Patent Document ID: 9679111
Application ID: 14072506
Patent Flag: 1

Claim One:
1. A hemodialysis system comprising: a hemodialysis machine comprising a blood pump; a modular drug delivery device comprising at least one erythropoiesis stimulating agent (ESA) pump, at least one iron replacement product pump, at least one ESA vial holder, and at least one iron replacement product vial holder; and a housing to which the blood pump and the modular drug delivery device are secured; a blood line set comprising multiple blood lines and a drip chamber in fluid communication with the multiple blood lines, at least one of the blood lines being connected to the drip chamber, the blood line set being connected to the blood pump in a manner such that, when the blood line set is connected to a patient and the blood pump is operated, blood of the patient is passed through the blood line set; a drug administration fluid line set comprising multiple drug lines, at least two of the drug lines of the drug line set being connected to the drip chamber of the blood line set, and the drug line set being connected to the at least one ESA pump and the at least one iron replacement product pump in a manner such that, when the drug line set is fluidly connected to an ESA vial contained in the at least one ESA vial holder and to an iron replacement product vial contained in the at least one iron replacement product vial holder, and the at least one ESA pump and the at least one replacement product pump are operated, ESA and iron replacement product are delivered from the ESA vial and the iron replacement vial, respectively, to the drip chamber of the blood line set via the drug line set; and a control unit comprising a mathematical model of erythropoiesis and iron metabolism and instructions that, when executed, cause the control unit to adjust the patient's undesired hematocrit and/or hemoglobin concentration to a value within a desired range at a predetermined time by i) employing the model to predict the patient's hematocrit and/or hemoglobin concentration at a predetermined time, the model including iron homeostasis, and by ii) operating the blood pump, the at least one ESA pump, and the at least one iron replacement product pump to deliver blood, ESA, and iron replacement product to the drip chamber via the at least one of the blood lines connected to the drip chamber and the at least two of the drug lines connected to the drip chamber, according to an ESA administration regimen predicted to adjust the patient's hematocrit and/or hemoglobin concentration to a value within the desired range at the predetermined time, wherein the mathematical model of erythropoiesis and iron metabolism comprises the functions: ⁢ ∂ ∂ t ⁢ p ⁡ ( t , μ p ) + ∂ ∂ μ p ⁢ p ⁡ ( t , μ p ) = β p ⁢ p ⁡ ( t , μ p ) , ⁢ ⁢ ∂ ∂ t ⁢ q ⁡ ( t , μ q ) + ∂ ∂ μ q ⁢ q ⁡ ( t , μ q ) = ( β q - α q ⁡ ( E ⁡ ( t ) ) ) ⁢ q ⁡ ( t , μ q ) , ⁢ ⁢ ∂ ∂ t ⁢ r ⁡ ( t , μ r ) + ∂ ∂ μ r ⁢ r ⁡ ( t , μ r ) = β r ⁢ r ⁡ ( t , μ r ) , ⁢ ⁢ ∂ ∂ t ⁢ s ⁡ ( t , μ s ) + v s ⁡ ( E ⁡ ( t ) ) ⁢ ∂ ∂ μ s ⁢ s ⁡ ( t , μ s ) = - α s ⁢ s ⁡ ( t , μ s ) , ⁢ ⁢ ∂ ∂ t ⁢ m ⁡ ( t , μ m ) + ∂ ∂ μ m ⁢ m ⁡ ( t , μ m ) = - α m ⁡ ( E ⁡ ( t ) , μ m ) ⁢ m ⁡ ( t , μ m ) , ⁢ ⁢ ⅆ ⅆ t ⁢ E end ⁡ ( t ) = 1 TBV ⁢ E in end ⁡ ( t ) - c deg end ⁢ E end ⁡ ( t ) , ⁢ ⁢ ⅆ ⅆ t ⁢ E ex ⁡ ( t ) = 1 TBV ⁢ E in ex ⁡ ( t ) - c deg ex ⁢ E ex ⁡ ( t ) , ⁢ ⁢ where ⁢ α q ⁡ ( E ⁡ ( t ) ) = a 1 - b 1 1 + ⅇ k 1 ⁢ E ⁡ ( t ) - c 1 + b 1 , ⁢ ⁢ v s ⁡ ( E ⁡ ( t ) ) = a 2 - b 2 1 + ⅇ - k 2 ⁢ E ⁡ ( t ) + c 2 + b 2. ⁢ ⁢ and α m ⁡ ( E ⁡ ( t ) , μ m ) = { γ m ⁡ ( μ m ) + min ⁡ ( c E E ⁡ ( t ) k E , b E ) , forE ⁡ ( t ) < τ E , μ min m , n ≤ μ m ≤ μ max m , n , γ m ⁡ ( μ m ) , otherwise , ⁢ ⁢ ⁢ with ⁢ ⁢ γ m ⁡ ( μ m ) = { α rand m for ⁢ ⁢ μ m ∈ [ μ min m , μ max m - δ ] , 3 ⁢ ⁢ α rand m ⁢ δ 2 ( μ m ) 2 - 2 ⁢ ( μ max m + δ ) ⁢ μ m + ( μ max m + 2 ⁢ ⁢ δ ) ⁢ μ max m for ⁢ ⁢ μ m ∈ [ μ max m - δ , μ max m ) , ∞ for ⁢ ⁢ μ m ≥ μ max m. ⁢ ⁢ ⁢ and ⁢ ⁢ ⅆ ⅆ t ⁢ a 1 ⁡ ( t ) = ⁢ k 41 ⁡ ( H ⁡ ( t ) ) ⁢ a 4 ⁡ ( t ) + a iv , total ⁡ ( t ) ⁢ δ t 0 ⁡ ( t ) + k gastro , 1 ⁡ ( H ⁡ ( t ) ) ⁢ a gastro ⁡ ( t ) + ⁢ k 51 ⁡ ( H ⁡ ( t ) ) ⁢ a 5 ⁡ ( t ) - k 15 ⁢ a 1 ⁢ ( t ) - ⁢ d 1 ⁡ ( ∫ μ min r μ max r ⁢ φ ⁡ ( μ r ) ⁢ r ⁡ ( t , μ r ) ⁢ ⅆ μ r + ∫ μ min s μ max s ⁢ φ ⁡ ( μ s ) ⁢ s ⁡ ( t , μ s ) ⁢ ⅆ μ s ) ⁢ a 1 ⁡ ( t ) , ⁢ ⁢ a 2 ⁡ ( t ) = ∫ μ min r μ max r ⁢ α ⁡ ( h , μ r ) ⁢ r ⁡ ( t , μ r ) ⁢ ⅆ μ r + ∫ μ min s η max s ⁡ ( t ) ⁢ α ⁡ ( h , η s ) ⁢ h ⁡ ( t , η s ) ⁢ s ⁡ ( t , μ min + ∫ t - η s t ⁢ v ⁡ ( E ⁡ ( s ) ) ⁢ ⅆ s ) ⁢ ⅆ η s ⁢ ⁢ ⁢ a 3 ⁡ ( t ) = ∫ μ min m μ max m ⁢ h ⁡ ( t - μ m , η max s ) ⁢ m ⁡ ( t , μ m ) ⁢ ⅆ μ m ⁢ ⁢ ⅆ ⅆ t ⁢ a 4 ⁡ ( t ) = ⁢ ∫ μ min r μ max r ⁢ α ⁡ ( h , μ r ) ⁢ h ⁡ ( t , μ r ) ⁢ r ⁡ ( t , μ r ) ⁢ ⅆ μ r + ⁢ ∫ μ min s η max s ⁡ ( t ) ⁢ α ⁡ ( h , η s ) ⁢ h ⁡ ( t , η s ) ⁢ s ⁡ ( t , μ min + ∫ t - η s t ⁢ v ⁡ ( E ⁡ ( s ) ) ⁢ ⅆ s ) ⁢ ⅆ η s + ⁢ ∫ μ min m μ max m ⁢ h ⁡ ( t - μ m , η max s ) ⁢ α m ⁡ ( E ⁡ ( t ) , μ m ) ⁢ m ⁡ ( t , μ m ) ⁢ ⅆ μ m - ⁢ k 41 ⁡ ( H ⁡ ( t ) ) ⁢ a 4 ⁡ ( t ) - k 45 ⁢ a 4 ⁡ ( t ) , ⁢ ⁢ ⁢ ⅆ ⅆ t ⁢ a 5 ⁡ ( t ) = k 15 ⁢ a 1 ⁡ ( t ) + k 45 ⁢ a 4 ⁡ ( t ) - k 51 ⁡ ( H ⁡ ( t ) ) ⁢ a 5 ⁡ ( t ) , ⁢ ⁢ ⅆ ⅆ t ⁢ H ⁡ ( t ) = 1 TBV ⁢ H prod ⁡ ( t ) - c deg H ⁢ H ⁡ ( t ) ; wherein TBV is a total blood volume, p(t,μ p ) is a population density of a BFU-E cell class at time t with maturity μ p , β p is a proliferation rate for BFU-E cells, q(t,μ q ) is a population density of a CFU-E cell class at time t with maturity μ q , β q is a proliferation rate for CFU-E cells, α q (E(t)) is an apoptosis rate for CFU-E cells which depends on erythropoietin (EPO)-concentration E(t) at time t, r(t,μ r ) is a population density of