A solenoid is a type of electromagnet formed by a helical coil of wire whose length is substantially greater than its diameter, which generates a controlled magnetic field. The coil can produce a uniform magnetic field in a volume of space when an electric current is passed through it.
André-Marie Ampère coined the term solenoid in 1823, having conceived of the device in 1820.
The helical coil of a solenoid does not necessarily need to revolve around a straight-line axis; for example, William Sturgeon's electromagnet of 1824 consisted of a solenoid bent into a horseshoe shape (similarly to an arc spring).
Solenoids provide magnetic focusing of electrons in vacuums,
notably in television camera tubes such as vidicons and image orthicons.
Electrons take helical paths within the magnetic field. These
solenoids, focus coils, surround nearly the whole length of the tube.
Physics
Infinite continuous solenoid
An infinite solenoid has infinite length but finite diameter.
"Continuous" means that the solenoid is not formed by discrete
finite-width coils but by many infinitely thin coils with no space
between them; in this abstraction, the solenoid is often viewed as a
cylindrical sheet of conductive material.
The magnetic field
inside an infinitely long solenoid is homogeneous and its strength
neither depends on the distance from the axis nor on the solenoid's
cross-sectional area.
This is a derivation of the magnetic flux density
around a solenoid that is long enough so that fringe effects can be
ignored. In Figure 1, we immediately know that the flux density vector
points in the positive z direction inside the solenoid, and in the negative z direction outside the solenoid. We confirm this by applying the right hand grip rule
for the field around a wire. If we wrap our right hand around a wire
with the thumb pointing in the direction of the current, the curl of the
fingers shows how the field behaves. Since we are dealing with a long
solenoid, all of the components of the magnetic field not pointing
upwards cancel out by symmetry. Outside, a similar cancellation occurs,
and the field is only pointing downwards.
Now consider the imaginary loop c that is located inside the solenoid. By Ampère's law, we know that the line integral of B
(the magnetic flux density vector) around this loop is zero, since it
encloses no electrical currents (it can be also assumed that the
circuital electric field
passing through the loop is constant under such conditions: a constant
or constantly changing current through the solenoid). We have shown
above that the field is pointing upwards inside the solenoid, so the
horizontal portions of loop c do not contribute anything to the
integral. Thus the integral of the up side 1 is equal to the integral of
the down side 2. Since we can arbitrarily change the dimensions of the
loop and get the same result, the only physical explanation is that the
integrands are actually equal, that is, the magnetic field inside the
solenoid is radially uniform. Note, though, that nothing prohibits it
from varying longitudinally, which in fact, it does.
A similar argument can be applied to the loop a to
conclude that the field outside the solenoid is radially uniform or
constant. This last result, which holds strictly true only near the
center of the solenoid where the field lines are parallel to its length,
is important as it shows that the flux density outside is practically
zero since the radii of the field outside the solenoid will tend to
infinity. An intuitive argument can also be used to show that the flux
density outside the solenoid is actually zero. Magnetic field lines only
exist as loops, they cannot diverge from or converge to a point like
electric field lines can (see Gauss's law for magnetism).
The magnetic field lines follow the longitudinal path of the solenoid
inside, so they must go in the opposite direction outside of the
solenoid so that the lines can form loops. However, the volume outside
the solenoid is much greater than the volume inside, so the density of
magnetic field lines outside is greatly reduced. Now recall that the
field outside is constant. In order for the total number of field lines
to be conserved, the field outside must go to zero as the solenoid gets
longer. Of course, if the solenoid is constructed as a wire spiral (as
often done in practice), then it emanates an outside field the same way
as a single wire, due to the current flowing overall down the length of
the solenoid.
This equation is valid for a solenoid in free space, which means the permeability of the magnetic path is the same as permeability of free space, μ0.
