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Insulin pump

An insulin pump is a medical device used for the administration of insulin in the treatment of diabetes mellitus, also known as continuous subcutaneous insulin therapy. The device configuration may vary depending on design. A traditional pump includes:
 * the pump (including controls, processing module, and batteries)
 * a disposable reservoir for insulin (inside the pump)
 * a disposable infusion set, including a cannula for subcutaneous insertion (under the skin) and a tubing system to connect the insulin reservoir to the cannula.

Other configurations are possible. More recent models may include disposable or semi-disposable designs for the pumping mechanism and may eliminate tubing from the infusion set.

An insulin pump is an alternative to multiple daily injections of insulin by insulin syringes or an insulin pen and allows for flexible insulin therapy when used in conjunction with blood glucose monitoring and carbohydrate counting.

Medical uses
Insulin pumps are used to deliver insulin on a continuous basis to a person with type I diabetes.

Advantages

 * Users report better quality of life (QOL) compared to using other devices for administering insulin. The improvement in QOL is reported in type 1 and insulin-requiring type 2 diabetes subjects on pumps.
 * The use of rapid-acting insulin for basal needs offers relative freedom from a structured meal and exercise regime previously needed to control blood sugar with slow-acting insulin.
 * Programmable basal rates allow for scheduled insulin deliveries of varying amounts at different times of the day. This is especially useful in controlling events such as the dawn phenomenon resulting in fewer and less severe low blood sugar events during the night.
 * Many users feel that bolusing insulin from a pump is more convenient and discreet than injection.
 * Insulin pumps make it possible to deliver more precise amounts of insulin than can be injected using a syringe. This supports tighter control over blood sugar and hemoglobin A1c levels, reducing the chance of long-term complications associated with diabetes. This is predicted to result in a long-term cost savings relative to multiple daily injections.
 * Many modern insulin pumps have a "bolus wizard" that calculates how much bolus insulin is needed, taking into account expected carbohydrate intake, blood sugar level, and still-active insulin.
 * Insulin pumps can provide an accurate record of insulin usage through their history menus. On many insulin pumps, this history can be uploaded to a computer and graphed for trend analysis.
 * Neuropathy is a troublesome complication of diabetes resistant to usual treatment. There are reports of alleviation or even total disappearance of resistant neuropathic pain with the use of insulin pumps.
 * Recent studies of use of insulin pumps in Type 2 diabetes have shown profound improvements in HbA1c, sexual performance, and neuropathy pain.

Disadvantages
Insulin pumps, cartridges, and infusion sets may be far more expensive than syringes used for insulin injection with several insulin pumps costing more than $6,000; necessary supplies can cost over $300. Another disadvantage of insulin pump use is a higher risk of developing diabetic ketoacidosis if the pump malfunctions. This can happen if the pump battery is discharged, if the insulin is inactivated by heat exposure, if the insulin reservoir runs empty, the tubing becomes loose and insulin leaks rather than being injected, or if the cannula becomes bent or kinked in the body, preventing delivery. Therefore, pump users typically monitor their blood sugars more frequently to evaluate the effectiveness of insulin delivery.
 * Since the insulin pump needs to be worn most of the time, pump users need strategies to participate in activities that may damage the pump, such as rough sports and activities in the water. Some users may find that wearing the pump all the time (together with the infusion set tubing) is uncomfortable or unwieldy.
 * Possibility of insulin pump malfunctioning, and having to resort back to multiple daily injections until a replacement becomes available. However most pump manufacturers will have a program that will get a new pump to the user within 24 hours or allow the user to buy a second pump as a backup for a small fee. Additionally the pump itself will make many safety checks throughout the day, in some cases up to 4,000,000 and may have a second microprocessor dedicated to this.
 * Users may experience scar tissue buildup around the inserted cannula, resulting in a hard bump under the skin after the cannula is removed. The scar tissue does not heal particularly fast, so years of wearing the pump and changing the infusion site will cause the user to start running out of viable "spots" to wear the pump. In addition, the areas with scar tissue buildup generally have lower insulin sensitivity and may affect basal rates and bolus amounts. In some extreme cases the insulin delivery will appear to have no/little effect on lowering blood glucose levels and the site must be changed.
 * Users may experience allergic reactions and other skin irritation from the adhesive on the back of an infusion set. Experience may vary according to the individual, the pump manufacturer, and the type of infusion set used.
 * A larger supply of insulin may be required in order to use the pump. Many units of insulin can be wasted while refilling the pump's reservoir, filling the tubing, or changing an infusion site. This may affect prescription and dosage information.

Accessibility
Use of insulin pumps is increasing because of:
 * Easy delivery of multiple insulin injections for those using intensive insulin therapy.
 * Accurate delivery of very small boluses, helpful for infants.
 * Growing support among doctors and insurance companies due to the benefits contributing to reducing the incidence of long-term complications.
 * Improvements in blood glucose monitoring. New meters require smaller drops of blood, and the corresponding lancet poke in the fingers is smaller and less painful.  These meters also support alternate site testing for the most routine tests for practically painless testing.

History
In 1974, the first insulin pump was created and was named the Biostator. The first pump was a 60 kg bedside device. It also had the capability of monitoring blood glucose levels, so this also doubles as the first continuous glucose monitor. Between 1978 and 1988, Robert Channon, working with Guy's Hospital and the Bristol Royal Infirmary, developed a series of miniature insulin infusion pumps. Today, insulin pumps are so small that they can fit in a pocket or a purse.

In 1984, an Infusaid implantable infusion device was used to treat a 22-year-old patient successfully.

The insulin pump was first endorsed in the United Kingdom in 2003 by the National Institute for Health and Care Excellence (NICE).

Developments
New insulin pumps are becoming "smart" as new features are added to their design. These simplify the tasks involved in delivering an insulin bolus.
 * insulin on board: This calculation is based on the size of a bolus, the time elapsed since the completion of the bolus, and a programmable metabolic rate. The pump software will estimate the insulin remaining in the bloodstream and relay it to the user.  This supports the process of performing a new bolus before the effects of the last bolus are complete and, thereby, helps prevent the user from overcompensating for high blood sugar with unnecessary correction boluses.
 * bolus calculators: Pump software helps by calculating the dose for the next insulin bolus. The user enters the grams of carbohydrates to be consumed, and the bolus "wizard" calculates the units of insulin needed.  It adjusts for the most recent blood glucose level and the insulin on board, and then suggests the best insulin dose to the user to approve and deliver.
 * custom alarms: The pump can monitor for activities during specific times of day and alarm the user if an expected activity did not occur. Examples include a missed meal bolus, a missed blood glucose test, a new blood glucose test 15 minutes after a low blood glucose test, etc.  The alarms are customized for each user.
 * touch bolus: For persons with visual impairments, this button on the pump can be used to bolus for insulin without using the display. This works with a system of beeps to confirm the bolus parameters to the pump user.  This feature is described as 'touch', 'audio', or 'easy' bolus depending on brand.  The feature was first introduced in the mid- to late 1990s.
 * interface to personal computers: Since the late 1990s, most pumps can interface with personal computers for managing and documenting pump programming and/or to upload data from the pump. This simplifies record keeping and can be interfaced with diabetes management software.
 * integration with blood glucose meters: Blood glucose data can be manually entered into the pump to support the bolus wizard for calculation of the next insulin bolus. Some pumps support an interface between the insulin pump and a blood glucose meter.
 * The Medtronic Diabetes Minimed Paradigm series of insulin pumps allow for radio frequency (RF) communication. This enables the pump to receive data from a Lifescan (in the US) or Bayer (in other countries) blood glucose meter.
 * The Animas Ping is a pump/blood glucose meter combo that connect to each other using radio frequency. They both can work independently of each other and each have their own history storage. The main purpose of the connection between the pump and the meter is that it allows boluses to be made from the meter or the pump. This is particularly useful when correcting for a high blood sugar as the meter remembers readings and automatically enters them in correction boluses if they are less than 15 minutes old.
 * The DANA Diabecare IISG insulin pump has a blood glucose meter in it. After a blood glucose check with the integrated glucometer, the user can use the bolus wizard to deliver a required bolus.
 * The Insulet OmniPod has a separate remote, also known as a Personal Diabetes Monitor (PDM), that features a built-in meter that uses Freestyle test strips. This eliminates the need to carry and manage a separate meter or transfer blood glucose results from device to device.
 * integration with continuous glucose monitoring systems: Some insulin pumps can be used as a display for interstitial glucose values obtained from a continuous glucose monitoring system or sensor.
 * The Minimed Paradigm series' RF link also supports a continuous blood glucose sensor known as the Paradigm REAL-Time Continuous Glucose Monitor that wirelessly provides an interstitial glucose value every 5 minutes on the pump screen. The Medtronic REAL-Time System was the first to link a continuous monitor with an insulin pump system. In the Minimed 530G with Enlite (in the US) or Paradigm Veo (in other countries), the pump can enter a low glucose suspend mode stopping all insulin delivery (bolus and basal insulin) if interstitial glucose values fall below the hypoglycemia threshold. In the Minimed 640G insulin pump series, low glucose suspend mode can also be entered based on predicted hypoglycemia.
 * The Animas Vibe is an insulin pump that is fully integrated with the Dexcom G4 Continuous Glucose Monitor. The two connect wirelessly to monitor and track blood glucose levels and detect patterns. The Dexcom G4 has the advantage of being designed to monitor glucose levels every five minutes throughout 7 days of continuous wear. The Animas Vibe was approved for use in Europe in 2011, and Canada and the United States in January and December 2014, respectively. NOTE: Animas insulin pumps are not available due to Johnson & Johnson's decision to cease operations at their Animas subsidiary.
 * The Tandem Diabetes Care t:Slim X2 was approved by the U.S. Food and Drug Administration in 2019 and is the first insulin pump to be designated as an alternate controller enabled (ACE) insulin pump. ACE insulin pumps allow users to integrate continuous glucose monitors, automated insulin dosing (AID) systems, and other diabetes management devices with the pump to create a personalized diabetes therapy system. Many users of the t:slim X2 integrate the pump with the Dexcom G6, a continuous glucose monitor approved by the FDA in 2018. It was the first CGM authorized for use in an integrated therapy system. The device does not require users to provide fingerstick calibrations and lasts for up to ten days.
 * Other options may include remote control, tubeless pod, touch screen interface, rechargeable battery, pre-filled insulin cartridge, and mobile bolus.

