Influence of Duodenal–Jejunal Implantation on Glucose ...

Research ArticleInfluence of DuodenalndashJejunal Implantation on GlucoseDynamics A Pilot Study Using Different Nonlinear Methods

David Cuesta-Frau 1 Daniel Novaacutek2 Vaclaacutev Burda2 Daniel Abasolo 3

Tricia Adjei4 Manuel Varela5 Borja Vargas 5 Milos Mraz67 Petra Kavalkova7

Marek Benes8 and Martin Haluzik 69

1Technological Institute of Informatics Universitat Politecnica de Valencia Alcoi Campus Plaza Ferrandiz y Carbonell 203801 Alcoi Spain2Department of Cybernetics Czech Technical University in Prague Prague Czech Republic3Centre for Biomedical Engineering Department of Mechanical Engineering Sciences Faculty of Engineering and Physical SciencesUniversity of Surrey Guildford UK4Department of Electrical and Electronic Engineering Imperial College London UK5Department of Internal Medicine Teaching Hospital of Mostoles Madrid Spain6Department of Diabetes Diabetes Centre Institute for Clinical and Experimental Medicine Prague Czech Republic7Department of Medical Biochemistry and Laboratory Diagnostics General University HospitalCharles University in Prague 1st Faculty of Medicine Prague Czech Republic8Hepatogastroenterology Department Transplant Centre Institute for Clinical and Experimental Medicine Prague Czech Republic9Obesitology Department Institute of Endocrinology and the Experimental Medicine CentreInstitute for Clinical and Experimental Medicine Prague Czech Republic

Correspondence should be addressed to David Cuesta-Frau dcuestadiscaupves

Received 6 July 2018 Revised 7 December 2018 Accepted 29 January 2019 Published 14 February 2019

Academic Editor Lucia Valentina Gambuzza

Copyright copy 2019 David Cuesta-Frau et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Diabetes is a disease of great and rising prevalence with the obesity epidemic being a significant contributing risk factorDuodenalndashjejunal bypass liner (DJBL) is a reversible implant that mimics the effects of more aggressive surgical procedures suchas gastric bypass to induce weight loss We hypothesized that DJBL also influences the glucose dynamics in type II diabetes basedon the induced changes already demonstrated in other physiological characteristics and parameters In order to assess the validityof this assumption we conducted a quantitative analysis based on several nonlinear algorithms (LempelndashZiv Complexity SampleEntropy Permutation Entropy and modified Permutation Entropy) well suited to the characterization of biomedical time seriesWe applied them to glucose records drawn from two extreme cases available of DJBL implantation before and after 10 monthsTheresults confirmed the hypothesis and an accuracy of 864 was achieved with modified Permutation Entropy Other metrics alsoyielded significant classification accuracy results all above 70 provided a suitable parameter configuration was chosen With theLeavendashOnendashOut method the results were very similar between 72 and 82 classification accuracy There was also a decreasein entropy of glycaemia records during the time interval studied These findings provide a solid foundation to assess how glucosemetabolism may be influenced by DJBL implantation and opens a new line of research in this field

1 Introduction

Diabetes mellitus is a chronic serious disorder that affectsnearly a half billion people in the world and its prevalenceis expected to grow significantly in the coming years [1]

It is also one of the greatest risk factors for cardiovasculardiseases In addition the economical impact of the associatedhealthcare expenditure is enormous [2]

The global obesity epidemic is a relevant risk factor fordiabetes among many other diseases As a result weight

HindawiComplexityVolume 2019 Article ID 6070518 10 pageshttpsdoiorg10115520196070518

2 Complexity

reduction methods have become a field of great medicaland scientific interest Successful long-term weight lossmaintenance by strategies such as changing dietary habitsor increasing physical activity is difficult [3] Other moreaggressive approaches are necessary especially when a sig-nificant weight reduction percentage is required or moreserious health consequences are involved

One of these approaches is the utilization of pharma-cotherapy which in the context of diabetes can be focusedon weight loss or on glucose control resulting in weightloss as a side effect [4] However the long-term outcomeis very limited [5] On the contrary the most successfulstrategies are based on surgical therapies The gastric bypassachieves permanent significant long-term weight reduc-tion in most of the patients that underwent this surgery[6]

Nevertheless the gastric bypass is a very invasive pro-cedure with pre- peri- and postoperative risks and pos-sible sequelae [7] An intermediate solution is the so-called Duodenal-jejunal Bypass Liner (DJBL) The DJBL isa reversible implantable device used to mimic the effectsof gastric by-pass by preventing the contact of chymuswith duodenum and proximal jejunum and delivering itin a less digested form to more distal parts of the intes-tine Obesity is a central physiopathological mechanism intype 2 diabetes mellitus (T2DM) and thus DJBL has beenused to improve metabolic control in obese patients withT2DM [8]

The effects of DJBL implantation are broad and dis-parate Many studies have assessed the impact of DJBL ona number of physiological parameters [9ndash12] We hypoth-esized that DJBL must have an influence on the glu-cose dynamics as some studies about glucose variabil-ity and DJBL have pinpointed [13] These dynamics ofthe glucose time series offer new insights into glucosemetabolism and there seems to be a direct correlationbetween (the loss of) variability in the glucose time seriesand the degree of deterioration in glucose metabolism [14ndash17]

The glucoregulatory system is effectively a complexsystem with several acting variables (caloric intake exer-cise) a number of active hormones (insulin glucagoncatecholamines growth hormone and incretins) and somewellndashestablished feedback and feedforward loops [18 19]The analysis of such a complex physiological system can beaddressed using system dynamics characterization methodsSeveral methods well suited to time series of limited durationwere used in this pilot study to characterize the effects ofDJBL Sample Entropy (SampEn) is a robust measure of regu-larity in sequences [20] whilst LempelndashZiv complexity (LZC)is an easy to compute nonlinear algorithm to estimate thecomplexity in time series [21] Permutation Entropy (PE) isanother complexitymeasure introduced by Bandt and Pompein 2002 [22] as a robust method to deal with real-world timeseries In spite of the proficiency of PE in time series analysesit neglects equalities within signals Modified PE (mPE) wasproposed to address this shortcoming in the original PEalgorithm [23]