If the solenoid is immersed in a material with relative permeability μr, then the field is increased by that amount:
In most solenoids, the solenoid is not immersed in a higher
permeability material, but rather some portion of the space around the
solenoid has the higher permeability material and some is just air
(which behaves much like free space). In that scenario, the full effect
of the high permeability material is not seen, but there will be an
effective (or apparent) permeability μeff such that 1 ≤ μeff ≤ μr.
The inclusion of a ferromagnetic core, such as iron,
increases the magnitude of the magnetic flux density in the solenoid
and raises the effective permeability of the magnetic path. This is
expressed by the formula
where μeff is the effective or apparent
permeability of the core. The effective permeability is a function of
the geometric properties of the core and its relative permeability. The
terms relative permeability (a property of just the material) and
effective permeability (a property of the whole structure) are often
confused; they can differ by many orders of magnitude.
For an open magnetic structure, the relationship between the
effective permeability and relative permeability is given as follows:
where k is the demagnetization factor of the core.
Finite continuous solenoid
A finite solenoid is a solenoid with finite length. Continuous means
that the solenoid is not formed by discrete coils but by a sheet of
conductive material. We assume the current is uniformly distributed on
the surface of the solenoid, with a surface current densityK; in cylindrical coordinates:
The magnetic field can be found using the vector potential, which for a finite solenoid with radius R and length l in cylindrical coordinates is
Where:
,
,
,
,
,
.
Here, , , and are complete elliptic integrals of the first, second, and third kind.
Using:
The magnetic flux density is obtained as
On the symmetry axis, the radial component vanishes, and the axial field component is
Inside the solenoid, far away from the ends (), this tends towards the constant value .
Short solenoid estimate
For the case in which the radius is much larger than the length of the solenoid (), the magnetic flux density through the centre of the solenoid (in the z direction, parallel to the solenoid's length, where the coil is centered at z=0) can be estimated as the flux density of a single circular conductor loop:
Irregular solenoids
Within the category of finite solenoids, there are those that are
sparsely wound with a single pitch, sparsely wound with varying pitches
(varied-pitch solenoid), or those with a varying radius for different
loops (non-cylindrical solenoids). They are called irregular solenoids.
They have found applications in different areas, such as sparsely wound
solenoids for wireless power transfer, varied-pitch solenoids for magnetic resonance imaging (MRI), and non-cylindrical solenoids for other medical devices.
The calculation of the intrinsic inductance and capacitance
cannot be done using those for the traditional solenoids, i.e. the
tightly wound ones. New calculation methods were proposed for the
calculation of intrinsic inductance and capacitance.
As shown above, the magnetic flux density within the coil is practically constant and given by
where μ0 is the magnetic constant, the number of turns, the current and the length of the coil. Ignoring end effects, the total magnetic flux through the coil is obtained by multiplying the flux density by the cross-section area :
A table of inductance for short solenoids of various diameter to
length ratios has been calculated by Dellinger, Whittmore, and Ould.
This, and the inductance of more complicated shapes, can be derived from Maxwell's equations. For rigid air-core coils, inductance is a function of coil geometry and number of turns, and is independent of current.
Similar analysis applies to a solenoid with a magnetic core, but
only if the length of the coil is much greater than the product of the
relative permeability
of the magnetic core and the diameter. That limits the simple analysis
to low-permeability cores, or extremely long thin solenoids. The
presence of a core can be taken into account in the above equations by
replacing the magnetic constant μ0 with μ or μ0μr, where μ represents permeability and μrrelative permeability. Note that since the permeability of ferromagnetic
materials changes with applied magnetic flux, the inductance of a coil
with a ferromagnetic core will generally vary with current.
Kidney dialysis (from Greekδιάλυσις, dialysis, 'dissolution'; from διά, dia, 'through', and λύσις, lysis, 'loosening or splitting') is the process of removing excess water, solutes, and toxins from the blood in people whose kidneys can no longer perform these functions naturally. This is referred to as renal replacement therapy. The first successful dialysis was performed in 1943.