MiniMed 670G is a type of insulin pump and sensor system created by Medtronic. It was approved by the US FDA in September 2016 and was the first approved hybrid closed loop system which senses a patient's basal insulin requirement and automatically adjusts its delivery to the body.

Mylife YpsoPump, developed by Ypsomed, was launched in Europe in 2016. Eli Lilly had planned to work with Ypsomed to introduce this to the United States, but that effort was terminated in 2022.

Omnipod 5: On January 28, 2022, Insulet Corporation announced the FDA has approved the Omnipod 5, the first tubeless closed loop insulin pump with Smartphone control, working with the Dexcom G6 Continuous Glucose Monitor. The Omnipod 5 will have a feature named SmartAdjust technology that allows for the increase, decrease, or suspension of insulin based on the user's custom blood glucose targets.

INSUL by AgVa: AgVa Healthcare announced that Insul by Agva is the world's most advanced and affordable Insulin pump. Features such as a built-in glucometer, Bluetooth connectivity, android and IOS app, as well as long-lasting and economical disposables.

Future developments

 * When insulin pump technology is combined with a continuous blood glucose monitoring system, the technology seems promising for real time control of the blood sugar level. Currently there are no mature algorithms to automatically control the insulin delivery based on feedback of the blood glucose level. When the loop is closed, the system may function as an artificial pancreas.
 * Insulin pumps are being used for infusing pramlintide (brand name Symlin, or synthetic amylin) with insulin for improved postprandial glycemic control compared to insulin alone.
 * Dual hormone insulin pumps that infuse either insulin or glucagon. In event of hypoglycemia, the glucagon could be triggered to increase the blood glucose. This would be particularly valuable in a closed loop system under the control of a glucose sensor. The Artificial Pancreas, currently in clinical trials for FDA approval, is a recently developed device designed with this technology in mind.
 * Ultrafast insulins. These insulins are absorbed more quickly than the currently available Humalog, Novolog, and Apidra which have a peak at about 60 minutes. Faster insulin uptake would theoretically coordinate with meals better, and allow faster recovery from hyperglycemia if the insulin infusion is suspended. Biodel is developing an ultrafast insulin

Dosing

An insulin pump allows the replacement of slow-acting insulin for basal needs with a continuous infusion of rapid-acting insulin.

The insulin pump delivers a single type of rapid-acting insulin in two ways:
 * a bolus dose that is pumped to cover food eaten or to correct a high blood glucose level.
 * a basal dose that is pumped continuously at an adjustable basal rate to deliver insulin needed between meals and at night.

Bolus shape
An insulin pump user can influence the profile of the rapid-acting insulin by shaping the bolus. Users can experiment with bolus shapes to determine what is best for any given food, which means that they can improve control of blood sugar by adapting the bolus shape to their needs.

A standard bolus is an infusion of insulin pumped completely at the onset of the bolus. It's the most similar to an injection. By pumping with a "spike" shape, the expected action is the fastest possible bolus for that type of insulin. The standard bolus is most appropriate when eating high carb low protein low fat meals because it will return blood sugar to normal levels quickly.

An extended bolus is a slow infusion of insulin spread out over time. By pumping with a "square wave" shape, the bolus avoids a high initial dose of insulin that may enter the blood and cause low blood sugar before digestion can facilitate sugar entering the blood. The extended bolus also extends the action of insulin well beyond that of the insulin alone. The extended bolus is appropriate when covering high fat high protein meals such as steak, which will be raising blood sugar for many hours past the onset of the bolus. The extended bolus is also useful for those with slow digestion (such as with gastroparesis or coeliac disease).

A combination bolus/multiwave bolus is the combination of a standard bolus spike with an extended bolus square wave. This shape provides a large dose of insulin up front, and then also extends the tail of the insulin action. The combination bolus is appropriate for high carb high fat meals such as pizza, pasta with heavy cream sauce, and chocolate cake.

A super bolus is a method of increasing the spike of the standard bolus. Since the action of the bolus insulin in the blood stream will extend for several hours, the basal insulin could be stopped or reduced during this time. This facilitates the "borrowing" of the basal insulin and including it into the bolus spike to deliver the same total insulin with faster action than can be achieved with spike and basal rate together. The super bolus is useful for certain foods (like sugary breakfast cereals) which cause a large post-prandial peak of blood sugar. It attacks the blood sugar peak with the fastest delivery of insulin that can be practically achieved by pumping.

Bolus timing
Since the pump user is responsible to manually start a bolus, this provides an opportunity for the user to pre-bolus to improve upon the insulin pump's capability to prevent post-prandial hyperglycemia. A pre-bolus is simply a bolus of insulin given before it is actually needed to cover carbohydrates eaten.

There are two situations where a pre-bolus is helpful:
 * 1) A pre-bolus of insulin will mitigate a spike in blood sugar that results from eating high glycemic foods.  Infused insulin analogs such as NovoLog and Apidra typically begin to reduce blood sugar levels 15 or 20 minutes after infusion.  As a result, easily digested sugars often hit the bloodstream much faster than infused insulin intended to cover them, and the blood sugar level spikes upward as a result.  If the bolus were infused 20 minutes before eating, then the pre-bloused insulin would hit the bloodstream simultaneously with the digested sugars to control the magnitude of the spike.
 * 2) A pre-bolus of insulin can combine a meal bolus and a correction bolus when the blood sugar is above the target range before a meal.  The timing of the bolus is a controllable variable to bring down the blood sugar level before eating again causes it to increase.

Similarly, a low blood sugar level or a low glycemic food might be best treated with a bolus after a meal is begun. The blood sugar level, the type of food eaten, and a person's individual response to food and insulin affect the ideal time to bolus with the pump.

Basal rate patterns
The pattern for delivering basal insulin throughout the day can also be customized with a pattern to suit the pump user.
 * A reduction of basal at night to prevent low blood sugar in infants and toddlers.
 * An increase of basal at night to counteract high blood sugar levels due to growth hormone in teenagers.
 * A pre-dawn increase to prevent high blood sugar due to the dawn effect in adults and teens.
 * In a proactive plan before regularly scheduled exercise times such as morning gym for elementary school children or after-school basketball practice for high school children.

Basal rate determination
Basal insulin requirements will vary between individuals and periods of the day. The basal rate for a particular time period is determined by fasting while periodically evaluating the blood sugar level. Neither food nor bolus insulin must be taken for 4 hours before or during the evaluation period. If the blood sugar level changes dramatically during evaluation, then the basal rate can be adjusted to increase or decrease insulin delivery to keep the blood sugar level approximately steady.

For instance, to determine an individual's morning basal requirement, they must skip breakfast. On waking, they would test their blood glucose level periodically until lunch. Changes in blood glucose level are compensated with adjustments in the morning basal rate. The process is repeated over several days, varying the fasting period, until a 24-hour basal profile has been built up which keeps fasting blood sugar levels relatively steady. Once the basal rate is matched to the fasting basal insulin need, the pump user will then gain the flexibility to skip or postpone meals such as sleeping late on the weekends or working overtime on a weekday.

Many factors can change insulin requirements and require an adjustment to the basal rate:
 * continued beta cell death following diagnosis of type 1 diabetes (honeymoon period)
 * growth spurts particularly during puberty
 * weight gain or loss
 * any drug treatment that affects insulin sensitivity (e.g. corticosteroids)
 * eating, sleeping, or exercise routine changes
 * whenever the control over hyperglycemia is degrading
 * and according to the seasons.

A pump user should be educated by their diabetes care professional about basal rate determination before beginning pump therapy.

Temporary basal rates
Since the basal insulin is provided as a rapid-acting insulin, the basal insulin can be immediately increased or decreased as needed with a temporary basal rate. Examples when this is helpful include:
 * As a passenger during a long car drive, when insulin needs are different due to inactivity.
 * While driving on an extended trip, to reduce the risk of hypoglycemia, a lower temporary basal rate may be programmed.
 * During and after spontaneous exercise or sports activities, when the body needs less insulin.
 * During illness or stress, when basal demand increases due to insulin resistance.
 * When blood ketones are present, when additional insulin is needed.
 * When on an extended fast (such as Ramadan, Lent, or Yom Kippur) when basal requirements may be lower.
 * During menses, when additional basal insulin might be needed.

Security
In August 2011, an IBM researcher, Jay Radcliffe, demonstrated a security flaw in insulin pumps. Radcliffe was able to hack the wireless interface used to control the pump remotely. Pump manufacturer Medtronic later said security research by McAfee uncovered a flaw in its pumps that could be exploited.

title: Insulin pump


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ISO 3166

ISO 3166 is a standard published by the International Organization for Standardization (ISO) that defines codes for the names of countries, dependent territories, special areas of geographical interest, and their principal subdivisions (e.g., provinces or states). The official name of the standard is Codes for the representation of names of countries and their subdivisions.

Parts
It consists of three parts:
 * ISO 3166-1, Codes for the representation of names of countries and their subdivisions – Part 1: Country codes, defines codes for the names of countries, dependent territories, and special areas of geographical interest. It defines three sets of country codes:
 * ISO 3166-1 alpha-2 – two-letter country codes which are the most widely used of the three, and used most prominently for the Internet's country code top-level domains (with a few exceptions).
 * ISO 3166-1 alpha-3 – three-letter country codes which allow a better visual association between the codes and the country names than the alpha-2 codes.
 * ISO 3166-1 numeric – three-digit country codes which are identical to those developed and maintained by the United Nations Statistics Division, with the advantage of script (writing system) independence, and hence useful for people or systems using non-Latin scripts.
 * ISO 3166-2, Codes for the representation of names of countries and their subdivisions – Part 2: Country subdivision code, defines codes for the names of the principal subdivisions (e.g., provinces, states, departments, regions) of all countries coded in ISO 3166-1.
 * ISO 3166-3, Codes for the representation of names of countries and their subdivisions – Part 3: Code for formerly used names of countries, defines codes for country names which have been deleted from ISO 3166-1 since its first publication in 1974.

Editions
The first edition of ISO 3166, which included only alphabetic country codes, was published in 1974. The second edition, published in 1981, also included numeric country codes, with the third and fourth editions published in 1988 and 1993 respectively. The fifth edition, published between 1997 and 1999, was expanded into three parts to include codes for subdivisions and former countries.