an erythroblast class at time t with maturity μ r , β r is a proliferation rate for erythroblasts, s(t,μ s ) is a population density of a marrow reticulocytes class at time t with maturity μ s , v s (E(t)) is a maturation velocity of cells leaving the erythroblast class an entering the reticulocytes population class which depends on EPO-concentration E(t) at time t, α s is an apoptosis rate for marrow reticulocytes, m(t,μ m ) is a population density of an erythrocyte class at time t with maturity μ m , α m (E(t),μ m ) is an apoptosis rate for erythrocytes which depends on EPO-concentration E(t) at time t and maturity μ m , E end (t) is an endogenous EPO concentration at time t, E in end (t) is an amount of EPO released by a patient's kidneys, c deg end is a degradation rate of endogenous EPO, E ex (t) is an exogenous EPO concentration at time t, E in ex (t) is an amount of EPO administered to the patient, c deg ex is a degradation rate of exogenous EPO, a 1 , b 1 , c 1 and k 1 are constants for the apoptosis rate for CFU-E cells, a 2 , b 2 , c 2 and k 2 are constants for the maturation velocity for marrow reticulocytes, γ m (μ m ) is a mortality rate of erythrocytes which depends on maturity μ m , b E , c E , and k E are constants in the mortality rate of erythrocytes, τ E is a threshold beneath which neocytolysis is triggered, μ min m,n is a lower bound of erythrocytes which are possibly exposed to neocytolysis, μ max m,n is an upper bound of erythrocytes which are possibly exposed to neocytolysis, α rand m is an intrinsic mortality rate for erythrocytes, δ t0 (t) is a Dirac delta impulse at a time of administration t 0 , H(t) is a hepcidin concentration and time t, α iv,total (t) is a total amount of iron intravenously administered at time t, α gastro (t) is an amount of iron in the duodenum of the patient at time t, k 15 is a transfer rate of iron from plasma to storage, k 41 is a transfer rate of iron from macrophages to plasma, k 45 is a transfer rate of iron from macrophages to plasma, k 51 is a transfer rate of iron from storage to plasma, k gastro is a transfer rate of iron in the duodenum of the patient, a 1 (t) is a concentration of iron in plasma at time t, a 2 (t) is a concentration of iron in a precursor cell compartment at time t, a 3 (t) is a concentration of iron in a erythrocyte cell compartment at time t, a 4 (t) is a concentration of iron in a macrophage compartment at time t, a 5 (t) is a concentration of iron in a storage compartment at time t, φ(μ) is a function describing a number of TfR on a cell with cell age μ, r(t,μ r ) is the density of erythroblasts, s(t,μ s ) is the density of bone marrow reticulocytes, h(t,μ(t)) denotes an amount of hemoglobin in a cell with age μ(t) at time t, and α(h,η) is a rate of apoptosis of precursor cells with calendric age η.