Microcirculation and microvasculature in breast tumors: pharmacokinetic analysis of dynamic MR image series. values in the Meng-Rosenthal-Rubin method is available online (Li K-L, Zhu XP. http://lib.stat.cmu.edu/R/CRAN/src/contrib/Descriptions/compOverlapCorr.html). A significance level of 0.05 was used for all tests. For assessing the impact of using population VIF as opposed to individual VIFs on the relationship between SER and = 8) Fosfructose trisodium with parameters 1 min?1 (marked with arrows). Open in a separate window FIG. 6 Representative pixel-by-pixel scatterplots of SER vs. 1 min?1 (arrows). With use of the Meng-Rosenthal-Rubin = 0.0001). However, increased = 0.22, = 5). DISCUSSION This article presents a shortcut of the two-compartment pharmacokinetic model (19) that can be used in breast DCE-MRI studies. Using computer simulations, we demonstrated that 1) the signal differences between each of two postcontrast scans and the reference precontrast scan can form a ratio, SER, that tracks the CACR for scans with short TR (?(Fig. 4). This makes high FAs attractive if quantitative DCE-MRI is the main concern; however, at the expense of a lower contrast to noise ratio, given a short TR. Based on the computer simulation using the Ernst equation, the highest contrast between tumor (= [0.55, 1.65, 2.75, 14.85] min. Because of the rapid heart rate in mice, a is the proton density, is the flip angle, TR is the repetition time, and em R /em 1 is the spin-lattice relaxation rate ( em R /em 1 1/ em T /em 1). Substituting em R /em 1 in Eq. [A1] with em R /em 1 at the three acquisition timepoints, em R /em 10, em R /em 11, and em R /em 12, the signal intensity at the three timepoints can be calculated as: math xmlns:mml=”http://www.w3.org/1998/Math/MathML” display=”block” id=”M11″ overflow=”scroll” mrow msub mi S /mi mn 0 /mn /msub mo = /mo mi M /mi mo ? /mo mi sin /mi mi /mi mo ? /mo mfrac mrow mn 1 /mn mo ? /mo mi exp /mi mo ( /mo mo ? NEU /mo mi TR /mi mo ? /mo msub mi R /mi mn 10 /mn /msub mo ) /mo /mrow mrow mn 1 /mn mo ? /mo mi cos /mi mi /mi mo ? /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 10 /mn /msub mo ) /mo /mrow /mfrac /mrow /math math xmlns:mml=”http://www.w3.org/1998/Math/MathML” display=”block” id=”M12″ overflow=”scroll” mrow msub mi S /mi mn 1 /mn /msub mo = /mo mi M /mi mo ? /mo mi sin /mi mi /mi mo ? /mo mfrac mrow mn 1 /mn mo ? /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 11 /mn /msub mo ) /mo /mrow mrow mn 1 /mn mo ? /mo mi cos /mi mi /mi mo ? /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 11 /mn /msub mo ) /mo /mrow /mfrac /mrow /math and math xmlns:mml=”http://www.w3.org/1998/Math/MathML” display=”block” id=”M13″ overflow=”scroll” mrow msub mi S /mi mn 2 /mn /msub mo = /mo mi M /mi mo ? /mo mi sin /mi mi /mi mo ? /mo mfrac mrow mn 1 /mn mo ? /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 12 /mn /msub mo ) /mo /mrow mrow mn 1 /mn mo ? /mo mi cos /mi mi /mi mo ? /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 12 /mn /msub mo ) /mo /mrow /mfrac /mrow /math [A2] The signal enhancement at em t /em em p /em 1 is: math xmlns:mml=”http://www.w3.org/1998/Math/MathML” display=”block” id=”M14″ overflow=”scroll” mrow msub mi S /mi mn 1 /mn /msub mo ? /mo msub mi S /mi mn 0 /mn /msub mo = Fosfructose trisodium /mo mi M /mi mo ? /mo mi sin /mi mi /mi mo /mo mfrac mrow mo ( /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 11 /mn /msub mo ) /mo mo ? /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 10 /mn /msub mo ) /mo mo ) /mo mo ( /mo mi cos /mi mi /mi mo ? /mo mn 1 /mn mo ) /mo /mrow mrow mo ( /mo mn 1 /mn mo ? /mo mi cos /mi mi /mi mo ? /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 11 /mn /msub mo ) /mo mo ) /mo mo ( /mo mn 1 /mn mo ? /mo mi cos /mi mi /mi mo ? /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 10 /mn /msub mo ) /mo mo ) /mo /mrow /mfrac /mrow /math [A3] Similarly, the signal enhancement at em t /em