## Artificial insemination

• Artificial insemination
Intervention
Schematic illustration of artificial insemination
ICD-9-CM 69.92
MeSH D007315
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Artificial insemination (AI) is the deliberate introduction of sperm into a female's uterus or cervix for the purpose of achieving a pregnancy through in vivo fertilization by means other than sexual intercourse. It is a fertility treatment for humans, and is a common practice in animal breeding, including dairy cattle (see Frozen bovine semen) and pigs.

Artificial insemination may employ assisted reproductive technology, sperm donation and animal husbandry techniques. Artificial insemination techniques available include intracervical insemination and intrauterine insemination. The primary beneficiaries of artificial insemination are women who desire to give birth to their own child. They may be in a heterosexual relationship but with the male partner suffering from male infertility, in a lesbian relationship or are single women. Intracervical insemination (ICI) is the easiest and most common insemination technique and can be used in the home for self-insemination without medical practitioner assistance. Compared to natural insemination (i.e., insemination by sexual intercourse), artificial insemination can be more expensive and more invasive, and may require professional assistance.

There are laws in some countries which restrict and regulate who can donate sperm and who is able to receive artificial insemination, and the consequences of such insemination. Some women who live in a jurisdiction which does not permit artificial insemination in the circumstance in which she finds herself may travel to another jurisdiction which permits it. (See Sperm donation laws by country and fertility tourism.)

${\displaystyle N={\frac {V_{s}\times c\times r_{s}}{n_{r}}}}$
${\displaystyle N={\frac {n_{s}}{n_{c}}}\times r_{s}}$
N is how many children a single sample can give rise to
ns is the number of vials produced per sample
nc is the number of vials used in a cycle
rs is the pregnancy rate per cycle
${\displaystyle n_{s}={\frac {V_{s}}{V_{v}}}}$
ns is the number of vials produced per sample
Vs is the volume of a sample
Vv is the volume of the vials used
${\displaystyle n_{c}={\frac {n_{r}}{n_{s}}}}$
nc is the number of vials used in a cycle
nr is the number of motile sperm recommended for use in a cycle
ns is the number of motile sperm in a vial
${\displaystyle n_{s}=V_{v}\times c}$
ns is the number of motile sperm in a vial
Vv is the volume of the vials used
c is the concentration of motile sperm in a sample
${\displaystyle N={\frac {V_{s}\times c\times r_{s}}{n_{r}}}\times {\frac {V_{v}}{V_{v}}}}$
N is how many children a single sample can help giving rise to
Vs is the volume of a sample
c is the concentration of motile sperm in a sample
rs is the pregnancy rate per cycle
nr is the number of motile sperm recommended for use in a cycles
Vv is the volume of the vials used (its value doesn't affect N and may be eliminated. In short, the smaller the vials, the more vials are used)
fc is the fraction of the volume that remains after centrifugation of the sample, which may be about half (0.5) to a third (0.33).
${\displaystyle N={\frac {V_{s}\times f_{c}\times c\times r_{s}}{n_{r}}}}$
• N is how many children a single sample can give rise to.
• Vs is the volume of a sample (ejaculate), usually between 1.0 mL and 6.5 mL
• c is the concentration of motile sperm in a sample after freezing and thawing, approximately 5–20 million per ml but varies substantially
• rs is the pregnancy rate per cycle, between 10% to 35%
• nr is the total motile sperm count recommended for vaginal insemination (VI) or intra-cervical insemination (ICI), approximately 20 million pr. ml.
• Hammond, John, et al., The Artificial Insemination of Cattle (Cambridge, Heffer, 1947, 61pp)
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