Dialysis may need to be initiated when there is a sudden rapid loss of kidney function, known as acute kidney injury (previously called acute renal failure), or when a gradual decline in kidney function, chronic kidney failure, reaches stage 5. Stage 5 chronic renal failure is reached when the glomerular filtration rate is 10–15% of the normal, creatinine clearance is less than 10 mL per minute, and uremia is present.
Dialysis is used as a temporary measure in either acute kidney injury or in those awaiting kidney transplant and as a permanent measure in those for whom a transplant is not indicated or not possible.
In West European countries, Australia, Canada, the United
Kingdom, and the United States, dialysis is paid for by the government
for those who are eligible.
Background
The kidneys
have an important role in maintaining health. When the person is
healthy, the kidneys maintain the body's internal equilibrium of water
and minerals (sodium, potassium, chloride, calcium, phosphorus,
magnesium, sulphate). The acidic metabolism
end-products that the body cannot get rid of via respiration are also
excreted through the kidneys. The kidneys also function as a part of the
endocrine system, producing erythropoietin, calcitriol and renin. Erythropoietin is involved in the production of red blood cells and calcitriol plays a role in bone formation.
Dialysis is an imperfect treatment to replace kidney function because
it does not correct the compromised endocrine functions of the kidney.
Dialysis treatments replace some of these functions through diffusion (waste removal) and ultrafiltration (fluid removal). Dialysis uses highly purified (also known as "ultrapure") water.
Principle
Dialysis works on the principles of the diffusion of solutes and ultrafiltration of fluid across a semi-permeable membrane.
Diffusion is a property of substances in water; substances in water
tend to move from an area of high concentration to an area of low
concentration.
Blood flows by one side of a semi-permeable membrane, and a dialysate,
or special dialysis fluid, flows by the opposite side. A semipermeable
membrane is a thin layer of material that contains holes of various
sizes, or pores. Smaller solutes and fluid pass through the membrane,
but the membrane blocks the passage of larger substances (for example,
red blood cells and large proteins). This replicates the filtering
process that takes place in the kidneys when the blood enters the
kidneys and the larger substances are separated from the smaller ones in
the glomerulus.
The two main types of dialysis, hemodialysis and peritoneal dialysis, remove wastes and excess water from the blood in different ways. Hemodialysis removes wastes and water by circulating blood outside the body through an external filter, called a dialyzer, that contains a semipermeable membrane. The blood flows in one direction and the dialysate flows in the opposite. The counter-current flow of the blood and dialysate maximizes the concentration gradient of solutes between the blood and dialysate, which helps to remove more urea and creatinine from the blood. The concentrations of solutes normally found in the urine (for example potassium, phosphorus
and urea) are undesirably high in the blood, but low or absent in the
dialysis solution, and constant replacement of the dialysate ensures
that the concentration of undesired solutes is kept low on this side of
the membrane. The dialysis solution has levels of minerals like potassium and calcium that are similar to their natural concentration in healthy blood. For another solute, bicarbonate, dialysis solution level is set at a slightly higher level than in normal blood, to encourage the diffusion of bicarbonate into the blood, to act as a pH buffer to neutralize the metabolic acidosis that is often present in these patients. The levels of the components of dialysate are typically prescribed by a nephrologist according to the needs of the individual patient.
In peritoneal dialysis, wastes and water are removed from the blood inside the body using the peritoneum
as a natural semipermeable membrane. Wastes and excess water move from
the blood, across the peritoneal membrane and into a special dialysis
solution, called dialysate, in the abdominal cavity.
In hemodialysis, the patient's blood is pumped through the blood compartment of a dialyzer, exposing it to a partially permeable membrane. The dialyzer is composed of thousands of tiny hollow synthetic fibers.
The fiber wall acts as the semipermeable membrane. Blood flows through
the fibers, dialysis solution flows around the outside of the fibers,
and water and wastes move between these two solutions.
The cleansed blood is then returned via the circuit back to the body.