ISO 3166 Maintenance Agency
The ISO 3166 standard is maintained by the ISO 3166 Maintenance Agency (ISO 3166/MA), located at the ISO central office in Geneva. Originally it was located at the Deutsches Institut für Normung (DIN) in Berlin. Its principal tasks are:
 * To add and to eliminate country names and to assign code elements to them;
 * To publish lists of country names and code elements;
 * To maintain a reference list of all country code elements and subdivision code elements used and their period of use;
 * To issue newsletters announcing changes to the code tables;
 * To advise users on the application of ISO 3166.

Members
There are fifteen experts with voting rights on the ISO 3166/MA. Nine are representatives of national standards organizations:

 * Association française de normalisation (AFNOR) – France
 * American National Standards Institute (ANSI) – United States
 * British Standards Institution (BSI) – United Kingdom
 * Deutsches Institut für Normung (DIN) – Germany
 * Japanese Industrial Standards Committee (JISC) - Japan
 * Standards Australia (SA) - Australia
 * Kenya Bureau of Standards (KEBS) - Kenya
 * Standardization Administration of China (SAC) - China
 * Swedish Standards Institute (SIS) – Sweden

The other six are representatives of major United Nations agencies or other international organizations who are all users of ISO 3166-1:

 * International Atomic Energy Agency (IAEA)
 * International Civil Aviation Organization (ICAO)
 * International Telecommunication Union (ITU)
 * Internet Corporation for Assigned Names and Numbers (ICANN)
 * Universal Postal Union (UPU)
 * United Nations Economic Commission for Europe (UNECE)

The ISO 3166/MA has further associated members who do not participate in the votes but who, through their expertise, have significant influence on the decision-taking procedure in the maintenance agency.

Codes beginning with "X"
Country codes beginning with "X" are used for private custom use (reserved), never for official codes. Despite the words "private custom", the use may include other public standards. ISO affirms that no country code beginning with X will ever be standardised. Examples of X codes include:

 * The ISO 3166-based NATO country codes (STANAG 1059, 9th edition) use "X" codes for imaginary exercise countries ranging from XXB for "Brownland" to XXY for "Yellowland", as well as for major commands such as XXE for SHAPE or XXS for SACLANT.
 * X currencies defined in ISO 4217.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: ISO 3166


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Intensive insulin therapy

Intensive insulin therapy or flexible insulin therapy is a therapeutic regimen for diabetes mellitus treatment. This newer approach contrasts with conventional insulin therapy. Rather than minimize the number of insulin injections per day (a technique which demands a rigid schedule for food and activities), the intensive approach favors flexible meal times with variable carbohydrate as well as flexible physical activities. The trade-off is the increase from 2 or 3 injections per day to 4 or more injections per day, which was considered "intensive" relative to the older approach. In North America in 2004, many endocrinologists prefer the term "flexible insulin therapy" (FIT) to "intensive therapy" and use it to refer to any method of replacing insulin that attempts to mimic the pattern of small continuous basal insulin secretion of a working pancreas combined with larger insulin secretions at mealtimes. The semantic distinction reflects changing treatment.

Rationale
Long-term studies like the UK Prospective Diabetes Study (UKPDS) and the Diabetes control and complications trial (DCCT) showed that intensive insulin therapy achieved blood glucose levels closer to non-diabetic people and that this was associated with reduced frequency and severity of blood vessel damage. Damage to large and small blood vessels (macro- and microvascular disease) is central to the development of complications of diabetes.

This evidence convinced most physicians who specialize in diabetes care that an important goal of treatment is to make the biochemical profile of the diabetic patient (blood lipids, HbA1c, etc.) as close to the values of non-diabetic people as possible. This is especially true for young patients with many decades of life ahead.

General description
A working pancreas continually secretes small amounts of insulin into the blood to maintain normal glucose levels, which would otherwise rise from glucose release by the liver, especially during the early morning dawn phenomenon. This insulin is referred to as basal insulin secretion, and constitutes almost half the insulin produced by the normal pancreas.

Bolus insulin is produced during the digestion of meals. Insulin levels rise immediately as we begin to eat, remaining higher than the basal rate for 1 to 4 hours. This meal-associated (prandial) insulin production is roughly proportional to the amount of carbohydrate in the meal.

Intensive or flexible therapy involves supplying a continual supply of insulin to serve as the basal insulin, supplying meal insulin in doses proportional to nutritional load of the meals, and supplying extra insulin when needed to correct high glucose levels. These three components of the insulin regimen are commonly referred to as basal insulin, bolus insulin, and high glucose correction insulin.

Two common regimens: pens, injection ports, and pumps
One method of intensive insulinotherapy is based on multiple daily injections (sometimes referred to in medical literature as MDI). Meal insulin is supplied by injection of rapid-acting insulin before each meal in an amount proportional to the meal. Basal insulin is provided as a once or twice daily injection of dose of a long-acting insulin.

In an MDI regimen, long-acting insulins are preferred for basal use. An older insulin used for this purpose is ultralente, and beef ultralente in particular was considered for decades to be the gold standard of basal insulin. Long-acting insulin analogs such as insulin glargine (brand name Lantus, made by Sanofi-Aventis) and insulin detemir (brand name Levemir, made by Novo Nordisk) are also used, with insulin glargine used more than insulin detemir. Rapid-acting insulin analogs such as lispro (brand name Humalog, made by Eli Lilly and Company) and aspart (brand name Novolog/Novorapid, made by Novo Nordisk and Apidra made by Sanofi Aventis) are preferred by many clinicians over older regular insulin for meal coverage and high correction. Many people on MDI regimens carry insulin pens to inject their rapid-acting insulins instead of traditional syringes. Some people on an MDI regimen also use injection ports such as the I-port to minimize the number of daily skin punctures.

The other method of intensive/flexible insulin therapy is an insulin pump. It is a small mechanical device about the size of a deck of cards. It contains a syringe-like reservoir with about three days' insulin supply. This is connected by thin, disposable, plastic tubing to a needle-like cannula inserted into the patient's skin and held in place by an adhesive patch. The infusion tubing and cannula must be removed and replaced every few days.

An insulin pump can be programmed to infuse a steady amount of rapid-acting insulin under the skin. This steady infusion is termed the basal rate and is designed to supply the background insulin needs. Each time the patient eats, he or she must press a button on the pump to deliver a specified dose of insulin to cover that meal. Extra insulin is also given the same way to correct a high glucose reading. Although current pumps can include a glucose sensor, they cannot automatically respond to meals or to rising or falling glucose levels.

Both MDI and pumping can achieve similarly excellent glycemic control. Some people prefer injections because they are less expensive than pumps and do not require the wearing of a continually attached device. However, the clinical literature is very clear that patients whose basal insulin requirements tend not to vary throughout the day or do not require dosage precision smaller than 0.5 IU, are much less likely to realize much significant advantage of pump therapy. Another perceived advantage of pumps is the freedom from syringes and injections, however, infusion sets still require less frequent injections to guide infusion sets into the subcutaneous tissue.

Intensive/flexible insulin therapy requires frequent blood glucose checking. To achieve the best balance of blood sugar with either intensive/flexible method, a patient must check his or her glucose level with a meter monitoring of blood glucose several times a day. This allows optimization of the basal insulin and meal coverage as well as correction of high glucose episodes.

Advantages and disadvantages
The two primary advantages of intensive/flexible therapy over more traditional two or three injection regimens are:
 * 1) greater flexibility of meal times, carbohydrate quantities, and physical activities, and
 * 2) better glycemic control to reduce the incidence and severity of the complications of diabetes.

Major disadvantages of intensive/flexible therapy are that it requires greater amounts of education and effort to achieve the goals, and it increases the daily cost for glucose monitoring four or more times a day. This cost can substantially increase when the therapy is implemented with an insulin pump and/or continuous glucose monitor.

It is a common notion that more frequent hypoglycemia is a disadvantage of intensive/flexible regimens. The frequency of hypoglycemia increases with increasing effort to achieve normal blood glucoses with most insulin regimens, but hypoglycemia can be minimized with appropriate glucose targets and control strategies. The difficulties lie in remembering to test, estimating meal size, taking the meal bolus and eating within the prescribed time, and being aware of snacks and meals that are not the expected size. When implemented correctly, flexible regimens offer greater ability to achieve good glycemic control with easier accommodation to variations of eating and physical activity.

A 2020 Cochrane systematic review did not find enough evidence of reduction of cardiovascular mortality, non-fatal myocardial infarction or non-fatal stroke when comparing insulin to metformin monotherapy.

Semantics of changing care: why "flexible" is replacing "intensive" therapy
Over the last two decades, the evidence that better glycemic control (i.e., keeping blood glucose and HbA1c levels as close to normal as possible) reduces the rates of many complications of diabetes has become overwhelming. As a result, diabetes specialists have expended increasing effort to help most people with diabetes achieve blood glucose levels as close to normal as achievable. It takes about the same amount of effort to achieve good glycemic control with a traditional two or three injection regimen as it does with flexible therapy: frequent glucose monitoring, attention to timing and amounts of meals. Many diabetes specialists no longer think of flexible insulin therapy as "intensive" or "special" treatment for a select group of patients but simply as standard care for most patients with type 1 diabetes.

Treatment devices used
The insulin pump is one device used in intensive insulinotherapy. The insulin pump is about the size of a beeper. It can be programmed to send a steady stream of insulin as basal insulin. It contains a reservoir or cartridge holding several days' worth of insulin, the tiny battery-operated pump, and the computer chip that regulates how much insulin is pumped. The infusion set is a thin plastic tube with a fine needle at the end. There are also newer "pods" which do not require tubing. It carries the insulin from the pump to the infusion site beneath the skin. It sends a larger amount before eating meals as "bolus" doses.

The insulin pump replaces insulin injections. This device is useful for people who regularly forget to inject themselves or for people who don't like injections. This machine does the injecting by replacing the slow-acting insulin for basal needs with an ongoing infusion of rapid-acting insulin.

Basal insulin: the insulin that controls blood glucose levels between meals and overnight. It controls glucose in the fasting state.

Boluses: the insulin that is released when food is eaten or to correct a high reading.