2 Materials and Methods

21 LempelndashZiv Complexity In order to compute LZC from atime series the signal must first be converted into a sequenceof symbols In this study the signal was parsed into a binarysequence using themedian as the threshold (119879119889) For an inputtime series x = 1199091 1199092 119909119871 of length 119871 the symbols in thebinary sequence 119875 = 1199041 1199042 119904119871 are created by

119904119894 = 0 if 119909119894 lt 1198791198891 if 119909119894 ge 119879119889

(1)

The binary sequence 119875 is then scanned from left to rightto identify the different subsequences held within it and acomplexity counter 119888 is increased by one every time a newsubsequence is found (a detailed description of the algorithmcan be found in [21]) This complexity counter needs to benormalized to obtain a measure of complexity independentof the length of the time series [24]

LZC = 119888119871log2119871 (2)

LZC captures the dynamics of the time series by reflectingthe rate of new subsequences present within it

22 Permutation Entropy PE is a method measuring theentropy within a time series based on the probability ofoccurrence of all possible permutations of a certain lengthwithin it [22] With the exception of LZC all other methodsused in this study require the selection of values for differentinput parameters In the case of PE the computation relieson the selection of the embedding dimension 119899 and the timedelay 119897 The choice of embedding dimension 119899 is determinedby the number of samples available as the number ofpermutations must be less than the length of the time series(ie 119899 le 119871) [22]

In order to compute PE as follows [23] embeddingvectors need to be created from the original time series asfollows

119883119894 = [119909119894 119909119894+119897 119909119894+(119899minus1)119897] (3)

For each embedding vector the lowest data point inthe embedding vector is assigned a 0 the second lowest 1and on until all data points in the embedding vector havebeen replaced with their ranking order Once all possibleembedding vectors in the time series have been created andranked PE can be calculated by applying Shannonrsquos Entropyto quantify the proportion of possible permutations withinthe time series

PE (119899 119897) = minus119896

sum119860=1

119875119860 ln119875119860 (4)

where 119896 is the number of different subsequence rankedvectors in the original time series and PA is the fraction of thesubsequence ranked vectors A less regular signal will have agreater range of embedding vectors and therefore a higherPE

Complexity 3

221 Modified Permutation Entropy One limitation of theoriginal PE algorithm is that it ignores any repeated valuesin the embedding vector assigning the first repeated valuein the vector a lower integer in the ranking than subsequentrepeatsThiswas addressedwith the introduction ofModifiedPermutation Entropy (mPE) [23] in which repeated valuesare given the same ranking value Then entropy is evaluatedapplying Shannonrsquos entropy as is done in PE [23]

222 Input Parameter Selection The outcome of PE will beinfluenced by the choice of embedding dimension 119899 and delay119897 A greater value of 119899 will give a greater possible range ofranking vectors and therefore a greater resolution It hasbeen recommended to use a range of values from 119899 = 3to 7 but the total number of permutations (given by 119899)must be less than the length of the original time series [22]However small embedding dimensions might be too smallto accurately track the dynamical changes in a signal [25]Hence PE and mPE were computed with 119899 = 4 to 6 In termsof the time delay a value of 1 was chosen as this would retainthe original relationships between data-points [23]

23 SampEn SampEn was first defined in [20] SampEnstarts by creating a set of embedded vectors x119894 of length119898

x119894 = 119909119894 119909119894+1 119909119894+119898minus1 (5)

where 119894 = 1 119871minus119898+1The distance between subsequencesis then defined as 119889119894119895 = max(|119909119894+119896 minus 119909119895+119896|) with 0 le 119896 le119898 minus 1 119895 = 119894 According to a predefined threshold 119903 twosubsequences are considered similar if 119889[119883119898(119894) 119883119898(119895)] le 119903This similarity is quantized for two consecutive subsequencelengths (119898 and 119898 + 1) with 119861119894(119903) number of 119895 such that119889[119883119898(119894) 119883119898(119895)] le 119903 and 119860 119894(119903) number of 119895 such that119889[119883119898+1(119894) 119883119898+1(119895)] le 119903 These two values 119861 and 119860 enablethe computation of the statistics associated with SampEn

119861119898119894 (119903) = 1119871 minus 119898 minus 1119861119894 (119903)

119861119898 (119903) = 1119871 minus 119898

119871minus119898

sum119894=1

119861119898119894 (119903)

119860119898119894 (119903) = 1119871 minus 119898 minus 1119860 119894 (119903)

119860119898 (119903) = 1119871 minus 119898

119871minus119898

sum119894=1

119860119898119894 (119903)

(6)

from which the final value for SampEn can be obtained

SampEn (119898 119903) = lim119873997888rarrinfin

(minuslog [119860119898 (119903)119861119898 (119903) ])

SampEn (119898 119903 119871) = minus log [119860119898 (119903)119861119898 (119903) ](for finite time series)

(7)

The length 119871 is usually given by the acquisition stage butthe parameters119898 and 119903must be carefully chosen to ensure an

optimal performance of SampEn relative to class separabilityThis selection will be detailed in Section 231

231 Input Parameter Selection The optimal selection ofregularity estimators parameters 119898 and 119903 is still an openquestion Frequent recommendations suggest adopting aparameter configuration in the vicinity of 119898 = 2 and 119903 =02 [26] Nevertheless this selection is lacking in terms ofgenericity asmanyworks have already demonstrated [27ndash31]

Although computationally more expensive we variedSampEnparameters from 1 to 3 for119898 and from001 to 030 for119903 in 001 steps (119903was notmultiplied by the standard deviationof the sequences since they were normalised in advance zeromean and unitary standard deviation) This enabled us toavoid the possible bias in the results due to the selection of aspecific method for SampEn parameter optimization despitestill looking at regions usually recommended for 119898 and 119903[20 26 32]

24 Experimental Dataset The database containing theexperimental data of glucose time series was drawn from adatabase used to assess the endocrine effects of DJBL [13]There were 91 records from 30 participants with type IIdiabetes (20 men and 10 women aged between 33 and 65)This database contained records taken before implantation(baseline BL- and 27 records) 1 month after implantation(01M+ 24 records) 10 months after implantation (10M+24 records) and 3 months after device removal (03M- 16records) Sampling frequency was 5 minutes An example ofrecords from each class in this database is shown in Figure 1A very detailed description of the subjects can be found in theoriginal paper [13]

