Cryopreservation moderates the thrombogenicity of arterial allografts during storage

Introduction Management of vascular infections represents a major challenge in vascular surgery. The use of cryopreserved vascular allografts could be a feasible therapeutic option, but the optimal conditions for their production and use are not precisely defined. Aims To evaluate the effects of cryopreservation and the duration of storage on the thrombogenicity of femoral artery allografts. Methods In our prospective study, eleven multi-organ-donation-harvested human femoral arteries were examined at five time points during storage at -80°C: before cryopreservation as a fresh native sample and immediately, one, twelve and twenty-four weeks after the cryopreservation. Cross-sections of allografts were perfused with heparin-anticoagulated blood at shear-rates relevant to medium-sized arteries. The deposited platelets and fibrin were immunostained. The thrombogenicity of the intima, media and adventitia layers of the artery grafts was assessed quantitatively from the relative area covered by fibrin- and platelet-related fluorescent signal in the confocal micrographs. Results Regression analysis of the fibrin and platelet coverage in the course of the 24-week storage excluded the possibility for increase in the graft thrombogenicity in the course of time and supported the hypothesis for a descending trend in fibrin generation and platelet deposition on the arterial wall. The fibrin deposition in the cryopreserved samples did not exceed the level detected in any of the three layers of the native graft. However, an early (up to week 12) shift above the native sample level was observed in the platelet adhesion to the media. Conclusions The hemostatic potential of cryopreserved arterial allografts was retained, whereas their thrombogenic potential declined during the 6-month storage. The only transient prothrombotic change was observed in the media layer, where the platelet deposition exceeded that of the fresh native grafts in the initial twelve weeks after cryopreservation, suggesting a potential clinical benefit from antiplatelet therapy in this time-window.


Detailed statistical approach I. Datasets
We conducted experiments over arteries from 11 donors (r=1, 2,…,11). Five arterial samples (j=1, 2,…,5) were taken from each artery, at different time points during the storage after the addition of the storage medium. The first arterial sample (j=1) was not treated with storage medium, whereas the arterial samples from two to five (j=2, 3,4,5) were kept in the storage medium less than 1 day for j=2, one week for j=3, 12 weeks for j=4, and 24 weeks for j=5. Each of the 55 arterial samples, Sr,j, were perfused with blood before being studied with the immunofluorescent method described in the "Methods" section and data from different regions of interest in the micrographs were analyzed. The regions were divided into six logical groups corresponding to the three layers of the artery (Adventitia for L=1, Media for L=2, and Intima for L=3) and to the measured thrombogenic factor (the percentage of area covered by fibrin for T=1 and the percentage of area covered by platelets for  L,T  L,T  L,T  L,T  L,T  L,T  L,T  j , j , j , j , j n ,j n ,j x , x , , x j , , , The first 1 The five fuzzy sample (2) The count of the observations, nj, in the fuzzy samples (2) depends on the layer (L), on the thrombogenic factor (T) and on treating time (j), which is summarised in Table 1.