Another device used in intensive insulinotherapy is the injection port. An injection port is a small disposable device, similar to the infusion set used with an insulin pump, configured to accept a syringe. Standard insulin injections are administered through the injection port. When using an injection port, the syringe needle always stays above the surface of the skin, thus reducing the number of skin punctures associated with intensive insulinotheraphy.

title: Intensive insulin therapy


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Inverse function

In mathematics, the inverse function of a function $f$ (also called the inverse of $f$) is a function that undoes the operation of $a$. The inverse of $a$ exists if and only if $f$ is bijective, and if it exists, is denoted by $$f^{-1} .$$

For a function $$f\colon X\to Y$$, its inverse $$f^{-1}\colon Y\to X$$ admits an explicit description: it sends each element $$y\in Y$$ to the unique element $$x\in X$$ such that $f^{ −1}$.

As an example, consider the real-valued function of a real variable given by $f^{ −1}$. One can think of $f$ as the function which multiplies its input by 5 then subtracts 7 from the result. To undo this, one adds 7 to the input, then divides the result by 5. Therefore, the inverse of $f$ is the function $$f^{-1}\colon \R\to\R$$ defined by $$f^{-1}(y) = \frac{y+7}{5} .$$

Definitions

Let $f$ be a function whose domain is the set $f$, and whose codomain is the set $f$. Then $f$ is invertible if there exists a function $f$ from $X$ to $Y$ such that $$g(f(x))=x$$ for all $$x\in X$$ and $$f(g(y))=y$$ for all $$y\in Y$$.

If $Y$ is invertible, then there is exactly one function $X$ satisfying this property. The function $f$ is called the inverse of $X$, and is usually denoted as $f(x) = y$, a notation introduced by John Frederick William Herschel in 1813.

The function $Y$ is invertible if and only if it is bijective. This is because the condition $$g(f(x))=x$$ for all $$x\in X$$ implies that $f$ is injective, and the condition $$f(g(y))=y$$ for all $$y\in Y$$ implies that $g$ is surjective.

The inverse function $f(x) = 5x − 7$ to $Y$ can be explicitly described as the function

 * $$f^{-1}(y)=(\text{the unique element }x\in X\text{ such that }f(x)=y)$$.

Inverses and composition
Recall that if $X$ is an invertible function with domain $f$ and codomain $g$, then

 * $$ f^{-1}\left(f(x)\right) = x$$, for every $$x \in X$$ and $$ f\left(f^{-1}(y)\right) = y$$ for every $$y \in Y $$.

Using the composition of functions, this statement can be rewritten to the following equations between functions:

 * $$ f^{-1} \circ f = \operatorname{id}_X$$ and $$f \circ f^{-1} = \operatorname{id}_Y, $$

where $f^{ −1}$ is the identity function on the set $g$; that is, the function that leaves its argument unchanged. In category theory, this statement is used as the definition of an inverse morphism.

Considering function composition helps to understand the notation $f^{ −1}$. Repeatedly composing a function $f^{ −1}$ with itself is called iteration. If $f$ is applied $f$ times, starting with the value $f$, then this is written as $id_{X}$; so $f^{ −1}$, etc. Since $f: X→X$, composing $f^{ n}(x)$ and $f^{ 2}(x) = f (f (x))$ yields $f^{ −1}(f (x)) = x$, "undoing" the effect of one application of $f$.

Notation
While the notation $f^{ −1}$ might be misunderstood, $f^{ n}$ certainly denotes the multiplicative inverse of $f^{ n−1}$ and has nothing to do with the inverse function of $f$. The notation $$f^{\langle -1\rangle}$$ might be used for the inverse function to avoid ambiguity with the multiplicative inverse.

In keeping with the general notation, some English authors use expressions like $f^{ −1}(x)$ to denote the inverse of the sine function applied to $f$ (actually a partial inverse; see below). Other authors feel that this may be confused with the notation for the multiplicative inverse of $(f(x))^{−1}$, which can be denoted as $f(x)$. To avoid any confusion, an inverse trigonometric function is often indicated by the prefix "arc" (for Latin arcus). For instance, the inverse of the sine function is typically called the arcsine function, written as $sin^{−1}(x)$. Similarly, the inverse of a hyperbolic function is indicated by the prefix "ar" (for Latin ārea). For instance, the inverse of the hyperbolic sine function is typically written as $sin (x)$. The expressions like $(sin (x))^{−1}$ can still be useful to distinguish the multivalued inverse from the partial inverse: $$\sin^{-1}(x) = \{(-1)^n \arcsin(x) + \pi n : n \in \mathbb Z\}$$. Other inverse special functions are sometimes prefixed with the prefix "inv", if the ambiguity of the $arcsin(x)$ notation should be avoided.

Squaring and square root functions
The function $arsinh(x)$ given by $sin^{−1}(x)$ is not injective because $$(-x)^2=x^2$$ for all $$x\in\R$$. Therefore, $X$ is not invertible.

If the domain of the function is restricted to the nonnegative reals, that is, we take the function $$f\colon [0,\infty)\to [0,\infty);\ x\mapsto x^2$$ with the same rule as before, then the function is bijective and so, invertible. The inverse function here is called the (positive) square root function and is denoted by $$x\mapsto\sqrt x$$.

Standard inverse functions
The following table shows several standard functions and their inverses:

Formula for the inverse
Many functions given by algebraic formulas possess a formula for their inverse. This is because the inverse $$f^{-1} $$ of an invertible function $$f\colon\R\to\R$$ has an explicit description as

 * $$f^{-1}(y)=(\text{the unique element }x\in \R\text{ such that }f(x)=y)$$.

This allows one to easily determine inverses of many functions that are given by algebraic formulas. For example, if $Y$ is the function

 * $$f(x) = (2x + 8)^3 $$

then to determine $$f^{-1}(y) $$ for a real number $X$, one must find the unique real number $f$ such that $f^{ −1}$. This equation can be solved:

 * $$\begin{align}

y        & = (2x+8)^3 \\ \sqrt[3]{y}  & = 2x + 8   \\ \sqrt[3]{y} - 8 & = 2x      \\ \dfrac{\sqrt[3]{y} - 8}{2} & = x. \end{align}$$

Thus the inverse function $f: R → [0,∞)$ is given by the formula

 * $$f^{-1}(y) = \frac{\sqrt[3]{y} - 8} 2.$$

Sometimes, the inverse of a function cannot be expressed by a closed-form formula. For example, if $n$ is the function

 * $$f(x) = x - \sin x ,$$

then $x$ is a bijection, and therefore possesses an inverse function $f(x) = x^{2}$. The formula for this inverse has an expression as an infinite sum:

 * $$ f^{-1}(y) =

\sum_{n=1}^\infty \frac{y^{n/3}}{n!} \lim_{ \theta \to 0} \left( \frac{\mathrm{d}^{\,n-1}}{\mathrm{d} \theta^{\,n-1}} \left( \frac \theta { \sqrt[3]{ \theta - \sin( \theta )} } \right)^n \right). $$

Properties
Since a function is a special type of binary relation, many of the properties of an inverse function correspond to properties of converse relations.

Uniqueness
If an inverse function exists for a given function $f$, then it is unique. This follows since the inverse function must be the converse relation, which is completely determined by $f$.

Symmetry
There is a symmetry between a function and its inverse. Specifically, if $x$ is an invertible function with domain $f$ and codomain $f$, then its inverse $f: X → Y$ has domain $X$ and image $Y$, and the inverse of $y ∈ Y$ is the original function $X$. In symbols, for functions $x ∈ X$ and $f(x)$,

 * $$f^{-1}\circ f = \operatorname{id}_X $$ and $$ f \circ f^{-1} = \operatorname{id}_Y.$$

This statement is a consequence of the implication that for $f$ to be invertible it must be bijective. The involutory nature of the inverse can be concisely expressed by
 * $$\left(f^{-1}\right)^{-1} = f.$$

The inverse of a composition of functions is given by
 * $$(g \circ f)^{-1} = f^{-1} \circ g^{-1}.$$

Notice that the order of $Y$ and $f$ have been reversed; to undo $f$ followed by $Y$, we must first undo $X$, and then undo $Y$.

For example, let $f^{ −1}(y)$ and let $x + a$. Then the composition $y − a$ is the function that first multiplies by three and then adds five,

 * $$(g \circ f)(x) = 3x + 5.$$

To reverse this process, we must first subtract five, and then divide by three,

 * $$(g \circ f)^{-1}(x) = \tfrac13(x - 5).$$

This is the composition $a − x$.

Self-inverses
If $Y$ is a set, then the identity function on $f$ is its own inverse:

 * $${\operatorname{id}_X}^{-1} = \operatorname{id}_X.$$

More generally, a function $a − y$ is equal to its own inverse, if and only if the composition $mx$ is equal to $m ≠ 0$. Such a function is called an involution.

Graph of the inverse
If $y⁄m$ is invertible, then the graph of the function

 * $$y = f^{-1}(x)$$

is the same as the graph of the equation

 * $$x = f(y) .$$

This is identical to the equation $x^{−1}$ that defines the graph of $1⁄x$, except that the roles of $1⁄y$ and $f$ have been reversed. Thus the graph of $y^{−1}$ can be obtained from the graph of $y$ by switching the positions of the $x$ and $f$ axes. This is equivalent to reflecting the graph across the line $x, y ≠ 0$.

Inverses and derivatives
The inverse function theorem states that a continuous function $f$ is invertible on its range (image) if and only if it is either strictly increasing or decreasing (with no local maxima or minima). For example, the function

 * $$f(x) = x^3 + x$$

is invertible, since the derivative $x^{p}$ is always positive.

If the function $f$ is differentiable on an interval $f$ and $y^{1/p}$ for each $x, y ≥ 0$, then the inverse $p$ is differentiable on $p > 0$. If $a^{x}$, the derivative of the inverse is given by the inverse function theorem,

 * $$\left(f^{-1}\right)^\prime (y) = \frac{1}{f'\left(x \right)}. $$

Using Leibniz's notation the formula above can be written as

 * $$\frac{dx}{dy} = \frac{1}{dy / dx}. $$

This result follows from the chain rule (see the article on inverse functions and differentiation).

The inverse function theorem can be generalized to functions of several variables. Specifically, a differentiable multivariable function $log_{a} y$ is invertible in a neighborhood of a point $f$ as long as the Jacobian matrix of $X$ at $Y$ is invertible. In this case, the Jacobian of $y > 0$ at $a > 0$ is the matrix inverse of the Jacobian of $Y$ at $X$.

