Drug-eluting Balloons Technical Review Figure 3: Paclitaxel Tissue Concentration
0.15 0.20 0.25
0.10 0.05
0 0 10 Figure 4: Master Curve
3.5 3.0
1.5 2.0 2.5
1.0 0.5
0 0 5 Hours
Table 2: Calculated Normalised Paclitaxel Levels Over 48 Hours
Time in Hours 0.05 0.10 0.25 0.50 0.75 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00
12.00 24.00 48.00
240.00 720.00
1.
Normalised Paclitaxel Level (Concentration) 10.98 6.30 3.03 1.70 1.25 1.00 0.72 0.57 0.48 0.42 0.37 0.33 0.30 0.28 0.26 0.24 0.14 0.08
0.045 0.012 0.005
Axel DI, Kunert W, Göggelmann C, et al., Paclitaxel inhibits arterial smooth-muscle-cell proliferation and migration in vitro and in vivo using local drug delivery, Circulation, 1997;96(2):636–45.
2. 10 15 y=x-0.8 20 30 40 Hours (long-term results) 50 60 Figure 5: Paclitaxel Tissue Concentration
10 12
6 8
4 2
0 0 0.5 1 1.5 Time in hours after local drug delivery (acute phase)
Gutenberg–Richter law for earthquake sizes, Pareto’s law of income distribution, structural self-similarity of fractals and scaling laws in biological systems. Research on the origins of power law relationships and efforts to observe and validate them in the real world is an active topic in many fields of science, including physics, computer science, geophysics and more.
Estimating the Exponent n from Empirical Data There are many ways of estimating the value of the scaling exponent n for a power law tail, but not all of them yield unbiased and consistent answers. The most reliable techniques are often based on the method of maximum likelihood. Alternative methods are often based on making a linear regression on either the log–log probability, the log–log cumulative distribution function or on log-binned data, but these approaches may be problematic as they can lead to highly biased estimates of the scaling exponent. The curve in Figure 4 can be calculated. In order to calculate the values, once we have one single time-dependent tissue value we can use the following equation (see Table 2):
y = x – 0.8 x = time in hours; y = paclitaxel level (concentration) in tissue
Once we have identified an appropriate function describing the tissue behaviour, we can extrapolate the curve for the values, which were unknown until now (see Figure 5).
What Can We Do with this Curve and Values? This curve and values mean:
• • •
• • •
no need for further animal trials to measure the time-dependent paclitaxel tissue level (concentration) for a prolonged time;
there is the possibility of analysing and evaluating data from different products;
paclitaxel tissue level (concentration) calculation of the first few minutes after drug delivery is possible;
establishing criteria to decrease prolonged toxicity is possible; calculating needed time for safe endothelisation is possible; and minimised toxicity when using long and large balloons is possible. n
Herdeg C, Oberhoff M, Baumbach A, et al., Local paclitaxel delivery for the prevention of restenosis: biological effects and efficacy in vivo, JACC, 2000;35(7):1969–76.
3. Kleiber M, Body size and metabolic rate, Physiological Rev, 1947;27:511–41.
4.
Simon HA, On a Class of Skew Distribution Functions, Biometrika, 1955;42:3–4.
2
76
INTERVENTIONAL CARDIOLOGY
Concentration
Concentration
Concentration
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74 |
Page 75 |
Page 76 |
Page 77 |
Page 78 |
Page 79 |
Page 80 |
Page 81 |
Page 82 |
Page 83 |
Page 84 |
Page 85 |
Page 86 |
Page 87 |
Page 88 |
Page 89 |
Page 90 |
Page 91 |
Page 92 |
Page 93 |
Page 94 |
Page 95 |
Page 96 |
Page 97 |
Page 98 |
Page 99 |
Page 100 |
Page 101 |
Page 102 |
Page 103 |
Page 104 |
Page 105 |
Page 106 |
Page 107 |
Page 108 |
Page 109 |
Page 110 |
Page 111 |
Page 112 |
Page 113 |
Page 114 |
Page 115 |
Page 116