Plot reticulocyte release age curves

vignettes/evidence-for-parameter-values.Rmd

@@ -28,6 +28,7 @@ This document collects sources of evidence for baseline parameter values.
 
 ```{r setup, class.source = 'fold-hide'}
 library(spleenrbc, warn.conflicts = FALSE)
+suppressPackageStartupMessages(library(ggplot2))
 suppressPackageStartupMessages(library(here))
 
 output_dir <- here("outputs")
@@ -101,6 +102,10 @@ baseline <- baseline |>
   dplyr::mutate(Evidence = dplyr::case_when(
     Parameter == "MaxFold" ~ "[Maximum fold increase in RBC production]",
     Parameter == "PMF" ~ "[Parasite multiplication]",
+    Parameter == "rho0" ~ "[Reticulocyte release from bone marrow]",
+    Parameter == "kappa" ~ "[Reticulocyte release from bone marrow]",
+    Parameter == "T_R" ~ "[Reticulocyte release from bone marrow]",
+    Parameter == "T_R_min" ~ "[Reticulocyte release from bone marrow]",
     .default = ""
   ))
 
@@ -158,6 +163,88 @@ The manuscript text also states:
 
 > The maturation time of the reticulocyte in the peripheral blood is taken as 1 day when the PCV is 0.45±0.5, 1.5 days when the PCV is 0.35±0.05, 2 days when the PCV is 0.25±0.05, and 3 days when the PCV is 0.15±0.05 (Hillman & Finch 1967).
 
-Accordingly, the residence time in the bone marrow decreases from 3.5 days when the PCV is 0.45±0.5, down to 1 day when the PCV is 0.15±0.05.
+Accordingly, the residence time in the bone marrow decreases from 3.5 days when the PCV is 0.45±0.5, down to 1.5 day when the PCV is 0.15±0.05.
+
+The following function provides a reasonable characterisation, while maintaining a release age of 3.5 days in the absence of anaemia:
+
+\begin{align}
+  t_r &= \begin{cases}
+    T_R & \text{when } \mathbf{U_c} > U_{ss}
+    \\
+    T_R^{\min} + (T_R - T_R^{\min}) \cdot \left(1 +
+      \exp\left[- s \cdot (U_{\mathrm{frac}} - i)\right]\right)^{-1}
+    & \text{when } \mathbf{U_c} \le U_{ss}
+  \end{cases}
+  \\
+  U_{\mathrm{frac}} &= \frac{\mathbf{U_c}}{U_{ss}} \\
+  s &= 10 \quad \mathrm{(slope)}
+  \\
+  i &= 0.5 \quad \mathrm{(inflection)}
+\end{align}
+
+```{r plot-retic-release, class.source = 'fold-hide'}
+orig_retic_release_age <- function(u_frac) {
+  T_R <- 3.5 * 24
+  T_R_min <- 24
+
+  pkg_data <- new.env()
+  utils::data("rbc_steady_state", package = "spleenrbc", envir = pkg_data)
+  u_ss <- pkg_data$rbc_steady_state
+
+  u_rbc <- pmin(u_frac * u_ss, u_ss)
+  scale <- log(u_ss) - log(u_rbc)
+  t_release <- T_R_min + (T_R - T_R_min) * exp(-100 * scale)
+  t_release
+}
+
+new_retic_release_age <- function(u_frac, inflection, slope) {
+  T_R <- 3.5 * 24
+  T_R_min <- 24
+  u_frac <- pmin(u_frac, 1)
+
+  scale <- T_R - T_R_min
+  T_R_min + scale / (1 + exp(- slope * (u_frac - inflection)))
+}
+
+plot_retic_release_age <- function() {
+  u_frac <- seq(from = 0, to = 1.0, by = 1e-3)
+  slope <- 10
+  inflection <- 0.5
+  orig_age <- orig_retic_release_age(u_frac)
+  new_age <- new_retic_release_age(u_frac, inflection, slope)
+
+  df <- data.frame(
+    u_pcnt = rep(100 * u_frac, 2),
+    age = c(orig_age, new_age),
+    equation = rep(c("Original", "New"), each = length(u_frac))
+  )
+
+  df_koepke <- data.frame(
+    hematocrit = c(45, 35, 25, 15),
+    age = 24 * c(3.5, 3.0, 2.5, 1.5)
+  ) |> dplyr::mutate(
+    u_pcnt = 100 * hematocrit / 45,
+    equation = "Koepke & Koepke (1986)"
+  )
+
+  ggplot(df, aes(u_pcnt, age / 24)) +
+    geom_line(mapping = aes(colour = equation)) +
+    geom_point(data = df_koepke) +
+    expand_limits(y = 0) +
+    scale_x_continuous(
+      "uRBC Population (% of steady-state)",
+      breaks = c(0, 33, 66.7, 100),
+      labels = c("0%", "33%", "67%", "100%")
+    ) +
+    ylab("Minimum age of release (days)") +
+    scale_colour_brewer(
+      "Equation: ",
+      palette = "Dark2"
+    ) +
+    theme(legend.position = "top")
+}
+
+plot_retic_release_age()
+```
 
 ## References {-}