Real-world examples
\begin{align} f^{-1} (f(C)) = {} & f^{-1}\left( \tfrac95 C + 32 \right) = \tfrac59 \left( (\tfrac95 C + 32 ) - 32 \right) =  C, \\ & \text{for every value of } C, \text{ and } \\[6pt] f\left(f^{-1}(F)\right) = {} & f\left(\tfrac59 (F - 32)\right) = \tfrac95 \left(\tfrac59 (F - 32)\right) + 32 = F, \\ & \text{for every value of } F. \end{align} $$ f(\text{Allan})&=2005, \quad & f(\text{Brad})&=2007 , \quad & f(\text{Cary})&=2001 \\ f^{-1}(2005)&=\text{Allan}, \quad & f^{-1}(2007)&=\text{Brad} , \quad & f^{-1}(2001)&=\text{Cary} \end{align} $$
 * Let $f$ be the function that converts a temperature in degrees Celsius to a temperature in degrees Fahrenheit, $$ F = f(C) = \tfrac95 C + 32 ;$$ then its inverse function converts degrees Fahrenheit to degrees Celsius, $$ C = f^{-1}(F) = \tfrac59 (F - 32) ,$$ since $$
 * Suppose $f$ assigns each child in a family its birth year. An inverse function would output which child was born in a given year. However, if the family has children born in the same year (for instance, twins or triplets, etc.) then the output cannot be known when the input is the common birth year. As well, if a year is given in which no child was born then a child cannot be named. But if each child was born in a separate year, and if we restrict attention to the three years in which a child was born, then we do have an inverse function. For example, $$\begin{align}
 * Let $g$ be the function that leads to an $f$ percentage rise of some quantity, and $f$ be the function producing an $g$ percentage fall. Applied to $100 with $g$ = 10%, we find that applying the first function followed by the second does not restore the original value of $100, demonstrating the fact that, despite appearances, these two functions are not inverses of each other.
 * The formula to calculate the pH of a solution is $xe^{x}$. In many cases we need to find the concentration of acid from a pH measurement. The inverse function $W (y)$ is used.

Partial inverses
Even if a function $f$ is not one-to-one, it may be possible to define a partial inverse of $X$ by restricting the domain. For example, the function

 * $$f(x) = x^2$$

is not one-to-one, since $x ≥ −1$. However, the function becomes one-to-one if we restrict to the domain $y ≥ −1/e$, in which case

 * $$f^{-1}(y) = \sqrt{y} . $$

(If we instead restrict to the domain $(2x + 8)^{3} = y$, then the inverse is the negative of the square root of $X$.) Alternatively, there is no need to restrict the domain if we are content with the inverse being a multivalued function:

 * $$f^{-1}(y) = \pm\sqrt{y} . $$

Sometimes, this multivalued inverse is called the full inverse of $f$, and the portions (such as √$f$ and −√$x$) are called branches. The most important branch of a multivalued function (e.g. the positive square root) is called the principal branch, and its value at $y$ is called the principal value of $f^{ −1}$.

For a continuous function on the real line, one branch is required between each pair of local extrema. For example, the inverse of a cubic function with a local maximum and a local minimum has three branches (see the adjacent picture).

These considerations are particularly important for defining the inverses of trigonometric functions. For example, the sine function is not one-to-one, since

 * $$\sin(x + 2\pi) = \sin(x)$$

for every real $f$ (and more generally $f^{ −1}$ for every integer $x$). However, the sine is one-to-one on the interval $y$, and the corresponding partial inverse is called the arcsine. This is considered the principal branch of the inverse sine, so the principal value of the inverse sine is always between −$f$ and $f$. The following table describes the principal branch of each inverse trigonometric function:

Left and right inverses
Function composition on the left and on the right need not coincide. In general, the conditions imply different properties of $I$. For example, let $f^{ −1}$ denote the squaring map, such that $f^{ −1}$ for all $p$ in $f:X → Y$, and let $f^{−1}:Y → X$ denote the square root map, such that $g ∘ f$$f$ for all $f^{ −1} ∘ g^{ −1}$. Then $f(x) = 3x$ for all $p$ in $f$; that is, $p$ is a right inverse to $f$. However, $f$ is not a left inverse to $R$, since, e.g., $g(x) = x + 5$.
 * 1) "There exists $x$ such that $g ∘ f$" and
 * 2) "There exists $F$ such that $(f^{ −1} ∘ g^{ −1})(x)$"

Left inverses
If $f : X → X$, a left inverse for $x$ (or retraction of $x$ ) is a function $f ∘ f$ such that composing $x$ with $f$ from the left gives the identity function $$g \circ f = \operatorname{id}_X\text{.}$$ That is, the function $f$ satisfies the rule
 * If $id_{X}$, then $y = f(x)$.

The function $y$ must equal the inverse of $f$ on the image of $x$, but may take any values for elements of $x$ not in the image.

A function $y$ with nonempty domain is injective if and only if it has a left inverse. An elementary proof runs as follows:
 * If $x$ is the left inverse of $n$, and $y = f^{ −1}(x)$, then $y = x$.
 * If nonempty $y = f(x)$ is injective, construct a left inverse $f^{ −1}$ as follows: for all $y = x$, if $[−\pi⁄2, π⁄2]$ is in the image of $\pi⁄2$, then there exists $f′(x) = 3x^{2} + 1$ such that $f′(x) ≠ 0$. Let $x ∈ I$; this definition is unique because $\pi⁄2$ is injective.  Otherwise, let $f^{ −1}$ be an arbitrary element of $g$.  For all $f(I)$, $y = f(x)$ is in the image of $g$.  By construction, $f : R^{n} → R^{n}$, the condition for a left inverse.

In classical mathematics, every injective function $f$ with a nonempty domain necessarily has a left inverse; however, this may fail in constructive mathematics. For instance, a left inverse of the inclusion $f^{ −1}$ of the two-element set in the reals violates indecomposability by giving a retraction of the real line to the set {0,1$)$}}.

Right inverses
A right inverse for $x$ (or section of $\sqrt{x}$ ) is a function $f(p)$ such that

 * $$f \circ h = \operatorname{id}_Y . $$

That is, the function $x$ satisfies the rule

 * If $$\displaystyle h(y) = x$$, then $$\displaystyle f(x) = y .$$

Thus, $pH = −log_{10}[H^{+}]$ may be any of the elements of $[0, ∞)$ that map to $g$ under $f$.

A function $g$ has a right inverse if and only if it is surjective (though constructing such an inverse in general requires the axiom of choice).

 * If $f$ is the right inverse of $f$, then $f$ is surjective. For all $$y \in Y$$, there is $$x = h(y)$$ such that $$f(x) = f(h(y)) = y$$.
 * If $f$ is surjective, $g$ has a right inverse $g$, which can be constructed as follows: for all $$y \in Y$$, there is at least one $$x \in X$$ such that $$f(x) = y$$ (because $g$ is surjective), so we choose one to be the value of $[H^{+}] = 10^{−pH}$.

Two-sided inverses
An inverse that is both a left and right inverse (a two-sided inverse), if it exists, must be unique. In fact, if a function has a left inverse and a right inverse, they are both the same two-sided inverse, so it can be called the inverse.

 * If $$g$$ is a left inverse and $$h$$ a right inverse of $$f$$, for all $$y \in Y$$, $$g(y) = g(f(h(y)) = h(y)$$.

A function has a two-sided inverse if and only if it is bijective.
 * A bijective function $f$ is injective, so it has a left inverse (if $f$ is the empty function, $$f \colon \varnothing \to \varnothing$$ is its own left inverse). $Y$ is surjective, so it has a right inverse. By the above, the left and right inverse are the same.
 * If $f$ has a two-sided inverse $g$, then $f$ is a left inverse and right inverse of $y$, so $f$ is injective and surjective.

Preimages
If $f(x) = x^{2}$ is any function (not necessarily invertible), the preimage (or inverse image) of an element $x^{2} = (−x)^{2}$ is defined to be the set of all elements of $f$ that map to $X$:

 * $$f^{-1}(\{y\}) = \left\{ x\in X : f(x) = y \right\} . $$

The preimage of $f$ can be thought of as the image of $f$ under the (multivalued) full inverse of the function $f$.

Similarly, if $f$ is any subset of $h$, the preimage of $X$, denoted $$f^{-1}(S) $$, is the set of all elements of $y$ that map to $f$:

 * $$f^{-1}(S) = \left\{ x\in X : f(x) \in S \right\} . $$

For example, take the function $x ≥ 0$. This function is not invertible as it is not bijective, but preimages may be defined for subsets of the codomain, e.g.

 * $$f^{-1}(\left\{1,4,9,16\right\}) = \left\{-4,-3,-2,-1,1,2,3,4\right\}$$.

The preimage of a single element $x ≤ 0$ – a singleton set $f^{ −1}(y)$ – is sometimes called the fiber of $f$. When $h$ is the set of real numbers, it is common to refer to $sin(x + 2\pin) = sin(x)$ as a level set.

title: Inverse function


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Inertia

Inertia is the tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes its speed or direction to change. It is one of the fundamental principles in classical physics, and described by Isaac Newton in his first law of motion (also known as The Principle of Inertia). It is one of the primary manifestations of mass, one of the core quantitative properties of physical systems. Newton writes:

"LAW I. Every object perseveres in its state of rest, or of uniform motion in a right line, except insofar as it is compelled to change that state by forces impressed thereon."

- Isaac Newton

In his 1687 work Philosophiæ Naturalis Principia Mathematica, Newton defined inertia as a property:

"DEFINITION III. The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavours to persevere in its present state, whether it be of rest or of moving uniformly forward in a right line."

Early understanding of inertial motion
Professor John H. Lienhard points out the Mozi – based on a Chinese text from the Warring States period (475–221 BCE) – as having given the first description of inertia. Before the European Renaissance, the prevailing theory of motion in western philosophy was that of Aristotle (384–322 BCE). On the surface of the Earth, the inertia property of physical objects is often masked by gravity and the effects of friction and air resistance, both of which tend to decrease the speed of moving objects (commonly to the point of rest). This misled the philosopher Aristotle to believe that objects would move only as long as force was applied to them. Aristotle said that all moving objects (on Earth) eventually come to rest unless an external power (force) continued to move them. Aristotle explained the continued motion of projectiles, after being separated from their projector, as an (itself unexplained) action of the surrounding medium continuing to move the projectile.