II. Distribution Functions and α-quantiles
Any approximation of the cumulative distribution function (CDF) of a random variable based on a random sample of variates of the random variable can be denoted as sample CDF (SCDF). The data in the fuzzy sample j  was used to construct three different forms of the SCDF.
The best-known form of SCDF is the empirical CDF (ECDF). The latter disregards the membership degrees in the fuzzy sample (so it can be constructed if a crisp sample is given). ECDF is a step function which jumps with 1/nj at any variate value in the sample: The second form of SCDF is the fuzzy ECDF (FECDF), which is a generalization of (4). FECDF is a step function, which jumps with i, j  at any variate value i, j x in the fuzzy sample: Both ECDF and FECDF do not have inverse and are not suitable to identify α-quantiles, because all conventional procedures usually identify those quantiles as one of the variates in the sample. Those SCDFs are useful in the Bootstrap procedures described below.
The preferred form of SCDF is a fuzzy version of the invertible CDF estimator with maximum count of nodes (FICDFmax) which is strictly increasing in the domain [xbeg,j, xend,j]. That method constructs Fj(x), as a linear interpolation on a set of Rj nodes: The where Fj(x) is strictly increasing, have been naturally selected as: The values of the nodes' strictly increasing ordinates ( for 1 2 Because the nodes in NDSj have strictly increasing abscissas, the FICDFmax function, Fj(x), can be constructed as: Because the nodes in NDS j have strictly increasing ordinates, the inverse FICDFmax function, Using the inverse FICDFmax function (12), any α-quantile describing the random variable X j can be implicitly estimated: The implicit estimates of the median, the lower quartile, and the upper quartile of the random The values of the increasing nodes' ordinates (qk,j ) are: The values of the strictly increasing nodes' abscissas (αk,j) in qNDSj are: The explicit estimates of the median, the lower quartile, and the upper quartile of the random The algorithm to estimate the p-values of the four Bootstrap one-tailed tests of (17) is described in [6].
The only modification was the substitution of the fuzzy mean value formula with the procedure (11)- Although each of those tests can operate on its own, it is more informative to use their results as a cluster providing complementary information for the solution of problem (16). In that way, we can avoid making random significance claims due to an odd low p-value in a single hypothesis test. Instead, the significance claims are based on evidence that at least half of the tests in Clhyp,k have identified significant difference in the population k th -quartile values of the random variable Xjb and Xjs. The adopted cluster approach to hypothesis testing is proposed and demonstrated in [7]. The performance of the Clhyp,k cluster of four fuzzy bootstrap tests is compared with the results of a bootstrap test performed using the above described algorithm on modified crisp samples     IV.

Significance of Quantitative Time Trends
We also investigated quantitively the influence of the storage medium treating time over the k th quartile of the thrombogenic factor concentration (i.e., for the lower quartile k=1, for the median k= , for The k th regression (18) The solution of the optimization problem (22), the goodness-of-fit measures of (18), and the p-value of the analytical t-test for the significance of the single regression slope bk,1 were calculated using the analytical Algorithm 1 from [8]. However, the classical regression assumptions for this analytical solution hardly hold and the results of the t-test about the significance of the estimated slope are unreliable. On the other hand, the structure of the problem (4 samples from which we derive the 4 regressand values and their precision) is suitable for fuzzy Bootstrap procedure to identify the distribution of the slope. We can use that distribution to find (100-100α )%-confidence interval for the slope (usually 95%-confidence interval). Even more important is that the identified distribution can provide the probabilities (Pand P 0+ ) for the slope to be negative and non-negative (if the estimate bk,1<0) or the probabilities (P + and P 0-) for the slope to be positive and non-positive (if the estimate bk,1>0). Such probabilities are a much better tool to determine the significance of the identified slope sign, than the p-value of any statistical test, because at the latter we can calculate only the probability for being wrong if we reject the null hypothesis, but never the probability of being right when accepting the alternative one. We adopted the conservative policy to assume negativity/positivity of the slope only when the probability for the non-negativity/non-positivity) is less than the preselected significance level, α (usually α = 0.05). Four different fuzzy Bootstrap procedures were applied for fuzzy sample generation which differ: a) in the type of the generated synthetic fuzzy sample, and b) in the sample distribution used in the synthetic fuzzy sample generation (as explained in III). We utilized the following Bootstrap procedure to determine the significance of the slope: 1) Select quartile (k=1,2,3), layer (L=1,2,3), and thrombogenic factor (T=1,2) 2) From L and T form 2 3 4 5 , , ,     according to (1) and (2) 3) Select the count of the pseudo-realities, N (usually N=10000)  (20) and (21)  We use the designation Clsign,k for the cluster of the four fuzzy k th -quartile Bootstrap procedures.
Although each of those procedures can operate on its own, it is more informative to use their results as a cluster providing complementary information for significance of the slope sign. That is another example of successful application of the cluster approach.