This interactive tool shows how biomarker concentrations change in the body over time. Based on figures 9.1 and 9.2 in Molecular Epidemiology: Principles and Practices, the tool lets you adjust key parameters like biological half-life and exposure patterns. These adjustments show how biomarkers accumulate and are eliminated from the body. Can you reach a steady state where the diffusion rate into the body equals the diffusion rate out?
Accumulation phase: biomarker builds up during exposure
Elimination phase: concentration decreases after exposure stops
Half-life determines both accumulation and elimination rates
Half-life can differ per matrix
Exposure variability creates fluctuations in biomarker levels
Half-life determines what period of exposure can possibly be reflected in a measurement
Sampling timing: half-life determines optimal collection windows. Biomarkers with a relatively short half-life are more sensitive to fluctuations of exposure
Summary measures: recent vs. usual vs. peak vs. cumulative exposure assessment will summarize levels in distinct ways
Model logic
Details
The tool uses a one-compartment pharmacokinetic model with first-order kinetics. In this model, the elimination rate stays proportional to the substance’s concentration, and concentration changes reflect the balance between intake (exposure) and elimination rates. We model this process using two equations:
\[
\begin{aligned}
& k=\frac{\ln (2)}{t_{1 / 2}} \\
& C_{\text {new }}=C_{\text {old }}+\left(\operatorname{Exposure}(t)-k \times C_{\text {old }}\right) \times \Delta t
\end{aligned}
\] Here, \(k\) represents the elimination constant, \(t_{1/2}\) the half-life, \(C\) the concentration, and \(\Delta t\) the time step (1 hour).
Exposure senarios
The model includes four different exposure patterns, each based on (somewhat) realistic environmental or occupational conditions. The dose for any hour, \(D(t)\), follows these patterns:
Constant Environmental: steady exposure at the average dose level. The exposure is the same 24/7: \[
D(t)=D_{\text {avg }}
\]
Constant Occupational: restricts exposure to weekdays during standard work hours (9 to 17 o’clock): \[D(t) = \begin{cases}
D_{\text{avg}} & \text{if weekday and } 9 \leq h < 17 \\
0 & \text{otherwise}
\end{cases}\]
Variable Environmental: this represents fluctuating environmental exposures with daily peaks. There’s a baseline exposure that gets boosted during certain hours, plus random day-to-day variation: \[D(t) = \begin{cases}
D_{\text{avg}} \cdot (1+\epsilon_V) & \text{during peak hours} \\
0.4 \cdot D_{\text{avg}} \cdot (1+\epsilon_V) & \text{during off-peak hours}
\end{cases}\]
Variable Occupational: combines occupational timing with random fluctuation: \[D(t) = \begin{cases}
D_{\text{avg}} \cdot (1+\epsilon_V) & \text{if weekday and } 9 \leq h < 17 \\
0 & \text{otherwise}
\end{cases}\]
The variability component \(\epsilon_V\) introduces randomness through the formula \((U(0,1)-0.5) \times V\), where \(V\) represents the variability factor you set and \(U(0,1)\) generates a random number between 0 and 1 from a uniform distribution.
Where this model simplifies
Details
The model is a useful starting point to get a sense of the basic relationship between exposure and internal concentration. However, by treating the human body as a single, well-mixed container it of course simplifies many biological realities. In reality, an exposure dose is not simply added, and the substance is not eliminated from a single compartment at a constant rate. I’m not a toxicologist myself, but I have tried to learn the (very) basics. So I used this as an opportunity to learn and write on where the reality is more messy as I think it’s always useful to know what an ideal model should capture.
The model assumes chemicals enter and exit the body through a single pathway, but actual ADME processes (Absorption, Distribution, Metabolism, and Excretion) following exposure involve multiple, complex routes. Inhaled chemicals bypass the liver and enter arterial blood directly, giving them immediate access to sensitive organs like the brain and heart. Ingested substances first pass through the liver, where enzymes can partially metabolize them before they reach general circulation. Skin absorption follows yet another pathway, delivering chemicals into venous blood. Each route creates different kinetic patterns that a single-compartment model cannot capture.
Once absorbed, chemicals do not distribute uniformly throughout the body as the model assumes. The circulatory system transports substances unevenly, and chemicals partition between blood and tissues based on blood flow, tissue composition, and the chemical’s own properties. For example, lipid-soluble compounds concentrate heavily in fatty tissues, while water-soluble substances remain largely in blood and other body water. This partitioning creates multiple body reservoirs with vastly different uptake and release rates.
The model treats elimination (excretion) as a simple, constant process, but the body actually transforms (metabolizes) most foreign chemicals through complex metabolic pathways. Cytochrome P-450 enzymes and other biotransformation systems can either detoxify substances or activate them into more harmful metabolites. High exposure levels can saturate these enzyme systems, causing elimination (excretion) rates to slow dramatically and violating the model’s assumption of first-order kinetics. When saturation occurs, chemicals persist in the body much longer than the constant half-life would predict.
Lastly, the model cannot capture the complex multi-compartment dynamics of persistent chemicals. While the model can accommodate long half-lives by adjusting the half-life parameter, it presents elimination as a smooth exponential decay from a single compartment. Fat tissue actually creates a separate reservoir for lipophilic compounds like PCBs and DDT. This can create a two-phased elimination pattern with rapid initial clearance from blood and organs, followed by very slow release from fat stores. During periods of weight loss or metabolic stress, stored chemicals can remobilize and create concentration spikes in circulation, causing internal (!) re-exposure long after external exposure has ceased. The single-compartment model does not show these dynamic phases caused by complex interplay between storage and release.
And in reality, all of these ‘parameters’ can differ from person to person..
Future stuff
Details
Originally, I wanted to create this little interactive visualization to illustrate variability in biomarkers and demonstrate how sampling design and summary measures matter in epidemiological studies. I use within-subject variation for this demonstration, but effective epidemiological studies also take the between-person variation into account, so I hope to incorporate the latter as well. I’m not sure how yet though.