Despite its general acceptance, Aristotle's concept of motion was disputed on several occasions by notable philosophers over nearly two millennia. For example, Lucretius (following, presumably, Epicurus) stated that the "default state" of the matter was motion, not stasis (stagnation). In the 6th century, John Philoponus criticized the inconsistency between Aristotle's discussion of projectiles, where the medium keeps projectiles going, and his discussion of the void, where the medium would hinder a body's motion. Philoponus proposed that motion was not maintained by the action of a surrounding medium, but by some property imparted to the object when it was set in motion. Although this was not the modern concept of inertia, for there was still the need for a power to keep a body in motion, it proved a fundamental step in that direction. This view was strongly opposed by Averroes and by many scholastic philosophers who supported Aristotle. However, this view did not go unchallenged in the Islamic world, where Philoponus had several supporters who further developed his ideas.

In the 11th century, Persian polymath Ibn Sina (Avicenna) claimed that a projectile in a vacuum would not stop unless acted upon.

Theory of impetus
In the 14th century, Jean Buridan rejected the notion that a motion-generating property, which he named impetus, dissipated spontaneously. Buridan's position was that a moving object would be arrested by the resistance of the air and the weight of the body which would oppose its impetus. Buridan also maintained that impetus increased with speed; thus, his initial idea of impetus was similar in many ways to the modern concept of momentum. Despite the obvious similarities to more modern ideas of inertia, Buridan saw his theory as only a modification to Aristotle's basic philosophy, maintaining many other peripatetic views, including the belief that there was still a fundamental difference between an object in motion and an object at rest. Buridan also believed that impetus could be not only linear but also circular in nature, causing objects (such as celestial bodies) to move in a circle. Buridan's theory was followed up by his pupil Albert of Saxony (1316–1390) and the Oxford Calculators, who performed various experiments which further undermined the Aristotelian model. Their work in turn was elaborated by Nicole Oresme who pioneered the practice of illustrating the laws of motion with graphs.

Shortly before Galileo's theory of inertia, Giambattista Benedetti modified the growing theory of impetus to involve linear motion alone:

"[Any] portion of corporeal matter which moves by itself when an impetus has been impressed on it by any external motive force has a natural tendency to move on a rectilinear, not a curved, path."

Benedetti cites the motion of a rock in a sling as an example of the inherent linear motion of objects, forced into circular motion.

Classical inertia
According to Charles Coulston Gillispie, inertia "entered science as a physical consequence of Descartes' geometrization of space-matter, combined with the immutability of God." The first physicist to completely break away from the Aristotelian model of motion was Isaac Beeckman in 1614. The term "inertia" was first introduced by Johannes Kepler in his Epitome Astronomiae Copernicanae (published in three parts from 1617 to 1621); however, the meaning of Kepler's term (which he derived from the Latin word for "idleness" or "laziness") was not quite the same as its modern interpretation. Kepler defined inertia only in terms of resistance to movement, once again based on the presumption that rest was a natural state which did not need explanation. It was not until the later work of Galileo and Newton unified rest and motion in one principle that the term "inertia" could be applied to these concepts as it is today. The principle of inertia, as formulated by Aristotle for "motions in a void", includes that a mundane object tends to resist a change in motion. The Aristotelian division of motion into mundane and celestial became increasingly problematic in the face of the conclusions of Nicolaus Copernicus in the 16th century, who argued that the Earth is never at rest, but is actually in constant motion around the Sun. Galileo, in his further development of the Copernican model, recognized these problems with the then-accepted nature of motion and, at least partially, as a result, included a restatement of Aristotle's description of motion in a void as a basic physical principle:

"A body moving on a level surface will continue in the same direction at a constant speed unless disturbed."

Galileo writes that "all external impediments removed, a heavy body on a spherical surface concentric with the earth will maintain itself in that state in which it has been; if placed in a movement towards the west (for example), it will maintain itself in that movement."

This notion, which is termed "circular inertia" or "horizontal circular inertia" by historians of science, is a precursor to but is distinct from Newton's notion of rectilinear inertia. For Galileo, a motion is "horizontal" if it does not carry the moving body towards or away from the center of the Earth, and for him, "a ship, for instance, having once received some impetus through the tranquil sea, would move continually around our globe without ever stopping." It is also worth noting that Galileo later (in 1632) concluded that based on this initial premise of inertia, it is impossible to tell the difference between a moving object and a stationary one without some outside reference to compare it against. This observation ultimately came to be the basis for Albert Einstein to develop the theory of special relativity.

Concepts of inertia in Galileo's writings would later come to be refined, modified, and codified by Isaac Newton as the first of his laws of motion (first published in Newton's work, Philosophiæ Naturalis Principia Mathematica, in 1687):

"Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon." Despite having defined the concept in his laws of motion, Newton did not actually use the term "inertia.” In fact, originally he viewed the respective phenomenon as being caused by "innate forces" inherent in matter, which resisted any acceleration. Given this perspective, and borrowing from Kepler, Newton attributed the term "inertia" to mean "the innate force possessed by an object which resists changes in motion"; thus, Newton defined "inertia" to mean the cause of the phenomenon, rather than the phenomenon itself. However, Newton's original ideas of "innate resistive force" were ultimately problematic for a variety of reasons, and thus most physicists no longer think in these terms. As no alternate mechanism has been readily accepted, and it is now generally accepted that there may not be one that we can know, the term "inertia" has come to mean simply the phenomenon itself, rather than any inherent mechanism. Thus, ultimately, "inertia" in modern classical physics has come to be a name for the same phenomenon as described by Newton's first law of motion, and the two concepts are now considered to be equivalent.

Relativity
Albert Einstein's theory of special relativity, as proposed in his 1905 paper entitled "On the Electrodynamics of Moving Bodies", was built on the understanding of inertial reference frames developed by Galileo, Huygens and Newton. While this revolutionary theory did significantly change the meaning of many Newtonian concepts such as mass, energy, and distance, Einstein's concept of inertia remained at first unchanged from Newton's original meaning. However, this resulted in a limitation inherent in special relativity: the principle of relativity could only apply to inertial reference frames. To address this limitation, Einstein developed his general theory of relativity ("The Foundation of the General Theory of Relativity", 1916), which provided a theory including noninertial (accelerated) reference frames.

In general relativity, the concept of inertial motion got a broader meaning. Taking into account general relativity, inertial motion is any movement of a body that is not affected by forces of electrical, magnetic, or other origin, but that is only under the influence of gravitational masses. Physically speaking, this happens to be exactly what a properly functioning three-axis accelerometer is indicating when it does not detect any proper acceleration.

Etymology
The term inertia comes from the Latin word iners, meaning idle or sluggish.

Rotational inertia
A quantity related to inertia is rotational inertia (→ moment of inertia), the property that a rotating rigid body maintains its state of uniform rotational motion. Its angular momentum remains unchanged unless an external torque is applied; this is called conservation of angular momentum. Rotational inertia is often considered in relation to a rigid body. For example, a gyroscope uses the property that it resists any change in the axis of rotation.

title: Inertia


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Ibanez

Ibanez (アイバニーズ) is a Japanese guitar brand owned by Hoshino Gakki. Based in Nagoya, Aichi, Japan, Hoshino Gakki were one of the first Japanese musical instrument companies to gain a significant foothold in import guitar sales in the United States and Europe, as well as the first brand of guitars to mass-produce seven-string and eight-string guitars. Ibanez manufactures effects, accessories, amps, and instruments in Japan, China, Indonesia, and the United States (at a Los Angeles-based custom shop). they marketed nearly 165 models of bass guitar, 130 acoustic guitars, and more than 300 electric guitars. After Gibson and Fender, Ibanez is considered the third biggest guitar brand.

History
The Hoshino Gakki company began in 1908 as the musical instrument sales division of the Hoshino Shoten, a bookstore chain. Hoshino Gakki decided in 1935 to make Spanish-style acoustic guitars, at first using the "Ibanez Salvador" brand name in honor of Spanish luthier Salvador Ibáñez, and later simply "Ibanez". Accordingly, the brand originally was spelled Ibanyesu (イバニェス) in Japan, reflecting the Spanish pronunciation, before changing its spelling in 1986 to the current name, which represents an English pronunciation of Ibanez.

The modern era of Ibanez guitars began in 1957. The late 1950s and 1960s Ibanez catalogues show guitars with some wild-looking designs, manufactured by Kiso Suzuki Violin, Guyatone, and their own Tama factory established in 1962. After the Tama factory stopped manufacturing guitars in 1966, Hoshino Gakki contracted the Teisco String Instruments Company to make Ibanez guitars. After the Teisco String Instrument factory closed in 1970, Hoshino Gakki contracted with FujiGen Gakki to make Ibanez guitars.

In the 1960s, Japanese guitar makers mainly copied American guitar designs, and Ibanez-branded copies of Gibson, Fender, and Rickenbacker models appeared. This resulted in the so-called lawsuit period.

As a result of the lawsuit, Hoshino Gakki introduced Ibanez models based on unique designs, such as the Iceman and the Roadstar series. The company has produced its own guitar designs ever since. The late 1980s and early 1990s were an important period for the Ibanez brand. Hoshino Gakki's relationship with guitarist Steve Vai resulted in the introduction of the Ibanez JEM and the Ibanez Universe models; after the earlier successes of the Roadstar and Iceman models in the late 1970s – early 1980s, Hoshino Gakki entered the superstrat market with the RG series, a lower-priced version of their JEM series.

Hoshino Gakki also had semi-acoustic, nylon- and steel-stringed acoustic guitars manufactured under the Ibanez name. Most Ibanez guitars were made by the FujiGen guitar factory in Japan up until the mid- to late 1980s, and from then on Ibanez guitars have also been made in other Asian countries such as Korea, China, and Indonesia. During the early 1980s, the FujiGen guitar factory also produced most of the Roland guitar synthesizers, including the Stratocaster-style Roland G-505, the twin-humbucker Roland G-202 (endorsed by Adrian Belew, Eric Clapton, Dean Brown, Jeff Baxter, Yannis Spathas, Christoforos Krokidis, Steve Howe, Mike Rutherford, Andy Summers, Neal Schon and Steve Hackett) and the Ibanez X-ING IMG-2010.