As can be seen in Figure 1 the original records werenoisy with missing samples and missing epochs completelyat random In order to avoid the influence of these artifacts onthe results missing single samples were linearly interpolated(mean substitution [33]) Records with less than 1440 samples(5 days) were excluded from the experiments since thenonlinear methods used in the analysis are also very sensitiveto number of samples [28] Record was then set to the central1440 samples if longer to also avoid border effects [34] (tissueequilibrium measuring device configuration calibrationand stabilization) As a result of all this preprocessing 60records out of 91 were finally available An example ofresulting signals is shown in Figure 2

Nevertheless these records have not been analysed yetfrom a system dynamics standpoint and our hypothesis wasfocused first on the two in principlemost different scenariosbefore DJBL implantation (BL-) and just before deviceremoval (10M+) The rationale for this specific selection isthat one month after implantation it will arguably be moredifficult to find changes in glucose dynamics due to the timepassed After DJBL removal the glucose metabolism tends toreturn to that of the baseline period [11 13] Furthermorequantitative endocrine effects seem to confirm that maindifferences are between these two stages as shown in Table 1Thus in this table 4 out of the 5 physiological featuresprovide significant differences between 10M+ and BL- giving

4 Complexity

0 500 1000 1500Samples

BL-

01M+

10M+

03M-Cl

ass (

ampl

itude

nor

mal

ised)

Figure 1 Example of raw glycaemia records from the database Records corresponding to baseline 1 month 10 months and 3 months afterDJBL removal are depicted Sampling frequency was 5 minutes Missing values were quite frequent (glucose readings spike down to 0 in theplots) Records like those shown here representing 03M- and BL- classes will be omitted in the experiments due to their short length

0 215 430 645 860 1075 1290Samples

BL-

01M+

10M+

03M-

Clas

s (am

plitu

de n

orm

alise

d)

Figure 2 Example of processed glycaemia records from the database Single missing samples were linearly interpolated longer missingepochs were removed and shorter than 5 day-time series were discarded Samples were taken from the central part of the records to avoidborder effects All these constraints are well featured in the changes that can be pinpointed with record 01M+ in this and previous Figure 1Records corresponding to baseline 1 month 10 months and 3 months after DJBL removal are depicted Sampling frequency was 5 minutes

quantitative support to the study selection This support is interms of a significance analysis of these differences obtainedusing Studentrsquos tndashtest (120572 = 005 sample size of 30 andnormality not required [35]) As shown in the 119901 column onlythe differences in hip circumference could not be consideredsignificant The final experimental set was composed of 11

BL- records (positives P in the classification analysis) of 1440samples and 11 10M+ records (negativesN) of the same lengthThese 22 records included the same 11 patients in both classesto ensure a paired test (7 males 4 females) and the others inthese classes were discarded The dataset is relatively smallbut the implantation of DJBL and glucose monitoring for

Complexity 5

m

r

083 072 061 05

001 010 020 030

Figure 3 AUC values obtained for SampEn with 119898 isin [1 3] and 119903 isin [001 030] Maximum is obtained for 119898 = 3 and 119903 = 009 withAUC= 08430 and 119901 = 00175

Table 1 Main characteristics and parameters of the completedatabase (Mean plusmn STD) Original results are taken from [13]

BL- 10M+ 119901Body weight (Kg) 1297 plusmn 44 1173 plusmn 43 119901 = 00450BMI (kmm2) 427 plusmn 12 384 plusmn 11 119901 lt 00001Glucose (mmolL) 123 plusmn 07 845 plusmn 05 119901 lt 00001Hip circumference (cm) 1328 plusmn 35 1262 plusmn 28 119901 = 02000HbA1119862 (mmolmol) 750 plusmn 34 584 plusmn 28 119901 lt 00001HBGI (Variability) 128 plusmn 82 74 plusmn 51 119901 = 00367

Table 2 Classification analysis results for PE in terms of highestAUC including sensitivity (proportion of 10M+ correctly iden-tified) specificity (proportion of BL- correctly identified) andaccuracy (proportion of total cases correctly classified) and theirsignificance 119901119899 AUC 119901 Sensitivity() Specificity() Accuracy()6 07355 00244 636 909 773

Table 3 Classification analysis results for mPE in terms of highestAUC including sensitivity specificity and accuracy and theirsignificance 119901119899 AUC 119901 Sensitivity() Specificity() Accuracy()4 07438 00244 727 818 7735 07769 00137 727 909 8186 07851 00098 727 100 864

several days is very difficult and costly in terms of workloadtime and resources

This table also includes a variability analysis result theHigh Blood Glucose Index (HBGI) This index attempts toimprove the assessment of glycaemic alterations through datatransformation and is a well-established tool to estimate therisk of hyperglycaemia in diabetic patients Average long-term blood glucose values are not a very reliable tool forglycemic control but the analysis of short-term peaks andvalleys has proven to have a much more clinical relevance[36] HBGI provides an estimation of the hyperglycaemiaprobability for the patients and its differences have beenfound to be statistically significant for BL- and 10M+ in thiscase

25 Class Separability Analysis The separability of classesBL- and 10M+ was assessed by means of the Area underCurve (AUC) of the associated Receiver Operating Curve

(ROC) AUCndashROC Statistical analyses based on pairedStudentrsquos tndashtest or the Wilcoxon signed rank test dependingon the distribution of the data were performed to assess thesignificance of the results The acceptance threshold was setat 120572 = 005

Additionally the classification capability of the resultswas quantified using the separability specificity and accuracyclassification performance indicators They were obtainedusing the closest point to (01) in the ROC as the classificationthreshold In this FRAMEWORK positives (P) were assignedto the BL- class negatives (N) to the 10M+ class beingsensitivity = TP (TP+FN) specificity = TN (TN+FP) andaccuracy = (TN + TP) (TN + TP + FN + FP )

3 Results

All four methods showed a decrease of complexity betweenBL- and 10M+ (ie decrease of LZC SampEn PE and mPEvalues) However for LZC differences between the 2 classeswere not significant (see Table 5) On the other hand differentcombination of input parameters in SampEn PE and mPEresulted in significant differences between classes

The results are expressed in terms of AUC statistical sig-nificance classification sensitivity specificity and accuracyThe threshold for classification was taken as the ROC pointclosest to point (01) These calculations were carried out forall the values in input parameters for which the AUC was atleast 070