Ultrafiltration occurs by increasing the hydrostatic pressure across the
dialyzer membrane. This usually is done by applying a negative
pressure to the dialysate compartment of the dialyzer. This pressure
gradient causes water and dissolved solutes to move from blood to
dialysate and allows the removal of several litres of excess fluid
during a typical 4-hour treatment.
In the United States, hemodialysis treatments are typically given in a
dialysis center three times per week (due in the United States to Medicare
reimbursement rules); however, as of 2005 over 2,500 people in the
United States are dialyzing at home more frequently for various
treatment lengths.
Studies have demonstrated the clinical benefits of dialyzing 5 to 7
times a week, for 6 to 8 hours. This type of hemodialysis is usually
called nocturnal daily hemodialysis and a study has shown it provides a significant improvement in both small and large molecular weight clearance and decreases the need for phosphate binders.
These frequent long treatments are often done at home while sleeping,
but home dialysis is a flexible modality and schedules can be changed
day to day, week to week. In general, studies show that both increased
treatment length and frequency are clinically beneficial.
Hemo-dialysis was one of the most common procedures performed in
U.S. hospitals in 2011, occurring in 909,000 stays (a rate of 29 stays
per 10,000 population).
In peritoneal dialysis, a sterile solution containing glucose (called dialysate) is run through a tube into the peritoneal cavity, the abdominal body cavity around the intestine, where the peritoneal membrane acts as a partially permeable membrane.
This exchange is repeated 4–5 times per day; automatic systems
can run more frequent exchange cycles overnight. Peritoneal dialysis is
less efficient than hemodialysis, but because it is carried out for a
longer period of time the net effect in terms of removal of waste
products and of salt and water are similar to hemodialysis. Peritoneal
dialysis is carried out at home by the patient, often without help. This
frees patients from the routine of having to go to a dialysis clinic on
a fixed schedule multiple times per week. Peritoneal dialysis can be
performed with little to no specialized equipment (other than bags of
fresh dialysate).
Hemofiltration is a similar treatment to hemodialysis, but it makes
use of a different principle. The blood is pumped through a dialyzer or
"hemofilter" as in dialysis, but no dialysate is used. A pressure
gradient is applied; as a result, water moves across the very permeable
membrane rapidly, "dragging" along with it many dissolved substances,
including ones with large molecular weights, which are not cleared as
well by hemodialysis. Salts and water lost from the blood during this
process are replaced with a "substitution fluid" that is infused into
the extracorporeal circuit during the treatment.
Hemodiafiltration
Hemodiafiltration
is a combination between hemodialysis and hemofiltration, thus used to
purify the blood from toxins when the kidney is not working normally and
also used to treat acute kidney injury (AKI).
Intestinal dialysis
In intestinal dialysis, the diet is supplemented with soluble fibres such as acacia fibre,
which is digested by bacteria in the colon. This baterial growth
increases the amount of nitrogen that is eliminated in fecal waste. An alternative approach utilizes the ingestion of 1 to 1.5 liters of non-absorbable solutions of polyethylene glycol or mannitol every fourth hour.
Indications
The decision to initiate dialysis or hemofiltration in patients with kidney failure depends on several factors. These can be divided into acute or chronic indications.
Depression and kidney failure symptoms can be similar to each
other. It's important that there's open communication between a dialysis
team and the patient. Open communication will allow giving a better
quality of life. Knowing the patients' needs will allow the dialysis
team to provide more options like: changes in dialysis type like home
dialysis for patients to be able to be more active or changes in eating
habits to avoid unnecessary waste products.
Acute indications
Indications for dialysis in a patient with acute kidney injury are summarized with the vowel mnemonic of "AEIOU":
Chronic dialysis may be indicated when a patient has symptomatic kidney failure and low glomerular filtration rate (GFR < 15 mL/min).
Between 1996 and 2008, there was a trend to initiate dialysis at
progressively higher estimated GFR, eGFR.
