the difficulty of displaying exact 0 in floating-point calculations in computer calculations, if the difference from 0 is 0.000001 or less, it will be regarded as 0.
- If there are no observations at the time zero in the case of repeated doses, the minimum value observed after the last dose is used as C
_{0}.

- For a single dose, C
_{0}will be assumed to be zero.

- In the case of repeated doses, the time will be counted from the time of the last dose.
- Intravenously rapid infusion (IV bolus)
- In the case of repeated doses, input concentration at the time right after the last dose will be used.
- Plot a concentration-time graph of the first two observations and find the slope on a semi-log scale. Perform a linear regression on the graph with time on the x-axis and concentration on the y-axis, transforming the concentration so that the base is the natural constant e.
- If the straight line from these first two observations has a negative slope, then the y-intercept of the linear regression is converted to the concentration (not log-transformed value) term and this value is assumed to be C
_{0}. - If the straight line from these first two observations has a positive slope, assume the first concentration observation to be C
_{0}.

- If the straight line from these first two observations has a negative slope, then the y-intercept of the linear regression is converted to the concentration (not log-transformed value) term and this value is assumed to be C
- If either of the first two observations contains a number equal to or less than zero, or a non-numeric term, the first concentration observation with a positive value is assumed to be C
_{0}. - If either of the first two observations contains a number or non-numeric term equal to or less than zero, and neither value is positive, assume zero for the value of C
_{0}.

#### Interpolation methods

There are three interpolation methods to choose from for calculating AUC and AUMC. If you choose the log-trapezoidal method, the interval where the concentration increases over time is still calculated according to the linear-trapezoidal method.

- Linear-Trapezoidal Method
- In a concentration-time plot, a straight line will be assumed for the time range between two points, meaning that the area under the curve (AUC
_{t}) between the two points is calculated as follows - If t
_{n}>t_{n-1}, it will be written as follows:

- In a concentration-time plot, a straight line will be assumed for the time range between two points, meaning that the area under the curve (AUC
- Log-Trapezoidal Method
- In a concentration-time plot, an exponential function will be assumed for the time range between two points, which means that the area under the curve (AUCt) between the two points is calculated as follows
- If t
_{n}>t_{n-1}, it will be written as follows:

- Linear-trapezoidal method with error correction
- Introduce a correction term that uses a first-order derivative to a linear-trapezoidal method that assumes a first-order expression between two points in a concentration-time plot. The underlying equation is as follows The level of error improves from
*O(h*for linear-trapezoidal to^{2})*O(h*. [Reference: J. J. Hart (1952), A Correction for the Trapezoidal Rule,^{4})*The American Mathematical Monthly*, pp. 33-37.] - In other words, the area under the curve (AUC
_{t}) between two points is calculated as follows. - If t
_{n}>t_{n-1}, it will be written as follows: - The slope between two points is approximated by assuming that the function df/dt is a linear function of the slope.

- Introduce a correction term that uses a first-order derivative to a linear-trapezoidal method that assumes a first-order expression between two points in a concentration-time plot. The underlying equation is as follows The level of error improves from

#### AUC_{last}

Calculates the area under the curve of the concentration-time curve from time 0 to the last observation time based on the interpolation method you selected. However, if you selected the log-trapezoidal formula, if two concentrations have the same value in an interval, or if one of the values is not positive, the linear-trapezoidal formula is used to calculate that interval.

#### AUC

Calculate the area under the curve (AUC) of the concentration-time curve from time 0 to infinity. Extrapolate by assuming that the concentration after the concentration at the time of the last observation decreases as a single exponential function. Do not calculate if λ_{Z} is negative (when the concentration in the terminal phase increases with time).

#### %Extrapolated_{AUC}

Indicates the percentage extrapolated when calculating the AUC.

#### AUC_{τ}

For repeated doses, calculates the area under the concentration-time curve from the time of the last dose to τ. The calculation method depends on the selected interpolation method.

#### AUMC_{last}

Calculates the area under the curve of the concentration-(time*time) curve from time 0 to the last observation based on the interpolation method you selected. However, if the log-trapezoidal formula is selected and the two concentrations are equal or non-positive in an interval, the area under the curve for that interval is calculated using the linear-trapezoidal formula.

#### AUMC

Calculate the area under the curve of the concentration-(time*time) curve from time 0 to time infinity. Concentrations after the concentration at the time of the last observation are extrapolated by assuming that the concentration-time curve follows an exponential function. If λ_{Z} is negative (the concentration of the terminal phase increases with time), it is not extrapolated to the time infinity.

#### %Extrapolated_{AUMC}

Indicates the extrapolated ratio when calculating AUMC.

#### AUMC_{τ}

In the case of repeated administration, the area under the curve of the concentration-(time*time) curve from the time of the last administration to τ is calculated. The calculation method depends on the selected interpolation method.

#### CL

Calculate systemic clearance.

For extravascular route data, since AUC includes bioavailability (F), it is calculated as:

For repeated dose data, CL_{ss} is calculated because steady state is assumed.

#### MRT

If the input data is repeated dose, AUC_{τ} and AUMC_{τ} would be calculated. In the case of single dose, AUC and AUMC would be calculated and utilized for the further estimation. In the case of extravascular input, The value of MRT will contain mean absorption time (or mean input time).

- Single dose

- Repeated dose

If the data indicates IV infusion, 주입 시간을 고려하여 계산합니다. T_{in}은 주입 시간을 의미합니다.

- 단회투여

- 반복투여

#### MRT_{last}

Estimated mean residence time calculated by the concentration from zero to the last sampling time.

- If it is not the IV infusion:

- In the case of IV infusion:

#### V_{ss}

The volume of distribution at steady-state. This will be calculated only in the case of IV bolus injection and continuous IV infusion because estimated MRT after extravascular input (e.g., oral administration) will contain the time delay by absorption and the mathmatical formula below cannot estimate the V_{ss}.

#### V_{Z}

The volume of distribution based on terminal phase.

- IV bolus or continuous IV infusion:

- Considering bioavailability (F) for extravascular input.

The steady-state will be assumed for the repeated dose, and the volume (V_{Z} or V_{Z}/F) will be calculated by below:

- IV bolus or continuous IV infusion:

- Considering bioavailability (F) for extravascular input.

#### Accumulation Index

In the case of repeated dose, the ratio of accumulated concentration by steady state will be estimated by below:

#### λ_{Z}

The slope of terminal phase. This parameter will be estimated by a linear regression of log-transformed concentration over time plot. The range of terminal phase will be determined by the biggest Adjusted R^{2}, but the higher number of observation for terminal phase will be selected if the difference of Adjusted R^{2} is smaller than 0.0001 among the comparison. The range before Tmax will not be included in the terminal phase. In the case of infusion, the observed concentrations during the infusion time will not be included in the terminal phase. If the data is not after IV bolus input, Tmax will not be included in the terminal phase.

At least three observation which is acceptable for the critera above is needed for the terminal phase estimation.

If the concentration increases during the terminal phase, λ_{Z} will not be estimated.

#### t_{1/2, terminal}

The terminal phase half-life.

#### Number of points to estimate λ_{Z}

The number of observations in the terminal phase which is selected by the method above (see section λ_{Z}).

#### R^{2}

The squared Pearson correlation coefficient for the estimation of λ_{Z}. The R^{2} will be calculated in the log-transformed concentration-time profiles.

#### Adjusted R^{2}

This parameter is calculated for the selection of the number of terminal phase. The Adjusted R^{2} is calculated because the R^{2} has tendency to become higher in the more number of observations.

#### C_{ss, avg}

The averaged concentration at the steady state.

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