Magic Circuit

Pseudo-nerves within the body of a magus.
Magic circuits are responsible for converting life force into magical energy, and for connecting to the underlying grand magecraft formula.
Because the number of magic circuits a person has is fixed at birth, magi lineages do what they can to improve themselves and create an heir with even one more magic circuit.
Once the magic circuits have been opened for the first time, the practitioner can switch them on and off at will.
Each practitioner visualizes the flipping of this switch in their own particular way. For Shirou, the image is that of a gun's firing hammer, while for Rin it is stabbing a heart with a knife.
This image tends to be related to how the circuits were opened for the very first time, so there even those who
can only open their circuits through sexual arousal or self-harm.
By the way, Shirou's number of magic circuits is an unexpectedly high 27.
Rin, on the other hand, has 40 main circuits, while her sub-circuits are 30 each.

Fate/side material: Fate Encyclopedia
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The pseudo-nerves existing in the body of a magus.
They are the paths that convert life force into magical energy, as well as the paths which connect to the foundations underlying Grand Rituals.
The number of Magic Circuits is determined at birth. Mage lineages will resort to any means to alter themselves in hope of giving their descendants just one more Circuit.
This is why magi from older lineages are more powerful.
In terms of the number of Magic Circuits, and the quality of the lineage, Cornelius Alba is undoubtedly a first rate magus.
In fact, neither Aozaki Touko nor Araya Souren have many Magic Circuits. Touko has about 20, Araya about 30.
Still, the two are considered geniuses: Touko has talents that are independent of her lineage. Araya's overwhelming power is probably a result of the anguish that he ceaselessly accumulated through the ages.

Garden of sinners Pamphlet: Kara no Kyoukai Settings Glossary
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The foundation for setting up magecraft. There are two types, but here it refers to the quality within a human body that makes a magus a magus.
Magic circuits are responsible for converting life force into magical energy, and for connecting to the underlying grand magecraft formula.
Basically, magecraft is a formula that causes nature interference by starting up and stabilizing a “rule already established in the world” with magical energy. Or to put it another way, the “rule” is a car, and the “magical energy” is the gasoline that makes it run.
In order to activate magecraft, three things are required: the necessary amount of magical energy, a key (password/spell/code), and magic circuits to inject the magical energy into the “engine.”
If we assume for a moment that magical energy is electricity, then magic circuits would be both the reactor that produces that electricity, as well as the pipelines for running the system.
Because vital activity is indispensable to the operation of this reactor, there is a common misconception that a magus' body = magic circuits. However, though quite rare, magic circuits that continue rotating on their own even after the practitioner's vital activity has stopped do exist.
The reason that an individual's magical energy (od) will be regenerated even if is totally used up is because the magic circuits are still operating. But on the other hand, without magic circuits, magical energy (od) will no longer be generated at all.
They are spread throughout the entire body as pseudo-nerves, and can basically be divided into cores, and pipes that connect these cores together. The pipes are similar to the synapses within the brain, constantly breaking off and reconnecting, but the cores never change.
Strictly speaking, these cores are the actual magic circuits.
They are considered to be a sort of internal organ, that will never increase or decrease in number. Of course, extracting and transplanting them is technically possible, but just like implanting an extra organ into a human body it should go without saying what will happen if you try it. Magic circuits, once lost, will never return.
As for what magi actually use these magic circuits for, well, that's covered in a different story.

Tsukihime Dokuhon Plus Period: Tsukihime Dictionary Revised
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The foundation for setting up magecraft. There are two types, but here it refers to the quality within a human body that makes a magus a magus.
Magic circuits are responsible for converting life force into magical energy, and for connecting to the underlying grand magecraft formula.
In Melty Blood, the unified gauge for using both EX moves and Arc Drives is called the “Magic Circuit.”

MB Act Cadenza PS2 Manual: Tsukihime Dictionary