A review of the evidence shows no benefit or potential harm with early
dialysis initiation, which has been defined by start of dialysis at an
estimated GFR of greater than 10 ml/min/1.732. Observational data from large registries of dialysis patients suggests that early start of dialysis may be harmful.
The most recent published guidelines from Canada, for when to initiate
dialysis, recommend an intent to defer dialysis until a patient has
definite kidney failure symptoms, which may occur at an estimated GFR of
5–9 ml/min/1.732.
Dialyzable substances
Characteristics
Dialyzable substances—substances removable with dialysis—have these properties:
Given
dialysis patients have little or no capacity to filtrate solutes and
regulate their fluid volume due to kidney dysfunction, missing dialysis is potentially lethal. These patients can be hyperkalaemic leading to cardiac dysrhythmias and potential cardiac arrest, as well as fluid in the alveoli of their lungs which can impair breathing.
Some medications can be used in the short term to decrease serum
potassium and stabilise the cardiac muscle so as to facilitate
stabilisation of acute patients in the setting of missed dialysis. Salbutamol and Insulin
can decrease serum potassium by up to 1.0mmol/L each by shifting
potassium from the extracellular space into the intracellular spaces
within skeletal muscle cells, and calcium gluconate
is used to stabilise the myocardium in hyperkalaemic patients, in an
attempt to reduce the likelihood of lethal arrhythmias arising from a
high serum potassium.
Given that dialysis patients have little to no kidney function, Furosemide is generally ineffective in combating pulmonary oedema due to missed dialysis. Instead, patients are often placed on CPAP, BIPAP, or high-flow oxygen to support breathing until they can be dialysed.
Pediatric dialysis
Over the past 20 years, children have benefited from major improvements in both technology and clinical management of dialysis. Morbidity
during dialysis sessions has decreased with seizures being exceptional
and hypotensive episodes rare. Pain and discomfort have been reduced
with the use of chronic internal jugular venous catheters and anesthetic
creams for fistula puncture. Non-invasive technologies to assess
patient target dry weight and access flow can significantly reduce
patient morbidity and health care costs. Mortality in paediatric and young adult patients on chronic hemodialysis is associated with multifactorial markers of nutrition, inflammation, anaemia
and dialysis dose, which highlights the importance of multimodal
intervention strategies besides adequate hemodialysis treatment as
determined by Kt/V alone.
Biocompatible synthetic membranes,
specific small size material dialyzers and new low extra-corporeal
volume tubing have been developed for young infants. Arterial and venous
tubing length is made of minimum length and diameter, a <80 ml to
<110 ml volume tubing is designed for pediatric patients and a
>130 to <224 ml tubing are for adult patients, regardless of blood
pump segment size, which can be of 6.4 mm for normal dialysis or 8.0mm
for high flux dialysis in all patients. All dialysis machine
manufacturers design their machine to do the pediatric dialysis. In
pediatric patients, the pump speed should be kept at low side, according
to patient blood output capacity, and the clotting with heparin dose
should be carefully monitored. The high flux dialysis (see below) is not
recommended for pediatric patients.
In children, hemodialysis
must be individualized and viewed as an "integrated therapy" that
considers their long-term exposure to chronic renal failure treatment.
Dialysis is seen only as a temporary measure for children compared with
renal transplantation because this enables the best chance of
rehabilitation in terms of educational and psychosocial functioning.
Long-term chronic dialysis, however, the highest standards should be
applied to these children to preserve their future "cardiovascular
life"—which might include more dialysis time and on-line
hemodiafiltration online hdf with synthetic high flux membranes with the
surface area of 0.2 m2 to 0.8 m2 and blood tubing
lines with the low volume yet large blood pump segment of 6.4/8.0 mm,
if we are able to improve on the rather restricted concept of
small-solute urea dialysis clearance.
