A set of lines intended to be attached to a blood or plasma filter, comprising: - an arterial line having a connector intended to be connected to the first compartment of a filter, - a pre-infusion channel for a local anticoagulation substance attached to the arterial line, - a container of local anticoagulation substance connected to the pre-infusion channel, - a venous blood line for extracorporeal blood or plasma treatment comprising: ∘ a first line portion intended to be connected to an outlet of the filter, ∘ a second line portion intended to be connected to a patient's vascular access, - a bubble trap; and - a container of solution re-establishing ion balance, characterized in that the venous blood line further comprises: ∘ an infusion site acting between the first line portion and the second line portion, and intended to inject into the blood line the solution reestablishing blood or plasma ion balance, comprising: ▪ a first main channel in fluid communication with the first line portion and having a first passage section, ▪ a second main channel in fluid communication with the second line portion and having a second passage section, ▪ means for the formation of a turbulence area located downstream from and in fluid communication with the first main channel, located upstream from and in fluid communication with the second main channel, these formation means comprising a first fluid passage means defining a reduction in the passage section and whose smallest passage section is smaller than the first passage section and smaller than the second fluid passage section, ▪ a secondary channel comprising an inlet for letting in a solution reestablishing ion balance and an outlet in fluid communication with at least one of the three elements chosen among the first main channel, the means for the formation of a turbulence area and the second main channel, wherein an inlet of the first line portion is intended to be connected to the outlet of the filter and an outlet of the second line portion is intended to be connected to a patient's vascular access, the bubble trap acting on the first line portion of the line upstream or downstream from the infusion site; the container of solution reestablishing ion balance being connected to the secondary channel of the infusion site. - an arterial line having a connector intended to be connected to the first compartment of a filter, - a pre-infusion channel for a local anticoagulation substance attached to the arterial line, - a container of local anticoagulation substance connected to the pre-infusion channel, - a venous blood line for extracorporeal blood or plasma treatment comprising: ∘ a first line portion intended to be connected to an outlet of the filter, ∘ a second line portion intended to be connected to a patient's vascular access, ∘ a first line portion intended to be connected to an outlet of the filter, ∘ a second line portion intended to be connected to a patient's vascular access, - a bubble trap; and - a container of solution re-establishing ion balance, ∘ an infusion site acting between the first line portion and the second line portion, and intended to inject into the blood line the solution reestablishing blood or plasma ion balance, comprising: ▪ a first main channel in fluid communication with the first line portion and having a first passage section, ▪ a second main channel in fluid communication with the second line portion and having a second passage section, ▪ means for the formation of a turbulence area located downstream from and in fluid communication with the first main channel, located upstream from and in fluid communication with the second main channel, these formation means comprising a first fluid passage means defining a reduction in the passage section and whose smallest passage section is smaller than the first passage section and smaller than the second fluid passage section, ▪ a secondary channel comprising an inlet for letting in a solution reestablishing ion balance and an outlet in fluid communication with at least one of the three elements chosen among the first main channel, the means for the formation of a turbulence area and the second main channel, ▪ a first main channel in fluid communication with the first line portion and having a first passage section, ▪ a second main channel in fluid communication with the second line portion and having a second passage section, ▪ means for the formation of a turbulence area located downstream from and in fluid communication with the first main channel, located upstream from and in fluid communication with the second main channel, these formation means comprising a first fluid passage means defining a reduction in the passage section and whose smallest passage section is smaller than the first passage section and smaller than the second fluid passage section, ▪ a secondary channel comprising an inlet for letting in a solution reestablishing ion balance and an outlet in fluid communication with at least one of the three elements chosen among the first main channel, the means for the formation of a turbulence area and the second main channel,