Cimar and Starfield were guitar and bass brands owned by Hoshino Gakki. In the 1970s, Hoshino Gakki and Kanda Shokai shared some guitar designs, and so some Ibanez and Greco guitars have the same features. The Greco versions were sold in Japan and the Ibanez versions were sold outside Japan. From 1982, Ibanez guitars have also been sold in Japan as well.

Guitar brands such as Antoria and Mann shared some Ibanez guitar designs. The Antoria guitar brand was managed by JT Coppock Leeds Ltd England. CSL was a brand name managed by Charles Summerfield Ltd England. Maurice Summerfield of the Charles Summerfield Ltd company contributed some design ideas to Hoshino Gakki and also imported Ibanez and CSL guitars into the UK from 1964 to 1987. The Maxxas brand name came about because Hoshino Gakki thought that the guitar did not fit in with the Ibanez model range and was therefore named Maxxas by Rich Lasner from Hoshino USA.

The "lawsuit" guitars
Harry Rosenbloom, founder of the (now-closed) Medley Music of Bryn Mawr, Pennsylvania, was manufacturing handmade guitars under the name "Elger". By 1965, Rosenbloom had decided to stop manufacturing guitars and chose to become the exclusive North American distributor for Ibanez guitars. In September 1972, Hoshino began a partnership with Elger Guitars to import guitars from Japan. In September 1981, Elger was renamed "Hoshino U.S.A.", retaining the company headquarters in Bensalem Township, Pennsylvania as a distribution and quality-control center.

On June 28, 1977, in the Philadelphia Federal District Court, a lawsuit was filed by the Norlin Corporation, the parent company of Gibson Guitars, against Elger/Hoshino U.S.A.'s use of the Gibson headstock design and logo. Hoshino settled out of court in early 1978 and the case was officially closed on February 2, 1978.

After the lawsuit, Hoshino Gakki abandoned the strategy of copying "classic" electric guitar designs, having already introduced a plethora of original designs. Hoshino was producing their original Artist models from 1974, introducing a set-neck model in 1975. In 1977, they upgraded and extended their Artist range and introduced a number of other top-quality original designs made to match or surpass famous American brands: the Performer and short-lived Concert ranges, which competed with the Les Paul; through-neck Musicians; Studios in fixed- and through-neck construction; the radically shaped Iceman; and the Roadster which morphed into the Roadstar range, precursor to the popular superstrat era in the mid-1980s. The newer Ibanez models began incorporating more modern elements into their design such as radical body shapes, slimmer necks, 2-octave fingerboards, slim pointed headstocks, higher-output electronics, humbucker/single-coil/humbucker (H/S/H) pickup configurations, locking tremolo bridges and different finishes.

Sub-brands

 * Ibanez J. Custom
 * The J. Custom series are the most exclusive and expensive guitars Ibanez offers. They are "envisioned to be the finest Japanese-made guitar in history". Built by some of the most skilled luthiers in Japan, they "represent every advance in design and technology Ibanez has developed over the last 20 years". As of 2022, they feature aftermarket pickups of the Dimarzio brand (DiMarzio® Air Norton™, DiMarzio® True Velvet™, DiMarzio® The Tone Zone® and DiMarzio® PAF® 7), 5 piece maple/wenge necks with Titanium reinforcement rods, ebony fingerboard with a tree of life fret board inlay, and Edge Zero tremolo systems. Even among J. Customs there are two tiers: most of the standard production J. Customs (the ones that appear in catalogs) are produced by FujiGen Gakki while the more limited production models are produced by Sugi Guitars. The Sugi-made models are typically produced in very limited numbers from one-offs to maybe a dozen copies of a single design.

 * Ibanez Prestige
 * The Prestige guitars are Ibanez's top-of-the-line models that are built in Japan. They feature higher quality materials, high craftsmanship, and higher quality bridges compared to other models.

 * Ibanez Premium
 * The Premium guitars are similar to other models but are built in Ibanez's Indonesian premium factory to premium quality standards.

 * Ibanez Gio
 * The Ibanez Gio are Ibanez' budget guitars, designed for high playability at low costs. Many high end Ibanez guitars are recreated in the more affordable Gio form, such as the RGA and ART models.

 * U.S.A. custom
 * USA custom range. Late 1980s to mid-1990s. Also known as Ibanez LACS (L.A. Custom Shop), services only their endorsed artists today.

Solid body electric guitars

 * Ibanez RG
 * 2017 Ibanez RG652FX WH.jpg The main characteristics that are common among all Ibanez RG guitars (RG stands for Roadstar Guitar ) are that they feature 24 frets and use thin necks, known as "Wizard", which allows for faster playing. The RG features a line up of guitars with both floating tremolo systems and fixed bridge systems.
 * Ibanez RGA
 * The Ibanez RGA was introduced at a time when the Ibanez RG series only had tremolo bridges. Since then, the RG series has introduced fixed bridge models, but Ibanez still produces the RGA series with an arched top to differentiate from the RG series. The arched top allows for added comfort while playing the guitar.
 * Ibanez RGD
 * The Ibanez RGD guitar was developed for heavy metal guitar players. The RGD features a 26.5" scale which allows for lower than standard guitar tuning while retaining standard string tension without use of thicker gauge strings. It also features an extra deep scoop cut on the lower horn for easy high fret access. Ibanez currently makes two Ibanez RGD Prestige models.
 * Ibanez S
 * The Ibanez S (Saber ) guitar has an extremely thin body made out of mahogany, and is available in 6, 7 and 8-string models. They may come with either 22 or 24 frets, depending on year of manufacture. The standard line currently have Wizard III necks that are slightly wider and thicker than the original Wizard. All S models have bodies that are thicker in the middle where the pickups are, and taper off towards the outer edges. The guitars use ZR (Zero Resistance), Lo-TRS, and variants of the Edge bridge system as well as fixed bridges. Ibanez currently makes 8 Prestige S-Series guitars.
 * Ibanez DN
 * The Ibanez DN guitar (DN stands for Darkstone) was developed for heavy metal guitar players. The main features of the DN are that it has a set-in neck for speed and playing comfort, medium frets, and coil tapped pickups. This guitar is currently discontinued.

 * Ibanez X
 * The Ibanez X guitars are Ibanez guitars that feature unconventional and unique body designs. An example would be the Ibanez Xiphos, which is stylized to look like the letter X. For all X guitars currently available and for more information, check the Ibanez Electric Guitar page in 2013. (as of 2013, variations may be: Halberd XH300 and Glaive XG300, Mick Thomson Signature MTM100, MTM10)
 * Ibanez Artist (AR)
 * The Ibanez Artist guitars were designed for heavy playing such as for heavy metal or traditional rock. The Artist ARZ is a single cutaway, 24 fret, 25" scale guitar that features a wide variety of bridges and pickups depending on the specific models. The Artist ART is a single cutaway, 22 fret, 24.75" scale guitar that features a hard tail bridge. The Ibanez AR is a reissued series originating from the 70s. The AR series features a set-in neck, double cutaway, with 22 frets on a 24.75" scale.
 * Ibanez FR
 * The Ibanez FR is a simple body type guitar that is designed to be played in many genres.
 * Ibanez Mikro
 * The Ibanez Mikro series are small form factor guitars designed for children, beginners, or guitar players looking for a guitar that is easy to transport.

Hollow body electric guitars

 * Ibanez Artcore series
 * The first Ibanez Artcore models were released in mid-2002 whose goal was to offer an affordable range of full-hollow and semi-hollow body guitars that appealed to entry level guitarists who were unable or unwilling to pay big money on high-priced guitars.

 * Ibanez Artcore Custom
 * Ibanez Artcore headstock.jpg The Artcore Custom is Ibanez's flagship model for the Artcore series. The bodies of the guitars are made of maple, the neck has a set-in construction type, and features wood control knobs and hand rolled frets.
 * Ibanez AK
 * The Ibanez AK is a guitar designed for jazz and blues type playing. It features a slim set-in neck with a body designed to easily access the higher frets. The AK is easily distinguishable by its sharper lower body horn (Florentine cutaway ?) that other Artcore guitars do not have.

Production signature guitars

 * JEM, Universe and Pia Series – Steve Vai Signature
 * JS – Joe Satriani Signature
 * PGM – Paul Gilbert Signature
 * APEX – Munky Signature
 * E-Gen – Herman Li Signature
 * NDM4 – Noodles Signature
 * PWM - Paul Waggoner Signature
 * KIKO - Kiko Loureiro Signature
 * STM2 – Sam Totman Signature
 * ORM – Omar Rodriguez Signature
 * MBM – Matt Bachand Signature
 * HRG – H. R. Giger Signature
 * GB – George Benson Signature
 * K7 – Head and Munky Signature
 * PM – Pat Metheny Signature
 * PS10 – Paul Stanley Signature
 * JSM – John Scofield Signature
 * AT – Andy Timmons Signature
 * TAM - Tosin Abasi Signature
 * RBM - Reb Beach Signature
 * JBM - Jake Bowen Signature
 * BBM - Ben Bruce Signature
 * JIVA - Nita Strauss Signature
 * TOD and TTHB - Tim Henson Signature
 * SLM - Scott LePage Signature
 * MAR - Mario Camarena Signature
 * EH - Erick Hansel Signature
 * YY - Yvette Young Signature
 * M8M - Mårten Hagström Signature
 * FTM - Fredrik Thordendal Signature
 * ICHI - Ichika Nito Signature
 * LB - Lari Basilio Signature