Specifically for SampEn all the AUC results are depictedas a heatmap in Figure 3 Most of the AUC values fall in the050minus060 region withmore promising results at low 119903 values(119903 lt 010 optimal region) and in the 020 zone (suboptimalregion)

In more detail the numerical results for the highest AUCregion are listed in Tables 2 3 and 4This corresponds to theoptimal parameter zone where some AUC values are above080

Tables 5 6 7 and 8 summarize the numerical resultsfor the two classes including mean and standard deviationThese values were computed using the parameter configura-tion scheme stated above It is important to note that someconfiguration parameters did not yield significant resultssuch as 119899 = 3 for PE (Table 6) and mPE (Table 7) Asin previous similar studies [37ndash39] it seems the greater theembedded dimension 119899 the better classification performanceusing PEndashbased measures

In order to better illustrate the differences betweenthe classes studied a LeavendashOnendashOut (LOO) test [37]

6 Complexity

Table 4 Classification analysis results for SampEn in terms of highest AUC including sensitivity specificity and accuracy and theirsignificance 119901119898 119903 AUC 119901 Sensitivity() Specificity() Accuracy()1 008 07933 00427 636 909 7731 009 08016 00305 727 818 7731 010 07933 00188 818 727 7731 016 07355 00648 727 727 7271 019 07768 00272 818 636 7271 020 07272 00451 545 909 7271 024 07603 00472 727 727 7271 025 07190 00583 727 636 6822 008 07603 00257 727 727 7272 009 08016 00289 818 727 7732 010 07933 00173 818 727 7732 019 07520 00288 727 636 6822 020 06942 00609 545 818 6822 024 07438 00462 727 727 7273 008 07933 00215 727 727 7273 009 08429 00271 727 909 8183 010 08264 00086 909 727 8183 016 07355 00532 818 636 7273 019 07272 00236 727 636 6873 020 07107 00596 455 818 6373 024 07355 00507 636 727 687

Table 5 LempelndashZiv Complexity individual mean and standarddeviation (STD) values of the two classes studied BL- and 10M+No significant differences between groups were found (119901 = 02920tndashtest)

Subject BL- 10M+1 02113 016762 01530 017493 00947 013114 01676 015305 01822 012396 02842 014577 01384 015308 01239 014579 01093 0102010 01822 0138411 01457 01676meanplusmnSTD 01629 plusmn 00528 01457 plusmn 00214

was applied using the data in Table 8 The classificationthreshold was set at the optimal SampEn value at whichthe classification accuracy was maximal For both classesthere were 3 misclassified instances Therefore the overallclassification accuracy using the LOO cross validation was727 As expected the performance was lower than usingall the records but still very significant This method wasalso applied to the Modified Permutation Entropy results in

Table 7 when 119899 = 6 In this case there were 2 misclassifiedinstances achieving a classification accuracy of 82

4 Discussion

Our results show that it is possible to identify the effectsof DJBL in the dynamics of glycaemia records with non-linear analysis methods A significant decrease in entropy(estimated with SampEn PE and mPE) of glycaemia recordsfrom BL- to 10M+ was observed Complexity quantifiedwith LZC also decreased in 10M+ but differences were notsignificant

There is no gold standard for the unsupervised selectionof parameters 119898 and 119903 for SampEn calculations despite thenumerous efforts in this regard [32 40 41] In order toleave no stone unturned we adopted a maximalist strategywhere a wide range of values were tested As a resultthis parameter analysis for SampEn provided an optimalcombination with 119898 = 3 and 119903 = 009 In this case theAUC was maximal AUC= 08429 with significant (rejecthypothesis) classification capabilities between BL- and M10+(sensitivity=727 specificity=909 and accuracy=818)However there were other values for119898 with 119903 in the vicinityof 009 that also yielded good significant accuracy In fact theresults seem to be almost independent of119898

The optimal value of 119903 (119903 = 009) falls practically withinthe usually recommended interval 119903 isin [01 025] [26] Thereis another region of acceptable results for 119903 = 019 Thesespecific values seem to be related to the resolution of the

Complexity 7

Table 6 Permutation Entropy individual mean and standard deviation (STD) values of the two classes studied BL- and 10M+ for 119899 =3 4 5 6 No significant differences between groups were found in some cases (Wilcoxon signed rank test)

119899 = 3 119899 = 4 119899 = 5 119899 = 6Subject BL- 10M+ BL- 10M+ BL- 10M+ BL- 10M+1 15131 11105 24970 15694 35541 20522 45778 255222 11824 11688 16784 16891 21995 22423 27291 279943 11279 11341 16425 15961 21819 20835 27465 258884 12189 11447 18155 16146 34558 21075 31213 261705 11358 11672 16402 16812 21761 22046 27335 272556 15166 11369 25011 15947 35701 20686 45942 256147 11220 11154 16156 15780 21372 20690 26745 256968 11527 11451 16876 16734 22577 22221 28539 278639 10638 11926 15742 17023 20880 22140 26170 2729310 11453 11244 16538 15727 21947 20412 27450 2503811 11117 10477 15838 14787 20904 19190 26209 23806mean 12082 11352 18083 16136 24460 21113 30921 26194STD 01566 00380 03475 00674 05607 00992 07512 01286119901 01475 00830 00420 00244Table 7 Modified Permutation Entropy individual mean and standard deviation (STD) values of the two classes studied BL- and 10M+ for119899 = 3 4 5 6 No significant differences between groups were found in some cases (Wilcoxon signed rank test)

119899 = 3 119899 = 4 119899 = 5 119899 = 6Subject BL- 10M+ BL- 10M+ BL- 10M+ BL- 10M+1 12301 09643 10896 07487 09834 06330 08655 055542 10249 09643 07971 07544 06723 06400 05899 056243 10423 10017 08249 07732 07040 06524 06221 057274 10570 10163 08500 07793 07328 06570 06524 057645 10029 10459 07879 08193 06727 06934 05950 060866 12328 10098 10879 07781 09837 06512 08738 056727 10468 10345 08252 08043 07048 06793 06239 059588 10517 10625 08359 08426 07106 07179 06281 063339 10296 10224 08266 07944 07080 06682 06271 0584910 10172 10273 08024 07876 06856 06590 06036 0573111 10093 10180 07913 07954 06703 06709 05910 05895mean 10677 10152 08650 07888 07480 06657 06611 05836STD 00828 00302 01123 00272 01180 00244 01048 00225119901 01748 00244 00137 00098

measurements which was 01 mmolL and the dissimilaritymeasure (119889 lt 01 and 119889 lt 02) As for the 119898 parametersignificant performance was achieved in all the cases tested