em p /em 2 is: math xmlns:mml=”http://www.w3.org/1998/Math/MathML” display=”block” id=”M15″ overflow=”scroll” mrow msub mi S /mi mn 2 /mn /msub mo ? /mo msub mi S /mi mn 0 /mn /msub mo = /mo mi M /mi mo ? /mo mi sin /mi mi /mi mo /mo mfrac mrow mo ( /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 12 /mn /msub mo ) /mo mo ? /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 10 /mn /msub mo ) /mo mo ) /mo mo ( /mo mi cos /mi mi /mi mo ? /mo mn 1 /mn mo ) /mo /mrow mrow mo ( /mo mn 1 /mn mo ? /mo mi cos /mi mi /mi mo ? /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 12 /mn /msub mo ) /mo mo ) /mo mo ( /mo mn 1 /mn mo ? /mo mi cos /mi mi /mi mo ? /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 10 /mn /msub mo ) /mo mo ) /mo /mrow /mfrac /mrow /math [A4] The ratio of signal enhancement at the two points is: math xmlns:mml=”http://www.w3.org/1998/Math/MathML” display=”block” id=”M16″ overflow=”scroll” mrow mfrac mrow msub mi S /mi mn 1 /mn /msub mo ? /mo msub mi S /mi mn 0 /mn /msub /mrow mrow msub mi S /mi mn 2 /mn /msub mo ? /mo msub mi S /mi mn 0 /mn /msub /mrow /mfrac mo = /mo mfrac mrow mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 11 /mn /msub mo ) /mo mo ? /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 10 /mn /msub mo ) /mo /mrow mrow mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 12 /mn /msub mo ) /mo mo ? /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 10 /mn /msub mo ) /mo /mrow /mfrac mo ? /mo mfrac mrow mn 1 /mn mo ? /mo mi cos /mi mi /mi mo ? /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 12 /mn /msub mo ) /mo /mrow mrow mn 1 /mn mo ? /mo mi cos /mi mi /mi mo ? /mo mi exp /mi mo ( /mo mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 11 /mn /msub mo ) /mo /mrow /mfrac /mrow /math [A5] For a short TR typically used for rapid acquisition and a low dose (0.1 mmol/kg) of Gd-DTPA administration, it can be assumed that TR ? em T /em 1; therefore, exp(-TR em R /em 1) 1-TR em R /em 1. Eq. [A5] can be rewritten as: math xmlns:mml=”http://www.w3.org/1998/Math/MathML” display=”block” id=”M17″ overflow=”scroll” mrow mfrac mrow msub mi S /mi mn 1 /mn /msub mo ? /mo msub mi S /mi mn 0 /mn /msub /mrow mrow msub mi S /mi mn 2 /mn /msub mo ? /mo msub mi S /mi mn 0 /mn /msub /mrow /mfrac mo = /mo mfrac mrow msub mi R /mi mn 11 /mn /msub mo ? /mo msub mi R /mi mn 10 /mn /msub /mrow mrow msub mi R /mi mn 12 /mn /msub mo ? /mo msub mi R /mi mn 10 /mn /msub /mrow /mfrac mo ? /mo mfrac mrow mn 1 /mn mo ? /mo mi cos /mi mi /mi mo + /mo mi cos /mi mi /mi mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 12 /mn /msub /mrow mrow mn 1 /mn mo ? /mo mi cos /mi mi /mi mo + /mo mi cos /mi mi /mi mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 11 /mn /msub /mrow /mfrac /mrow /math [A6] Remembering that em C(tp /em 1) = ( em R /em 11 ? em R /em 10)/ ?1 and em C(tp /em 2) = ( em R /em 12 ? em R /em 10)/ ?1, where ?1 is em T /em 1 relaxivity of Gd-DTPA, SER in tissues can therefore be expressed as: math xmlns:mml=”http://www.w3.org/1998/Math/MathML” display=”block” id=”M18″ overflow=”scroll” mrow mi SER /mi mo = /mo mfrac mrow msub mi S /mi mn 1 /mn /msub mo ? /mo msub mi S /mi mn 0 /mn /msub /mrow mrow msub mi S /mi mn 2 /mn /msub mo ? /mo msub mi S /mi mn 0 /mn /msub /mrow /mfrac mo = /mo mfrac mrow mi C /mi mo ( /mo msub mi t /mi mrow mi p /mi mn 1 /mn /mrow /msub mo ) /mo /mrow mrow mi C /mi mo ( /mo msub mi t /mi mrow mi p /mi mn 2 /mn /mrow /msub mo ) /mo /mrow /mfrac mo ? /mo mfrac mrow mn 1 /mn mo ? /mo mi cos /mi mi /mi mo + /mo mi cos /mi mi /mi mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 12 /mn /msub /mrow mrow mn 1 /mn mo ? /mo mi cos /mi mi /mi mo + /mo mi cos /mi mi /mi mo ? /mo mi TR /mi mo ? /mo msub mi R /mi mn 11 /mn /msub /mrow /mfrac /mrow /math [A7] By defining a factor, em A /em , as SER/CACR, where CACR em C(tp /em 1)/ em C(tp /em 2), we can rewrite Eq. 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