For most drugs, the time to reach steady state is four to five half-lives if the drug is given at regular intervals—no matter the number of doses, the dose size, or the dosing interval. A half-life is how long it takes for half of the drug to be eliminated from the body. If a single dose is given every half-life, half of the first dose will be cleared from the body before the next dose.
So, after the second dose, there will be 1. Half of that is eliminated and then the next dose is given, meaning there are now 1. At dose 5 after five half-lives , there will be close to two doses in the body, which means one entire dose is eliminated each dosing interval. If we continue dosing at the same frequency, the amount we dose will be eliminated during each dosing interval. As a result, drug concentrations in the body remain constant steady. Another way to think about steady state:.
But a very simple way to remember it is that the average C ss is the total exposure AUC over one dosing interval divided by the duration of the dosing interval. For a drug with a short half-life, steady state is achieved pretty quickly.
By solving for C p , you get the following:. As a further simplification, we know that there is a relationship between dose, clearance, and bioavailability shown by the following equation:. Thus, the average concentration at steady state is simply the total exposure over 1 dosing interval divided by the time of the dosing interval.
So while concentrations rise and fall during a dosing interval at steady state, the average concentration does not change. Furthermore, the only factors that control C ss are the dose, the dosing interval, and the clearance. Assuming clearance cannot be altered by a clinician, the steady state levels of drug can be modulated using the dose and the dosing interval. Lower doses and longer intervals will result in lower C ss values, while higher doses and shorter intervals will give higher C ss values.
The situation is even simpler for intravenously administered drugs where you can directly calculate the C ss using the following equation:. This can also be extended to different dose levels if you assume dose proportionality. The time to reach steady state is defined by the elimination half-life of the drug.
If you have a drug with a long half life, you can achieve a target steady state level more quickly by using a loading dose. However, it will take 10 days to achieve steady state. Therefore you could achieve the target C ss more quickly by administering one 60 mg dose followed by 30 mg doses to achieve steady state levels within 2 days.
The 60 mg dose is called a loading dose , and the 30 mg dose is the maintenance dose or dose to maintain steady state. Also, within the field of electronics, a steady state is the condition of equilibrium in a network or circuit that happens as the effects of the transients are no longer viable. Furthermore, a steady state is achieved after the initial, oscillations, or turbulence dissipates.
Moreover, when a system is experiencing a steady state, the system is considered to be stable. Furthermore, steady-state analysis is an invaluable component in the design process. In general, nearly every process or system has both a steady state and a transient state. Also, a steady state establishes after a specific time in your system.
However, a transient state is essentially the time between the beginning of the event and the steady state. Therefore, in terms of a definition, a transient state is when a process variable or variables changes, but before the system reaches a steady state.
Also, transient time is the time it takes for a circuit to change from one steady state to the next. For example, if you activate a switch within a circuit containing an inductor or capacitor , the component will utilize the resulting change in current or voltage, thus causing the system to take a considerable amount of time to reach a new steady state.
Moreover, you can define a transient by stating that if a quantity is at rest and a change in time takes place, thus changing the current state, a transient has occurred. I briefly mentioned the importance of determining the steady state.
Also, we have further evidence of the importance of steady state determination when we examine design specifications. As I am sure you are aware, designers convey design specifications in terms of these characteristics. Furthermore, the analysis of a system's steady state characteristics provides an overall understanding of how a device will perform and function.
Moreover, there are several analysis methods in use to determine the steady state and the transient state of a system or process. One such method is the Sinusoidal Steady State Analysis. It is a method of analysis in use to analyze AC circuits using identical techniques for solving direct current circuits.
Also, the ability of a power system or electrical machine to regain its original or previous state is called Steady State Stability. A steady-state economy seeks to find an equilibrium between production growth and population growth. In a steady state economy, the population would be stable with birth rates closely matching death rates and production rates similarly matching the depreciation or consumption of goods.
A steady-state economy aims for the efficient use of natural resources and also seeks fair distribution of the wealth generated from the development of those resources. In a steady-state economy, success would be measured by how stable gross domestic product GDP is, rather than by GDP growth being the main measure of economic health.
A steady-state economy seeks stability over the long-term and may be judged on a local, regional, or national scale. Steady-state economies would still grow and contract, but the idea is to minimize the severity of these fluctuations. Ecological and environmental economists —major supporters of the idea of a steady-state economy—have long held that the environment cannot support an unlimited growth of production and wealth.
Their reasoning is that constant economic growth is closely tied to more rapid consumption of scarce natural resources, and it also comes at the cost of an increasing ecological footprint. The concept of a steady-state economy actually reaches back to classical economics, although it is now more commonly associated with economist Herman Daly. Economists, such as John Stuart Mill, David Ricardo, and Adam Smith, all assumed that growth would eventually plateau as competitive advantages, the division of labor, and resource availability reached natural limits.
Without economic growth, the expectation was that population growth would naturally stabilize. In practice, however, technology and the uneven nature of global economic development have enabled longer periods of growth than were ever thought possible. Starting in the s, however, ecological economists started to point out that humankind was rapidly depleting resources and impacting natural ecosystems at an unprecedented rate and on an unimaginable scale. It is important to note that a steady-state economy is distinct from a stagnant economy.
In a stagnant economy the lack of growth is characterized by unemployment and economic pain. A steady-state economy seeks to distribute wealth from production more broadly, ensuring economic security for the broadest number of people possible. Although human well-being within ecological constraints is the intention of the steady-state economy, economists have continued to argue over some of how this concept could be applied and what the actual impacts would be.
There is no modern day economy that can be truly said to be steady-state, but economists have started measuring and ranking countries based on biophysical and social indicators. Most countries measured in this way continue to have growing resource consumption with mixed results on how this growth is translating to better lives for their citizens. Many of these studies point to wealthy countries needing to lead on reducing their resource consumption as developing nations have not enjoyed the social gains to a point where stability is desirable yet.
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