As is also the case with SampEn there is no consensus onthe choice of input parameter values for the calculation of PEand mPE However some guidelines exist and were followedin this pilot study Firstly the delay was equal to 1 to guaranteethat no downsampling of the original time serieswould occurSecondly the embedding dimension determining the size ofthe permutation vectors was selected taking into account itsupper limit [22] and the reported results showing that smallembedding dimensions could fail to identify changes in thedynamics of a signal [25] Therefore a range of values from119899 = 4 to 6 was tested with results showing that greatervalues of 119899 lead to better discrimination between both classes

The highest accuracy was observed with 119899 = 6 for both PE(7727) and mPE (8636) with the latter outperformingSampEn It is worth noting that the entropy of glucose timeseries estimated with PE and mPE decreases from class BL-to 10M+ for all subjects but two but the subjects wherethis decrease is not observed are different for both methodsFurthermore our results suggest that mPE is a more accuratemethod to characterize subtle differences in glucose timeseries than PE

Despite the analysis limitations due to small databasesize records length and artifacts the results confirmed thereare differences between BL- and 10M+ records that can beassociated with changes in the underlying glucose dynamicsafter DJBL implantation With a high degree of accuracy(864) it was possible to correctly distinguish between the

8 Complexity

Table 8 SampEn individual mean and standard deviation (STD)values of the two classes studied BL- and 10M+

119898 = 3 119903 = 009 119898 = 2 119903 = 025Subject BL- 10M+ BL- 10M+1 05020 03604 02972 023042 04304 03668 01667 023843 03730 04253 01639 016434 04354 03909 02069 015625 04862 03874 02337 019846 06553 02854 03584 012507 04030 03541 01414 017978 03798 03709 01602 015309 03021 02585 01112 0166610 04130 03449 02151 0171011 03906 03079 02126 01957mean 04337 03502 02061 01799STD 00914 00489 00714 00337119901 00073 00234

two classes As far as we know this is the first evidence in thisclassification context beyond variability and it opens a newperspective for the research of the DJBL implantation effects

The results are consistent For most of the cases whereAUC was relatively high (AUCgt 075) the hypothesis wasrejected and the classification accuracy was higher than 70The opposite also holds true when no significant differencewas apparent Namely there is a good correlation among allthe features used to assess the classification capabilities therewere no antagonistic results (AUCgt 075 with 119901 gt 120572)5 Conclusions

This paper explored the possible influence on the glucosedynamics of DJBL implantation The study used severalnonlinear methods The best results were obtained withmPE calculated with an embedding dimension of 6 andwith SampEn with input parameter values 119898 = 3 and119903 = 009 although many other parameter configurationsyielded suboptimal but relevant results A similar approachwas followed in other previous works related to blood glucose[42] or body temperature time series [43]

The performance of the method proposed could arguablybe enhanced using other methods of theoretically betterconsistency [44] For instance other modifications of PE canbe considered like fine-grained PE based on incorporatingthe size of the differences between datandashpoints into permu-tations and not just ranking them from smallest to largest[45] or the weighted PE based on weighting permutationpatterns depending on the amplitudes of their constituentdatandashpoints [46] Other effects should be studied such asthe influence of the artifacts the characterization of thetimendashofndashday variations (chronobiology) and the possibledifferences between other stages of the DJBL implantationThe availability of a validated set of methods for glucosedynamics assessment will arguably become a powerful toolfor the study of disease onset and progression

In summary theDJBL implantation does alter the glucosemetabolism of the subjects and these changes can be detectedby an analysis as the one proposed in this paper Thisanalysis may increase the clinical uses of the new informationgathered Additionally there is room for improvement interms of more accuracy andor more classes

Data Availability

Data are not available at this point due to data protectionregulations

Ethical Approval

All procedures performed in studies involving human partic-ipants were in accordance with the ethical standards of theinstitutional andor national research committee and withthe 1964 Helsinki declaration and its later amendments orcomparable ethical standards

Consent

Informed consent was obtained from all individual partici-pants included in the study

Conflicts of Interest

The authors declare that there are no conflicts of interest

Acknowledgments

The Czech clinical partners were supported by DRO IKEM000023001 and RVO VFN 64165 The Czech technicalpartners were supported by Research Centre for Informat-ics grant numbers CZ021010016 minus 0190000765 andSGS16231OHK33T13mdashSupport of interactive approachesto biomedical data acquisition and processing No fundingwas received to support this researchwork by the Spanish andBritish partners

References

[1] N G Forouhi and N J Wareham ldquoEpidemiology of diabetesrdquoMedicine vol 42 no 12 pp 698ndash702 2014

[2] T Seuring O Archangelidi and M Suhrcke ldquoThe economiccosts of type 2 diabetes a global systematic reviewrdquo Pharma-coEconomics vol 33 no 8 pp 811ndash831 2015

[3] J P Kassirer andMAngell ldquoLosingWeightmdashAn Ill-FatedNewYearrsquos Resolutionrdquo The New England Journal of Medicine vol338 no 1 Article ID 9414332 pp 52ndash54 1998

[4] L VanGaal and E Dirinck ldquoPharmacological approaches in thetreatment and maintenance of weight lossrdquo Diabetes Care vol39 pp S260ndashS267 2016

[5] E C Mun G L Blackburn and J B Matthews ldquoCurrent statusof medical and surgical therapy for obesityrdquo Gastroenterologyvol 120 no 3 pp 669ndash681 2001

[6] S N Kothari A J Borgert K J Kallies M T Baker and BT Grover ldquoLong-term (gt10-year) outcomes after laparoscopic

Complexity 9

roux-en-y gastric bypassrdquo Surgery for Obesity and RelatedDiseases vol 6 no 13 pp 972ndash978 2016

[7] E PWeledji ldquoOverview of gastric bypass surgeryrdquo InternationalJournal of Surgery Open vol 5 pp 11ndash19 2016