Discontinued guitars

 * Ibanez R series, also known as the Radius series, are famous for having lightweight aerofoil-profiled basswood bodies. The main endorser was Joe Satriani before he was given his own Signature JS series. The Radius series is now discontinued.
 * RT series – Superstrat design with 24 frets. Discontinued in 1994.
 * RX series – Superstrat design but with 22 frets instead. Discontinued in 1998, and currently only exists as GRX (budget model of RX series).
 * Axstar (a.k.a. Axstar by Ibanez) – discontinued
 * EDR/EXR – Ergodyne series – discontinued
 * MC – Musician series – Discontinued – Neck-through construction (except for MC-100, which has a bolt-on neck), with 24 frets (two octaves) – As with the Artist models of the late 1970s, some of these guitars were equipped with trisound switches, and some models (MC 400 and MC 500) were equipped with active electronics.
 * ST – Studio series 1977–82 offset double cutaway ranging from bolt on to fixed and through necks with pairs of V2 distortion humbuckers. 24 frets and 25.5" scale.
 * CN – Concert range 1977–79 like a bolt on neck Artist with slightly offset cutaways.
 * SB70 – Studio & Blazer spot build: Mixing Studio series double cutaway, ash bodies with Blazer series 21 fret bolt on maple necks, and sporting a fixed brass bridge, 2 Super 70 Humbuckers, 1 vol, 2 tone knobs, a pickup selector switch, and a phase mini-toggle switch (which gives a unique strat-like quack sound), an estimated 300-400 of these were assembled, mostly in 1982. A cult following has emerged, as these guitars are rare, and sell for 3x-4x their original price. Learn more at The Unofficial SB70 Registry: https://www.ibanezcollectors.com/forum/index.php?topic=20623.0
 * BL – Blazer series 1980–82 – fixed bridge strat-like with maple necks and mahogany or ash bodies sporting 3 single coil pickups (Super 6 or BL) or 2 Super 70 humbuckers.
 * ARC-100/300 (Retro Series)
 * ARX-100/300 (Retro Series)
 * AR-100/200 (black vintage top)
 * V Series – Flying V's – discontinued
 * Ibanez Artcore Series – Ibanez's full and semi-hollow guitar line, with some models discontinued since their debut in 2002.
 * Ibanez Jet King 2 and Jet King 1 – A modern remake of the Ibanez Rhythm maker, vintage looking and sounding guitars.
 * Radius series – discontinued, a modified version is now taken over by the Joe Satriani signature series which features a multi-radius neck.
 * EX Series – Manufactured in Korea and Japan (rare).
 * PL – Pro Line series
 * RR – Rocket Roll
 * DT – Destroyer
 * IC – Iceman - a radical shape endorsed and used by Paul Stanley, Various pickup combinations.
 * Talman Series – discontinued
 * CN Concert Series – This was a short lived series produced in 1978 then discontinued soon afterwards. It features an asymmetric double cutaway body with two humbuckers, a hard tail bridge and a bolt on neck. The top end model (the CN250) was one of the earliest guitars to feature "half vine" fingerboard inlays.
 * Power II series (540PII) - extended length lower cutaway, wide (1 3/4")nut, available in H-H or H-S with edge trem. Often erroneously assumed to be an Alex Skolnick signature model due to his picture in the 88-89 catalogue with a 540PII. Primarily released for the Japanese market, although it has the Bensalem Penn. neck plate.
 * AFD – Artfield
 * GR – Ghostrider series, arched-top double cutaway design. 24$3⁄4$" scale length. Most notably played by Shawn Lane.
 * Cimar by Ibanez

 * ICJ100WZ – Jay Yuenger Signature
 * K7 – Korn Signature
 * Stanley Jordan Signature
 * AH10 – Allan Holdsworth Signature
 * LR10 – Lee Ritenour Signature
 * JP20 – Joe Pass Signature
 * MFM – Marty Friedman Signature
 * MTM – Mick Thomson Signature
 * VM1 – Vinnie Moore Signature
 * FGM – Frank Gambale Signature
 * JPM – John Petrucci Signature
 * RBM2NT – Reb Beach Signature
 * DMM1 – Daron Malakian Signature
 * MMM – Mike Mushok Signature
 * RS1010SL – Steve Lukather Signature
 * STM1 – Sam Totman Signature
 * NDM1 and NDM2 – Noodles Signature

Bass guitar models

 * SR (Soundgear) Series
 * Middle-class model range in the new millennium, though it included expensive high-end and top-of-the-line Japanese models in the late 1980s and 1990s. Later top offerings were branded as Signature and SR Prestige models for clearer segmentation, and all non-Prestige model production moved outside Japan. Current models from the SR250 and up feature soap bar-style humbuckers with active EQ.
 * SR Prestige
 * High-end versions of the Ibanez Soundgear (SR-5004/5/6 & SR-4004/5/6) Bass Guitars made in Japan using exotic woods and high-quality custom Bartolini pickups & new "PWC-III" Power Curve III 3-band EQ with EQ bypass switch to bypass the electronics and take the bass signal directly from the pickups to the output jack. All Japanese-built current production models are in the Prestige series.
 * SR Premium
 * Nordstrand pickups. Indonesian-built.

 * AFFIRMA series - solidbody basses designed by Rolf Spuler and made in Japan
 * AFR - set neck, one magnetic pickup, and a piezo bridge
 * Original series was launched in the early 1990s, a reissue series was released 2020
 * ARTCORE Series- Archtop Basses
 * ARTIST (Model 2626B - Carved-top solid-body set-neck bass, twin humbuckers, made late Seventies.)
 * AFB200 – Hollow-body bass guitar
 * AGB200 – Semihollow-body bass guitar
 * ATK Series
 * ATK 300 4 string model
 * ATK 305 5 string model
 * ATK 1200, the Prestige version of the standard ATK, has extra neck pickup
 * ATK 800E, to be released in 2012, a Premium version of the standard ATK. Has extra neck pickup
 * ATK 805E, to be released in 2012, a Premium version of the standard ATK. Has extra neck pickup, 5-string model
 * Blazer
 * BTB (Boutique Bass) Series
 * BTB 400QM (discontinued)
 * BTB 406QM (Special Edition 6 String Model)
 * BTB Prestige – High-end range which are made in Japan.
 * BTB Iron Label Standard
 * BTB Iron Label Multiscale
 * Ergodyne Series - Bodies made from Luthite polymer.
 * EDA Series
 * EDB Series
 * EDC Series
 * EWB Series
 * GARTB 20
 * GATK 20 – More affordable version of the ATK.
 * GAXB Series (discontinued)
 * GSR Series- A lower-cost version of the Soundgear Series
 * GSR 100 – The original GSR bass guitar (Discontinued)
 * GSR 100 EX
 * GSR 105 EX
 * GSR 180
 * GSRM 20
 * GSR 250 M
 * GSR 200
 * GSR 200 FM – The GSR but with different color designs such as sunburst.
 * GSR 205 – Nominated for Ibanez's "Best of Model" award
 * GSR 205 FM
 * ICB (Iceman) Series
 * JTK (Jet King) Series
 * JUMPSTART Series- Similar to the GSR Series, named for the Jumpstart Pack which comes with amp and other accessories.
 * Musician Series
 * ROADGEAR Series
 * SRX (Soundgear) Series
 * EX series
 * Roadstar Series
 * S series
 * STUDIO series - Late Seventies bolt-on neck alternative to the Musician series. Included an 8-string bass.
 * TR Series

Signature basses

 * K5 Fieldy
 * A custom 5-string Soundgear design w/ "K5" Inlay centered on 12th fret. It was based around a late-1990s then-top-of-the-line Soundgear SR885 owned by the artist, retaining the shape and electronics, but with different colour options and a change of woods to suit his preferences. Early models were Japanese-built, but production later moved to other Asian countries, around the same time Japanese models were rebranded with the Prestige moniker and positioned as the absolute top of the line.

 * SDB – Sharlee D'Angelo Signature bass
 * PRB – Paul Romanko Signature bass
 * GWB – Gary Willis Signature bass
 * MDB – Mike D'Antonio Signature bass
 * DTB – Dionald Tubang Signature bass
 * GVB - Gerald Veasley Signature bass
 * VWB1 – Verdine White Signature bass (discontinued)
 * PGB - Paul Gray Signature and Tribute bass (discontinued)
 * DWB - Doug Wimbish Series

Acoustic guitar models

 * AE Series
 * AE5LG
 * AEL Series
 * AES Series
 * DT Series
 * EP9 Series
 * EW Series
 * GA Series
 * JAMPACK Series
 * MANDOLIN Series
 * MANN Series (Canadian distribution only)
 * MASA Series
 * PF Series
 * PC series
 * TALMAN Series
 * V Series
 * Concord
 * SAGE Series
 * A300AVV acoustic/electric single cutaway (Ambiance series)

Guitar amplifiers

 * IBZ
 * IBZ15GR
 * IBZ10G
 * TBX Tone Blaster Series
 * TSA
 * TSA15/TSA15H
 * TSA30/TSA30H

Bass amplifiers

 * Promethean
 * IBZ
 * Sound Wave

Acoustic amplifiers

 * Troubadour

Effect pedals
In the 1970s, the Nisshin Onpa company who owned the Maxon brand name, developed and began selling a series of effect pedals in Japan. Hoshino Gakki licensed these for sale using the name Ibanez outside Japan. These two companies eventually began doing less and less business together until Nisshin Onpa ceased manufacturing the TS-9 reissue for Hoshino Gakki in 2002.

 * ToneLok Series
 * AP7 Analog Phaser
 * AW7 Autowah
 * CF7 Stereo Chorus/Flanger
 * DE7 Stereo Delay/Echo
 * DS7 Distortion
 * FZ7 Fuzz
 * LF7 Lo-Fi
 * PD7 Phat Hed Bass Overdrive
 * SB7 Synthesizer Bass
 * SH7 Seventh Heaven
 * SM7 Smashbox
 * TC7 Tri Mode Chorus
 * TS7 Tube Screamer
 * WD7 Weeping Demon
 * WD7JR Weeping Demon Junior
 * 8 Series
 * AD-80 Analog Delay 1979-1981
 * TS808 Tube Screamer 1979 - 1981
 * 9 series
 * AD9 Analog Delay
 * AF9 Auto Filter
 * BB9 Bottom Booster
 * BC9 Bi-Mode Chorus
 * CP9 Compressor/Limiter
 * CS9 Stereo Chorus
 * FL9 Flanger
 * GE9 Graphic EQ
 * JD9 Jet Driver
 * OD9 Overdrive
 * PQ9 Parametric EQ
 * PT9 Phaser
 * SD9 Sonic Distortion
 * SM9 Super Metal
 * ST9 Super Tube Screamer
 * TS9 Tube Screamer
 * TS9B Bass Tube Screamer
 * TS9DX Turbo Tube Screamer
 * TS930TH 30th Anniversary Tube Screamer
 * Wah Pedals
 * WD7
 * WH10V3

title: Ibanez