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rslab.Rmd
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rslab.Rmd
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---
title: "Introduction to rslab"
output:
rmarkdown::html_vignette:
fig_width: 6
fig.align: 'center'
fig.asp: 0.618
dpi: 320
toc: true
warning: FALSE
message: FALSE
vignette: >
%\VignetteIndexEntry{Introduction to rslab}
%\VignetteEngine{knitr::rmarkdown}
%\VignetteEncoding{UTF-8}
---
```{r, include = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
dpi = 300,
warning = FALSE,
message = FALSE,
out.width = "100%",
comment = "#>"
)
```
## BTPS Calculator
[Spirometry test](https://en.wikipedia.org/wiki/Spirometry) is a procedure that measures lung volumes and air flow parameters which calculate from inspiratory and expiratory gas volumes of a human subject.
The gas volumes/flows obtained by the spirometer are in **ATPS** (Ambient Temperature and Pressure Saturated) conditions which its volumes also depends on environmental conditions including room temperature.
The obtained volumes/flows must be converted to gas condition in **BTPS** (Body Temperature, Pressure, water vapor Saturated) which gives more accurate representation of actual volumes/flows within the lungs.
\
[BTPS correction factor](https://nddmed.com/_Resources/Persistent/8a716ac3fd123ce0becd7b56596582d4fc4c0c47/appnote-btps-correction-v01r.pdf) is a coefficient used to convert flow and volume measured at ambient conditions (ATPS) to the conditions within the lungs (BTPS).
`get_btps_factor()` is a function to obtain the BTPS correction factor.
```{r setup}
library(rslab)
```
```{r btps}
# BTPS correction factor at room temperature = 27 degree celsius
btps_factor27 <- get_btps_factor(temp = 27)
btps_factor27
```
If Tidal Volume (TV) was measured as 500 ml at room temperature of 27 degree celsius, the
TV in the lung at BTPS (body temperature, pressure, water vapor saturated) would be:
```{r}
# TV (ml) at BTPS
500 * btps_factor27
```
If you want to convert several lung volumes or flow (from ATPS to BTPS), use `lung_vol_atps_btps()` and the result will be shown as a tibble.
```{r lung_vol_conv}
lung_vol_atps_btps(
temp = 27,
FEV1 = 3.5,
FVC = 4.5,
PEF = 450,
TV = 0.5,
IC = 2.5,
EC = 2.5,
VC = 4.5
)
```
## Metabolic Rate & Oxygen Consumption Calculator
In a laboratory experiment using [Harvard Spirometer](https://www.somatco.com/Recording-Spirometer-50-1833-50-1817.pdf), this package provides functions to calculate metabolic rate and oxygen consumption by input a displacement in x-and y-direction of Harvard spirometer tracing, height and weight of the subject, and environmental conditions which are temperature and barometric pressure.
### Oxygen Consumption
In Harvard spirometer tracing, horizontal direction (x-direction) represents time (default paper speed = 25 mm/min) whereas vertical direction (y-direction) represents usage of oxygen (1 mm = 30 ml of oxygen). With a little bit of calculation, we can derived an oxygen consumption in unit of L/hr in the **ATPS** condition (**A**mbient **T**emperature and barometric **P**ressure **S**aturated with water vapor condition).
You can use `get_oxycons()` to calculate oxygen consumption and it will also provide other info printed to R console as well.
```{r oxycons}
oxycons <- get_oxycons(x = 15, # displacement in x-direction = 15 mm
y = 80, # displacement in y-direction = 80 mm
paper_speed = 25 # Paper speed of the kymograph = 25 mm/min
)
```
### Metabolic Rate
To calculate metabolic rate, we must first convert oxygen consumption $\dot{V}_{o_2}$ at **ATPS** to **STPD** (**S**tandard **T**emperature of 0掳C and a barometric **P**ressure of 760 mmHg, and in a **D**ry state).
STPD correction factor can be used to convert gas in ATPS to BTPS condition.
It has a linear relationship with barometric pressure and temperature.
Therefore, `get_STPD_factor()` can be used to predict STPD factor using `baro` and `temp_c` as predictors. (It use multiple linear regression model behind the scene.)
```{r stpd_760_25}
stpd_760_25 <- get_STPD_factor(
baro = 760, # Barometric pressure at the recording site.
temp_c = 25 # Temperature in celsius at the recording site.
)
```
Correction can be made by multiply oxygen consumption $\dot{V}_{o_2}$ at ATPS to STPD correction factor.