[8] S R H Patel D Hakim J Mason and N Hakim ldquoTheduodenal-jejunal bypass sleeve (EndoBarrier GastrointestinalLiner) for weight loss and treatment of type 2 diabetesrdquo Surgeryfor Obesity and Related Diseases vol 9 no 3 pp 482ndash484 2013

[9] C de Jonge S S Rensen F J Verdam et al ldquoImpact ofDuodenal-Jejunal Exclusion on Satiety Hormonesrdquo ObesitySurgery vol 26 no 3 pp 672ndash678 2016

[10] P Jirapinyo A V Haas and C C Thompson ldquo549 effect ofthe duodenal-jejunal bypass liner on glycemic control in type-2diabetic patients with obesity a meta-analysis with secondaryanalysis on weight loss and hormonal changesrdquoGastrointestinalEndoscopy vol 85 no 5 pp AB82ndashAB83 2017

[11] E G de Moura G S Lopes B da Costa Martins et al ldquoEffectsof duodenal-jejunal bypass liner (EndoBarrier) on gastricemptying in obese and type 2 diabetic patientsrdquoObesity Surgeryvol 25 no 9 pp 1618ndash1625 2015

[12] R Munoz A Dominguez F Munoz et al ldquoBaseline glycatedhemoglobin levels are associated with duodenal-jejunal bypassliner-inducedweight loss in obese patientsrdquo Surgical Endoscopyvol 28 no 4 pp 1056ndash1062 2014

[13] P Kavalkova M Mraz P Trachta et al ldquoEndocrine effectsof duodenalndashjejunal exclusion in obese patients with type 2diabetes mellitusrdquo Journal of Endocrinology vol 231 no 1 pp11ndash22 2016

[14] M Varela ldquoThe route to diabetes Loss of complexity in theglycemic profile from health through the metabolic syndrometo type 2 diabetesrdquo Diabetes Metabolic Syndrome and ObesityTargets andTherapy vol Volume 1 pp 3ndash11 2008

[15] H Ogata K Tokuyama S Nagasaka et al ldquoLong-range corre-lated glucose fluctuations in diabetesrdquo Methods of Informationin Medicine vol 46 no 2 pp 222ndash226 2007

[16] C Rodrıguez de Castro L Vigil B Vargas et al ldquoGlucosetime series complexity as a predictor of type 2 diabetesrdquoDiabetesMetabolism Research and Reviews vol 30 2017

[17] M Varela C Rodriguez L Vigil E Cirugeda A Colas and BVargas ldquoGlucose series complexity at the threshold of diabetesrdquoJournal of Diabetes vol 7 no 2 pp 287ndash293 2015

[18] R A DeFronzo ldquoPathogenesis of type 2 diabetes mellitusrdquoMedical Clinics of North America vol 88 no 4 pp 787ndash8352004

[19] J Gagliardino ldquoPhysiological endocrine control of energyhomeostasis and postprandial blood glucose levelsrdquo EuropeanReview for Medical and Pharmacological Sciences vol 9 no 2pp 75ndash92 2005

[20] J S Richman and J R Moorman ldquoPhysiological time-seriesanalysis using approximate entropy and sample entropyrdquoAmer-ican Journal of Physiology-Heart and Circulatory Physiology vol278 no 6 pp H2039ndashH2049 2000

[21] X-S Zhang R J Roy and E W Jensen ldquoEEG complexity as ameasure of depth of anesthesia for patientsrdquo IEEE Transactionson Biomedical Engineering vol 48 no 12 pp 1424ndash1433 2001

[22] C Bandt and B Pompe ldquoPermutation entropy a naturalcomplexitymeasure for time seriesrdquoPhysical ReviewLetters vol88 Article ID 174102 2002

[23] C Bian C Qin Q D Y Ma and Q Shen ldquoModifiedpermutation-entropy analysis of heartbeat dynamicsrdquo PhysicalReview E Statistical Nonlinear and Soft Matter Physics vol 85no 2 Article ID 021906 2012

[24] A Lempel and J Ziv ldquoOn the complexity of finite sequencesrdquoIEEE Transactions on Information Theory vol 22 no 1 pp 75ndash81 1976

[25] Y Cao W-W Tung J B Gao V A Protopopescu and L MHively ldquoDetecting dynamical changes in time series using theper-mutation entropyrdquo Physical Review E Statistical Nonlinearand Soft Matter Physics vol 70 no 4 Article ID 046217 2004

[26] S M Pincus I M Gladstone and R A Ehrenkranz ldquoAregularity statistic for medical data analysisrdquo Journal of ClinicalMonitoring and Computing vol 7 no 4 pp 335ndash345 1991

[27] C Liu C Liu P Shao et al ldquoComparison of different thresholdvalues r for approximate entropy Application to investigate theheart rate variability between heart failure and healthy controlgroupsrdquo Physiological Measurement vol 32 no 2 pp 167ndash1802011

[28] J M Yentes N Hunt K K Schmid J P Kaipust D McGrathand N Stergiou ldquoThe appropriate use of approximate entropyand sample entropy with short data setsrdquo Annals of BiomedicalEngineering vol 41 no 2 pp 349ndash365 2013

[29] C K Karmakar A H Khandoker R K Begg M Palaniswamiand S Taylor ldquoUnderstanding ageing effects by approximateentropy analysis of gait variabilityrdquo in Proceedings of the 200729th Annual International Conference of the IEEE Engineeringin Medicine and Biology Society pp 1965ndash1968 Lyon FranceAugust 2007

[30] S Kim D J Kim and J Jeong The Effect of Alcohol onCortical Complexity in Healthy Subjects Measured by Approxi-mate Entropy Springer Berlin Heidelberg Berlin HeidelbergGermany 2007

[31] J F Restrepo G Schlotthauer and M E Torres ldquoMaximumapproximate entropy and r threshold A new approach forregularity changes detectionrdquo Physica A Statistical Mechanicsand its Applications vol 409 pp 97ndash109 2014

[32] L Zhao S Wei C Zhang et al ldquoDetermination of sampleentropy and fuzzy measure entropy parameters for distinguish-ing congestive heart failure fromnormal sinus rhythm subjectsrdquoEntropy vol 17 no 9 pp 6270ndash6288 2015

