A method of deriving blood perfusion indices, for a region of interest by operating a computer program on intensity data input to a computer, comprising: a. obtaining intensity data generated by a contrast agent in a ROI wherein said ROI comprises tissue; b. measuring said intensity data to provide a tissue contrast agent curve C(t) in said tissue, wherein said C(t) is a known intensity profile measured against time; characterised in that, c. measuring an arterial input function AIF a (t) in a vessel leading to said ROI, wherein said AIF a (t) is a known intensity profile measured against time; d. estimating a tissue blood flow F t and a tissue impulse residue function R e (t) by deconvolving C ( t) = ( F t / k H) AlF a ( t) X R e ( t), wherein k H = (1 - H a) /(1 - H t) is a correction constant using different values of an arterial hematocrit H a and a tissue hematocrit H t, wherein said H a has a value of about 0.45, wherein said H t has a value of about 0.25, wherein when said AIF a (t) in a major artery comprises no delay and no dispersion, said C(t) can be derived by a convolution of said AIF a (t) and said R e (t); e. determining a blood flow rate F t and an estimated tissue impulse residue function R e (t) using a said C(t) and a tissue input function AIFt(t) by deconvolving the relation C(t)= (F t /k H)AIF t (t) X R e (t), wherein said A I Ft(t) comprises AIF t ( t) = AIF a ( t) X h a ( t), wherein h a (t) is a vascular transport function, wherein for t < t 1, h a (t) = 0 and for t ≥ t 1, h a t = 1 σ 1 ⁢ e - t - t 1 / σ 1, wherein the initial estimate of a delay time t 1 can be determined by the maximum position of said R e (t), wherein σ 1 =(t 1)(β 1)/(1-β 1), wherein β 1 is a known relative dispersion value having a range from 0 to 1; f. simulating a tissue contrast agent concentration curve C s ( t), wherein C s ( t) = (F t /k H)AIF t (t) X R s (t) and R s t = 1 - ∫ 0 t ⁢ h s τ ⁢ d τ, wherein, said h s t = 1 σ 2 ⁢ e - t - t 2 / σ ⁢ 2 for t≥ t 2, and said h s ( t) = 0 for t < t 2, wherein 1/σ 2 is a peak height, wherein t 2 + σ 2 is a mean transit time of an estimated tissue transport function h e (t) in said tissue, wherein h e (t) is derived from said R e (t), wherein h e (t) =-dR e (t)/dt; g. using an iterative least squares method to fit the said simulated C s (t) to said measured tissue curve C(t) with four adjustable parameters (F t, t 1, t 2 and σ 2); h. calculating the blood perfusion indices from the adjustable parameters wherein said perfusion indices may include any one or more of blood flow, blood volume, mean transit time, arterial delay time, arterial dispersion time or relative arterial dispersion, tissue dispersion time and relative tissue dispersion. a. obtaining intensity data generated by a contrast agent in a ROI wherein said ROI comprises tissue; b. measuring said intensity data to provide a tissue contrast agent curve C(t) in said tissue, wherein said C(t) is a known intensity profile measured against time; characterised in that, c. measuring an arterial input function AIF a (t) in a vessel leading to said ROI, wherein said AIF a (t) is a known intensity profile measured against time; d. estimating a tissue blood flow F t and a tissue impulse residue function R e (t) by deconvolving C ( t) = ( F t / k H) AlF a ( t) X R e ( t), wherein k H = (1 - H a) /(1 - H t) is a correction constant using different values of an arterial hematocrit H a and a tissue hematocrit H t, wherein said H a has a value of about 0.45, wherein said H t has a value of about 0.25, wherein when said AIF a (t) in a major artery comprises no delay and no dispersion, said C(t) can be derived by a convolution of said AIF a (t) and said R e (t); e. determining a blood flow rate F t and an estimated tissue impulse residue function R e (t) using a said C(t) and a tissue input function AIFt(t) by deconvolving the relation C(t)= (F t /k H)AIF t (t) X R e (t), wherein said A I Ft(t) comprises AIF t ( t) = AIF a ( t) X h a ( t), wherein h a (t) is a vascular transport function, wherein for t < t 1, h a (t) = 0 and for t ≥ t 1, h a t = 1 σ 1 ⁢ e - t - t 1 / σ 1, wherein the initial estimate of a delay time t 1 can be determined by the maximum position of said R e (t), wherein σ 1 =(t 1)(β 1)/(1-β 1), wherein β 1 is a known relative dispersion value having a range from 0 to 1; f. simulating a tissue contrast agent concentration curve C s ( t), wherein C s ( t) = (F t /k H)AIF t (t) X R s (t) and R s t = 1 - ∫ 0 t ⁢ h s τ ⁢ d τ, wherein, said h s t = 1 σ 2 ⁢ e - t - t 2 / σ ⁢ 2 for t≥ t 2, and said h s ( t) = 0 for t < t 2, wherein 1/σ 2 is a peak height, wherein t 2 + σ 2 is a mean transit time of an estimated tissue transport function h e (t) in said tissue, wherein h e (t) is derived from said R e (t), wherein h e (t) =-dR e (t)/dt; g. using an iterative least squares method to fit the said simulated C s (t) to said measured tissue curve C(t) with four adjustable parameters (F t, t 1, t 2 and σ 2); h. calculating the blood perfusion indices from the adjustable parameters wherein said perfusion indices may include any one or more of blood flow, blood volume, mean transit time, arterial delay time, arterial dispersion time or relative arterial dispersion, tissue dispersion time and relative tissue dispersion.