First-order elimination is the assumption that lets DoseCurve plot a single exponential decay. Here is when that assumption holds, when it doesn't, and what zero-order kinetics looks like in practice.
The DoseCurve chart is an exponential decay. That shape only appears if the body clears the drug at a rate proportional to how much is currently present — what pharmacologists call first-order kinetics. Almost all injectable hormones, peptides and small molecules follow first-order kinetics at the doses people actually use, which is why a single-exponential model is a reasonable starting approximation. This page covers what the assumption actually says, why most drugs obey it, and the small number of cases where it breaks down.
As with every page on DoseCurve, this is educational background reading. It is not a recommendation to use any compound at any dose, and it does not replace a conversation with a qualified clinician.
A first-order process is one where the rate of change is proportional to the current amount:
d(amount)/dt = −k · amount
Solving that differential equation gives an exponential decay:
amount(t) = amount(0) · exp(−k · t)
The rate constant k is related to half-life by k = ln(2) / half_life. Doubling the amount doubles the elimination rate; halving it halves the rate. The fraction cleared per unit time is constant.
This is the assumption behind DoseCurve's chart. Every dose, regardless of size, decays at the same percentage per day.
First-order elimination shows up whenever the elimination machinery (mostly hepatic enzymes and renal filtration) is operating well below its capacity. At typical therapeutic plasma concentrations, the enzymes responsible for metabolising a drug are not saturated — they are processing whatever is presented to them and have plenty of headroom. Under those conditions the elimination rate is proportional to substrate availability, which is the textbook definition of first-order kinetics.
Most prescribed and prescription-grade injectables (testosterone esters, nandrolone esters, GLP-1 agonists, growth-hormone-releasing peptides, BPC-157, glucocorticoids, depo-progestins) sit comfortably in this regime at physiological doses. That is why the same half-life is quoted across a wide dose range — because the elimination rate scales with the amount, the half-life itself does not change.
When the elimination enzymes are saturated, the rate of clearance no longer scales with the amount present. Instead it caps out at the enzyme's maximum throughput. The plot of amount vs time becomes a straight line rather than an exponential — clearance is a fixed quantity per unit time, not a fixed fraction.
This is zero-order kinetics, and it is described by Michaelis-Menten saturation:
rate = (Vmax · concentration) / (Km + concentration)
When the concentration is much smaller than Km, the system behaves as first-order. When the concentration is much larger than Km, it behaves as zero-order. The transition between the two regimes is called the mixed-order zone.
Classic clinical examples of saturable kinetics include ethanol (saturated at typical recreational levels — half-life is not a constant), phenytoin at the upper end of its therapeutic range, high-dose aspirin, and some chemotherapy agents. The implication for a model like DoseCurve is that a single half-life value would be misleading in those situations — the half-life would lengthen as the dose increased.
Two practical consequences for the kind of compounds DoseCurve is most often used with:
1. Half-life is approximately constant across normal dose ranges. Doubling your dose, within reason, doubles the area under the curve but does not change how fast each dose decays. The chart shape is preserved; only the height scales. This is why "200 mg weekly" and "100 mg twice weekly" produce identical averages but different peak-to-trough ratios.
2. Steady state is predictable. Because each dose clears at the same fractional rate, the time to reach steady state on a repeated schedule is governed only by the half-life — roughly four to five half-lives, regardless of dose size. That is what the dashboard's "time to steady state" metric is calculating.
Even when overall elimination is first-order, the body is not a single well-mixed compartment. Injected drugs first reach the bloodstream, then distribute into peripheral tissues, then redistribute back as plasma levels fall. Most drugs show a brief early-phase rapid decline (alpha phase) followed by a slower terminal decline (beta phase) on a true two-compartment plot.
For oil-depot esters the picture is more complex still: there is an absorption phase from the depot itself, a distribution phase into tissues, and an elimination phase. The DoseCurve model collapses all of this into a single elimination half-life. The simplification is acceptable because:
If you need true two-compartment fidelity (for example, when interpreting an early post-injection blood draw against a long-ester schedule), a single-exponential model will miss the early peak. Bloodwork at known time points is the only reliable way to anchor that.
If you have bloodwork at multiple doses and the change in serum concentration is not proportional to the change in dose, that is a red flag for saturable kinetics or for changing absorption or clearance. The proportional check is rough but useful: doubling a dose should double the area under the curve over a full cycle, all else being equal. If it doesn't, the system isn't behaving first-order, and the underlying reason is worth a conversation with your prescriber rather than a re-tune of the DoseCurve inputs.