[33] K L Masconi T E Matsha R T Erasmus and A P KengneldquoEffects of different missing data imputation techniques on theperformance of undiagnosed diabetes risk predictionmodels ina mixed-ancestry population of South Africardquo PLoS ONE vol10 no 9 pp 1ndash12 2015

[34] R L Weinstein S L Schwartz R L Brazg J R Bugler T APeyser and G V McGarraugh ldquoAccuracy of the 5-day freestylenavigator continuous glucose monitoring system Comparisonwith frequent laboratory reference measurementsrdquo DiabetesCare vol 30 no 5 pp 1125ndash1130 2007

[35] J de Winter ldquoUsing the studentrsquos tndashtest with extremely smallsample sizesrdquo Practical assessment research and evaluation vol18 no 10 pp 1ndash12 2013

[36] C Weber and O Schnell ldquoThe assessment of glycemic vari-ability and its impact on diabetes-related complications Anoverviewrdquo Diabetes Technology amp Therapeutics vol 11 no 10pp 623ndash633 2009

[37] D Cuesta-Frau P Miro-Martınez S Oltra-Crespo et alldquoModel selection for body temperature signal classificationusing both amplitude and ordinality-based entropy measuresrdquoEntropy vol 20 no 11 2018

[38] D Cuesta-Frau P Miro-Martınez S Oltra-Crespo J Jordan-Nunez B Vargas and L Vigil ldquoClassification of glucose records

10 Complexity

from patients at diabetes risk using a combined permuta-tion entropy algorithmrdquo Computer Methods and Programs inBiomedicine vol 165 pp 197ndash204 2018

[39] D CuestandashFrau M VarelandashEntrecanales A MolinandashPico andB Vargas ldquoPatterns with equal values in permutation entropyDo they really matter for biosignal classificationrdquo Complexityvol 2018 pp 1ndash15 2018

[40] C C Mayer M Bachler M Hortenhuber C Stocker AHolzinger and SWassertheurer ldquoSelection of entropy-measureparameters for knowledge discovery in heart rate variabilitydatardquo BMC Bioinformatics vol 15 no 6 article no S2 2014

[41] S Lu X Chen J K Kanters I C Solomon and K H ChonldquoAutomatic selection of the threshold value r for approximateentropyrdquo IEEE Transactions on Biomedical Engineering vol 55no 8 article no 8 pp 1966ndash1972 2008

[42] L Crenier M Lytrivi A Van Dalem B Keymeulen and BCorvilain ldquoGlucose complexity estimates insulin resistance ineither nondiabetic individuals or in type 1 diabetesrdquoThe Journalof Clinical Endocrinology amp Metabolism vol 101 no 4 p 14902016

[43] D Cuesta M Varela P Miro et al ldquoPredicting survival incritical patients by use of body temperature regularity mea-surement based on approximate entropyrdquoMedical amp BiologicalEngineering amp Computing vol 45 no 7 pp 671ndash678 2007

[44] W Chen J Zhuang W Yu and Z Wang ldquoMeasuring complex-ity using FuzzyEn ApEn and SampEnrdquoMedical Engineering ampPhysics vol 31 no 1 pp 61ndash68 2009

[45] L Xiao-Feng andWYue ldquoFine-grained permutation entropy asameasure of natural complexity for time seriesrdquoChinese PhysicsB vol 18 no 7 pp 2690ndash2695 2009

[46] B Fadlallah B Chen A Keil and J Prıncipe ldquoWeighted-permutation entropy a complexity measure for time seriesincorporating amplitude informationrdquo Physical Review E Sta-tistical Nonlinear and Soft Matter Physics vol 87 no 2 ArticleID 022911 2013

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of


Mathematical Problems in Engineering

Applied MathematicsJournal of


Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of



Engineering Mathematics

International Journal of


Operations ResearchAdvances in

Journal of


Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

2 Complexity

reduction methods have become a field of great medicaland scientific interest Successful long-term weight lossmaintenance by strategies such as changing dietary habitsor increasing physical activity is difficult [3] Other moreaggressive approaches are necessary especially when a sig-nificant weight reduction percentage is required or moreserious health consequences are involved

One of these approaches is the utilization of pharma-cotherapy which in the context of diabetes can be focusedon weight loss or on glucose control resulting in weightloss as a side effect [4] However the long-term outcomeis very limited [5] On the contrary the most successfulstrategies are based on surgical therapies The gastric bypassachieves permanent significant long-term weight reduc-tion in most of the patients that underwent this surgery[6]

Nevertheless the gastric bypass is a very invasive pro-cedure with pre- peri- and postoperative risks and pos-sible sequelae [7] An intermediate solution is the so-called Duodenal-jejunal Bypass Liner (DJBL) The DJBL isa reversible implantable device used to mimic the effectsof gastric by-pass by preventing the contact of chymuswith duodenum and proximal jejunum and delivering itin a less digested form to more distal parts of the intes-tine Obesity is a central physiopathological mechanism intype 2 diabetes mellitus (T2DM) and thus DJBL has beenused to improve metabolic control in obese patients withT2DM [8]

The effects of DJBL implantation are broad and dis-parate Many studies have assessed the impact of DJBL ona number of physiological parameters [9ndash12] We hypoth-esized that DJBL must have an influence on the glu-cose dynamics as some studies about glucose variabil-ity and DJBL have pinpointed [13] These dynamics ofthe glucose time series offer new insights into glucosemetabolism and there seems to be a direct correlationbetween (the loss of) variability in the glucose time seriesand the degree of deterioration in glucose metabolism [14ndash17]

The glucoregulatory system is effectively a complexsystem with several acting variables (caloric intake exer-cise) a number of active hormones (insulin glucagoncatecholamines growth hormone and incretins) and somewellndashestablished feedback and feedforward loops [18 19]The analysis of such a complex physiological system can beaddressed using system dynamics characterization methodsSeveral methods well suited to time series of limited durationwere used in this pilot study to characterize the effects ofDJBL Sample Entropy (SampEn) is a robust measure of regu-larity in sequences [20] whilst LempelndashZiv complexity (LZC)is an easy to compute nonlinear algorithm to estimate thecomplexity in time series [21] Permutation Entropy (PE) isanother complexitymeasure introduced by Bandt and Pompein 2002 [22] as a robust method to deal with real-world timeseries In spite of the proficiency of PE in time series analysesit neglects equalities within signals Modified PE (mPE) wasproposed to address this shortcoming in the original PEalgorithm [23]