Dialysis in different countries
In the United Kingdom
The National Health Service provides dialysis in the United Kingdom. In England, the service is commissioned by NHS England. About 23,000 patients use the service each year. Patient transport services are generally provided without charge, for patients who need to travel to dialysis centres. Cornwall Clinical Commissioning Group
proposed to restrict this provision to patients who did not have
specific medical or financial reasons in 2018 but changed their minds
after a campaign led by Kidney Care UK and decided to fund transport for
patients requiring dialysis three times a week for a minimum or six
times a month for a minimum of three months.
A UK study found that receiving dialysis at home is less costly than receiving dialysis in hospital.
However, many people in the UK prefer to receive dialysis in hospital
for various reasons such as providing regular social contact.
Encouraging people to have dialysis at home could lead to savings for
the NHS, as well as reducing the impact of dialysis on people's social
and professional lives.
In the United States
Since 1972, insurance companies in the United States have covered the cost of dialysis and transplants for all citizens.
By 2014, more than 460,000 Americans were undergoing treatment, the
costs of which amount to six percent of the entire Medicare budget.
Kidney disease is the ninth leading cause of death, and the U.S. has one
of the highest mortality rates for dialysis care in the industrialized
world. The rate of patients getting kidney transplants
has been lower than expected. These outcomes have been blamed on a new
for-profit dialysis industry responding to government payment policies.
A 1999 study concluded that "patients treated in for-profit dialysis
facilities have higher mortality rates and are less likely to be placed
on the waiting list for a renal transplant than are patients who are
treated in not-for-profit facilities", possibly because transplantation
removes a constant stream of revenue from the facility. The insurance industry has complained about kickbacks and problematic relationships between charities and providers.
In China
The Government of China
provides the funding for dialysis treatment. There is a challenge to
reach everyone who needs dialysis treatment because of the unequal
distribution of health care resources and dialysis centers. There are 395,121 individuals who receive hemodialysis or peritoneal dialysis in China per year. The percentage of the Chinese population with Chronic Kidney Disease is 10.8%.
The Chinese Government is trying to increase the amount of peritoneal
dialysis taking place to meet the needs of the nation's individuals with
Chronic Kidney Disease.
In Australia
Dialysis is provided without cost to all patients through Medicare, with 75% of all dialysis being administered as haemodialysis to patients three times per week in a dialysis facility. The Northern Territory has the highest incidence rate per population of haemodialysis, with Indigenous Australians having higher rates of Chronic Kidney Disease and lower rates of functional kidney transplants than the broader population. The remote Central Australian town of Alice Springs, despite having a population of approximately 25000, has the largest dialysis unit in the Southern Hemisphere.
Many people must move to Alice Springs from remote Indigenous
communities to access health services such as haemodialysis, which
results in housing shortages, overcrowding, and poor living conditions.
History
In 1913, Leonard Rowntree and John Abel of Johns Hopkins Hospital developed the first dialysis system which they successfully tested in animals. A Dutch doctor, Willem Johan Kolff, constructed the first working dialyzer in 1943 during the Nazi occupation of the Netherlands. Due to the scarcity of available resources, Kolff had to improvise and build the initial machine using sausage casings, beverage cans, a washing machine
and various other items that were available at the time. Over the
following two years (1944–1945), Kolff used his machine to treat 16
patients with acute kidney failure,
but the results were unsuccessful. Then, in 1945, a 67-year-old
comatose woman regained consciousness following 11 hours of hemodialysis
with the dialyzer and lived for another seven years before dying from
an unrelated condition. She was the first-ever patient successfully
treated with dialysis. Gordon Murray of the University of Toronto
independently developed a dialysis machine in 1945. Unlike Kolff's
rotating drum, Murray's machine used fixed flat plates, more like modern
designs. Like Kolff, Murray's initial success was in patients with acute renal failure. Nils Alwall of Lund University
in Sweden modified a similar construction to the Kolff dialysis machine
by enclosing it inside a stainless steel canister. This allowed the
removal of fluids, by applying a negative pressure to the outside
canister, thus making it the first truly practical device for
hemodialysis. Alwall treated his first patient in acute kidney failure
on 3 September 1946.