A set of lines and a blood or plasma filter, comprising: - an arterial line having a connector connected to a first compartment of the filter, - a pre-infusion channel for a local anticoagulation substance attached to the arterial line, - a venous blood line for extracorporeal blood or plasma treatment comprising: ∘ a first line portion having an inlet connected to an outlet of the filter, ∘ a second line portion having an outlet intended to be connected to a patient's vascular access, 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. - an arterial line having a connector connected to a first compartment of the filter, - a pre-infusion channel for a local anticoagulation substance attached to the arterial line, - a venous blood line for extracorporeal blood or plasma treatment comprising: ∘ a first line portion having an inlet connected to an outlet of the filter, ∘ a second line portion having an outlet intended to be connected to a patient's vascular access, 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. ∘ a first line portion having an inlet connected to an outlet of the filter, ∘ a second line portion having an outlet intended to be connected to a patient's vascular access, ∘ 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.