2 Materials and Methods

21 LempelndashZiv Complexity In order to compute LZC from atime series the signal must first be converted into a sequenceof symbols In this study the signal was parsed into a binarysequence using themedian as the threshold (119879119889) For an inputtime series x = 1199091 1199092 119909119871 of length 119871 the symbols in thebinary sequence 119875 = 1199041 1199042 119904119871 are created by

119904119894 = 0 if 119909119894 lt 1198791198891 if 119909119894 ge 119879119889

(1)

The binary sequence 119875 is then scanned from left to rightto identify the different subsequences held within it and acomplexity counter 119888 is increased by one every time a newsubsequence is found (a detailed description of the algorithmcan be found in [21]) This complexity counter needs to benormalized to obtain a measure of complexity independentof the length of the time series [24]

LZC = 119888119871log2119871 (2)

LZC captures the dynamics of the time series by reflectingthe rate of new subsequences present within it

22 Permutation Entropy PE is a method measuring theentropy within a time series based on the probability ofoccurrence of all possible permutations of a certain lengthwithin it [22] With the exception of LZC all other methodsused in this study require the selection of values for differentinput parameters In the case of PE the computation relieson the selection of the embedding dimension 119899 and the timedelay 119897 The choice of embedding dimension 119899 is determinedby the number of samples available as the number ofpermutations must be less than the length of the time series(ie 119899 le 119871) [22]

In order to compute PE as follows [23] embeddingvectors need to be created from the original time series asfollows

119883119894 = [119909119894 119909119894+119897 119909119894+(119899minus1)119897] (3)

For each embedding vector the lowest data point inthe embedding vector is assigned a 0 the second lowest 1and on until all data points in the embedding vector havebeen replaced with their ranking order Once all possibleembedding vectors in the time series have been created andranked PE can be calculated by applying Shannonrsquos Entropyto quantify the proportion of possible permutations withinthe time series

PE (119899 119897) = minus119896

sum119860=1

119875119860 ln119875119860 (4)

where 119896 is the number of different subsequence rankedvectors in the original time series and PA is the fraction of thesubsequence ranked vectors A less regular signal will have agreater range of embedding vectors and therefore a higherPE

Complexity 3




x119894 = 119909119894 119909119894+1 119909119894+119898minus1 (5)


119861119898119894 (119903) = 1119871 minus 119898 minus 1119861119894 (119903)

119861119898 (119903) = 1119871 minus 119898

119871minus119898

sum119894=1

119861119898119894 (119903)

119860119898119894 (119903) = 1119871 minus 119898 minus 1119860 119894 (119903)

119860119898 (119903) = 1119871 minus 119898

119871minus119898

sum119894=1

119860119898119894 (119903)

(6)



(minuslog [119860119898 (119903)119861119898 (119903) ])


(7)








4 Complexity

0 500 1000 1500Samples

BL-

01M+

10M+

03M-Cl

ass (

ampl

itude

nor

mal

ised)


0 215 430 645 860 1075 1290Samples

BL-

01M+

10M+

03M-

Clas

s (am

plitu

de n

orm

alise

d)




Complexity 5

m

r

083 072 061 05

001 010 020 030











3 Results







6 Complexity






4 Discussion




Complexity 7








8 Complexity








Data Availability


Ethical Approval


Consent




Acknowledgments


References







Complexity 9


































10 Complexity

















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 3




x119894 = 119909119894 119909119894+1 119909119894+119898minus1 (5)


119861119898119894 (119903) = 1119871 minus 119898 minus 1119861119894 (119903)

119861119898 (119903) = 1119871 minus 119898

119871minus119898

sum119894=1

119861119898119894 (119903)

119860119898119894 (119903) = 1119871 minus 119898 minus 1119860 119894 (119903)

119860119898 (119903) = 1119871 minus 119898

119871minus119898

sum119894=1

119860119898119894 (119903)

(6)



(minuslog [119860119898 (119903)119861119898 (119903) ])


(7)








4 Complexity

0 500 1000 1500Samples

BL-

01M+

10M+

03M-Cl

ass (

ampl

itude

nor

mal

ised)


0 215 430 645 860 1075 1290Samples

BL-

01M+

10M+

03M-

Clas

s (am

plitu

de n

orm

alise

d)




Complexity 5

m

r

083 072 061 05

001 010 020 030











3 Results







6 Complexity






4 Discussion




Complexity 7








8 Complexity








Data Availability


Ethical Approval


Consent




Acknowledgments


References







Complexity 9


































10 Complexity

















Journal of












Journal of







Volume 2018






Volume 2018








4 Complexity

0 500 1000 1500Samples

BL-

01M+

10M+

03M-Cl

ass (

ampl

itude

nor

mal

ised)


0 215 430 645 860 1075 1290Samples

BL-

01M+

10M+

03M-

Clas

s (am

plitu

de n

orm

alise

d)




Complexity 5

m

r

083 072 061 05

001 010 020 030











3 Results







6 Complexity






4 Discussion




Complexity 7








8 Complexity








Data Availability


Ethical Approval


Consent




Acknowledgments


References







Complexity 9


































10 Complexity

















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 5

m

r

083 072 061 05

001 010 020 030











3 Results







6 Complexity






4 Discussion




Complexity 7








8 Complexity








Data Availability


Ethical Approval


Consent




Acknowledgments


References







Complexity 9


































10 Complexity

















Journal of












Journal of







Volume 2018






Volume 2018








6 Complexity






4 Discussion




Complexity 7








8 Complexity








Data Availability


Ethical Approval


Consent




Acknowledgments


References







Complexity 9


































10 Complexity

















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 7








8 Complexity








Data Availability


Ethical Approval


Consent




Acknowledgments


References







Complexity 9


































10 Complexity

















Journal of












Journal of







Volume 2018






Volume 2018








8 Complexity








Data Availability


Ethical Approval


Consent




Acknowledgments


References







Complexity 9


































10 Complexity

















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 9


































10 Complexity

















Journal of












Journal of







Volume 2018






Volume 2018








10 Complexity

















Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








Influence of Duodenal–Jejunal Implantation on Glucose ...

Documents

Transcript of Influence of Duodenal–Jejunal Implantation on Glucose ...