Apparatus, program and method for determining cerebral blood flow
Abstract:
[Object] To provide a method for accurately determining cerebral blood flows both in rest state and under medication with less invasive operations.[Solution] Cerebral blood flow is determined based on a formula represented by the following formulas (1) or (2) for a time under medication that continuously follows a resting time. B ⁡ ( t ) = k 1 ⁢ ⅇ - k 2 ⁢ t 3 ⁢ mC f ⁢ ∫ 0 t 3 ⁢ S ⁡ ( τ ) ⁢ ⅇ k 2 ⁢ τ ⁢ ⅆ τ ⁡ ( ⅇ - k 2 ⁢ d ⁡ ( t - t 3 ) ) + k 1 ⁢ d ⁢ mC f ⁢ ∫ t 3 t ⁢ ( S ⁡ ( τ ) + S ⁡ ( τ - t 3 ) ) · ⅇ - k 2 ⁢ d · ( t - τ ) ⁢ ⅆ τ ⁡ ( t ≥ t 3 ) ( 1 ) ∫ t 5 t 6 ⁢ B ⁡ ( t ) ⁢ ⅆ t = k 1 k 2 ⁢ d ⁢ ⅇ - k 2 ⁢ t 3 ⁢ mC f ⁢ ∫ 0 t 3 ⁢ S ⁡ ( τ ) ⁢ ⅇ k 2 ⁢ τ ⁢ ⅆ τ · ( ⅇ - k 2 ⁢ d ⁡ ( t 5 - t 3 ) - ⅇ - k 2 ⁢ d ⁡ ( t 6 - t 3 ) ) + ∫ t 5 t 6 ⁢ k 1 ⁢ d ⁢ mC f ⁢ ∫ t 3 t ⁢ ( S ⁡ ( τ ) + S ⁡ ( τ - t 3 ) ) · ⅇ - k 2 ⁢ d · ( t - τ ) ⁢ ⅆ τ ⁢ ⅆ t ⁡ ( t ≥ t 3 ) ( 2 ) (B(t): the radiation count at the time of t, t3: the time when a radioisotope medicine is administered, t5: the time when acquisition of the imaging data started for the state under medication, t6: the time when acquisition of the imaging data finished for the state under medication, mCf: a scaling factor, k1: cerebral blood flow rest state, k2: the blood-outflow-rate-constant of brain tissues rest state, k1d: a cerebral blood flow under medication, and k2d: the blood-outflow-rate-constant of brain tissues under medication).
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