```{r}
oxycons * stpd_760_25 # Unit in L/hr
```
Finally, metabolic rate can be calculated by times an oxygen consumption $\dot{V}_{o_2}$ (L/hr) at STPD to a caloric equivalent of oxygen (Cal/hr) divided by Body Surface Area (BSA) in m^2^, which can be calculated by [DuBois & DuBois formula](http://www-users.med.cornell.edu/~spon/picu/calc/bsacalc.htm) (DuBois D, DuBois EF)
<!-- $$ -->
<!-- Met \ Rate \ (Cal/m^2/hr) = \frac{ \dot{V}_{o_2} (L/hr) \times CalEqi \ O_2 \ (Cal/hr)}{ BSA \ (m^2) } -->
<!-- $$ -->
<!--  -->
\
$$
Met \ Rate \ (Cal/m^2/hr) = \frac{ \dot{V}_{o_2} (L/hr) \times CalEqi \ O_2 \ (Cal/hr)}{ BSA \ (m^2) }
$$
\
`get_metabolic_rate()` is a final wrapper function that calculate metabolic rate; moreover, it also reports metabolic rate along with oxygen consumption and other related parameters printed to the R console.
```{r}
get_metabolic_rate(x = 15, # displacement in x-direction = 15 mm
y = 80, # displacement in y-direction = 80 mm
paper_speed = 25, # Paper speed of the kymograph = 25 mm/min
baro = 760, # Barometric pressure at the recording site.
temp_c = 25, # Temperature in celsius at the recording site.
wt_kg = 70, # Subject's weight in kilogram
ht_cm = 180, # Subject's height in centimetre
cal_eqi_oxygen = 4.825 # Caloric equivalent of Oxygen at RQ = 0.82
)
```
## Simulation of Harvard Spirometer Tracing
### Simulate Data
In this section, contrary to the previous, we will simulate data to plot Harvard spirometer tracing from the respiratory parameters.
\
`sim_Harvard_tracing()` is the function to simulates volume-time tracing data produced by breathing of a hypothetical subject as recorded by the Harvard spirometer.
The input parameters can be categorized into the followings:
- **Function to Simulate 1 Respiratory Cycle:** as supply by the argument `f`, the default, currently, is a cosine (`cos`) function which might give a rough representation of 1 respiratory cycle. (It is not a physiologic representation of respiratory waveform. I still need more research on this.)
- **Amplitude and Wavelength of the sinusoidal function:** this can be calculated by knowing the Respiratory Rate (`RR`), Tidal Volume (`TV`), and paper speed (`paper_speed`)
- **Slope and Y-intercept of an Oxygen Line:** the oxygen line, i.e., the linear line fitted from the lowest points of each respiratory waveform, can be simulated by knowing its slope ($\beta_1$), y-intercept ($\beta_0$), and random error term ($\epsilon$).
- **Slope ($\beta_1$)** can be calculated from an oxygen consumption (argument `oxycons`) and paper speed (`paper_speed`).
- **Y-intercept ($\beta_0$)** can be specified directly from the user.
- And, **a random error ($\epsilon$)** can be generated from a Gaussian distribution with $\mu$ = 0, and `sd` as specified.
```{r tracing_df}
tracing_df <- sim_Harvard_tracing(
f = "cos", # Cosine function to represent 1 respiratory cycle
t_start = 0, # First `x` value will be started at time = 0 minute
t_end = 1, # Last `x` value will be ended at time = 1 minute
paper_speed = 25, # Paper speed in mm/minute
y_int_O2_line = 5, # Y-intercept of an oxygen line
oxycons = 10, # Oxygen consumption is 10 L/hr (default unit)
TV = 500, # Tidal Volume is 500 ml
RR = 20, # Respiratory Rate is 20 /min
seq_x_by = 0.01, # This control resolution of simulated data
epsilon_sd = 0.3, # Add random variation sampled from Gaussian distribution with mean = 0, sd = 0.3
seed = 1, # Seed to generate the random variation
)
head(tracing_df)
```
### Plot
With a little help of `{ggplot2}` package, the tracing can then be visualized.
```{r}
library(ggplot2)
library(latex2exp)
theme_set(theme_bw())
```
```{r}
ggplot(tracing_df) +
geom_path(aes(x, y)) +
geom_smooth(aes(x, y_O2_line), method = "lm", formula = "y~x",
linetype = "dashed") +
expand_limits(y = 0) +
labs(title = "Simulation of Harvard Spirometer Tracing",
subtitle = TeX("(TV = 500 ml, RR = 20/min, $\\dot{V}_{O_2}$ = 10 L/hr)"),
x = "x (mm)", y = "y (mm)")
```
### Behind the Tracing
If you curious about the **mathematical model** that underlies this simulated tracing, please visit [this article](https://lightbridge-ks.github.io/rslab/articles/mod-tracing.html).