Chemical reaction engineering methodologies for post-contrastographic biomedical imaging analysis

Special theme research article

Chemical reaction engineering methodologies for post-contrastographic biomedical imaging analysis

Valentina Russo* and Luisa Di Paola

Faculty of Engineering, University Campus Bio-Medico of Rome, Via Alvaro del Portillo 21, 00128 Rome, Italy

Received 2 July 2013; Revised 27 October 2013; Accepted 3 November 2013

ABSTRACT: Post-contrastographic techniques represent an innovative method to identify pathologies out of anomalousperfusion of specific drugs (contrast agent) in ill body regions. In this framework, pharmacokinetics provides general modelsto describe the spatio-temporal distribution of drugs within the body: Simple model relies on the concept of compartment,that is, a body region with uniform properties. So, whole body can be thought of as made up of different compartments,interacting with each other by mass flows; this scheme reminds us of the typical sketch of a chemical process, whose activeelements are tanks exchanging mass flows with each other.

In this framework, chemical engineering fundamentals (transport phenomena and chemical reaction engineering) providethe basic tools to represent the dynamic evolution of biological systems, once they can be sketched in terms of interactingcompartments. The quantitative analysis, thus, is based on physically representative models, whose parameters describephysiological properties.

In this work, we present a physiologically based pharmacokinetics model based on a joint, multiscale representation ofbody seen at global (systemic compartment) and local (region of interest compartment) scales: This model is able to facedifferent limits of benchmark physiologically based pharmacokinetics models (Tofts, Brix, and Patlak), providingmeaningful and quantitative model parameters, descriptive of contrast-enhanced physiological key properties. We applythe model to the analysis of dynamic magnetic resonance imaging with a contrast agent perfusion in Crohn’s disease. Allin all, we are going to demonstrate the method that can discriminate among ill and sane tissues, whereas the systemicparameters remain substantially invariant.

The model complies very well with clinical data, assessing the vascularization degree through characteristic properties(permeation characteristic time), and the spatial analysis assesses the vascular distribution around the suspect lesions. Thisresult fosters the application of this class of models for the clinical assessment of hypervascularizing pathologies.

All in all, out of their classical field of application, chemical reaction engineering traditional methods are shown to help inthe quantitative analysis of biomedical images, which are, as for now, the cutting-edge methodologies in the post-contrastographic imaging field. © 2014 Curtin University of Technology and John Wiley & Sons, Ltd.

KEYWORDS: pharmacokinetics; multicompartmental models; dynamic contrast enhancement MRI; Crohn’s diseaseassessment

INTRODUCTION

Chemical Engineering Science provides a generalframework of use inmathematical biology and medicine:The requirement of quantitative, albeit descriptive,models has been increasing in the last years to cope withthe multitude of clinical and biological data.[1]

For instance, the application of the reaction/diffusionalong with growth kinetics has provided the physicalbasis to build up models for cancer growth, able tointerpret tumour growth data and even forecast thetumour evolution upon chemotherapeutics.[2–4]

In this framework, pharmacokinetics (PK) devotedto the interpretation of the spatio-temporal drugevolution in body is a natural playground for chemicalengineers. Physiologically based PK (PBPK) includesexplicit physical models to describe the exchange ofdrugs between different body regions, as stated byK. B. Bischoff since 1968[5]; it could benefit fromcommon and general tools of chemical engineering(mass transport and balances, binding thermodynamicsand chemical reactor engineering) to provide quantitativemodels with physiologically meaningful parameters.[6–8]

Compartmental modelling is an elective methodologyin PBPK: Living bodies are complex systems,[7] made upof different tissues and organs, committed to differentfunctions; so, a very compact, yet effective, descriptionis provided in terms of compartments, representing

*Correspondence to: Luisa Di Paola, Faculty of Engineering,University Campus Bio-Medico of Rome, Via Alvaro del Portillo21, 00128 Rome, Italy. E-mail: [email protected]

© 2014 Curtin University of Technology and John Wiley & Sons, Ltd.Curtin University is a trademark of Curtin University of Technology

ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERINGAsia-Pac. J. Chem. Eng. (2014)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/apj.1803

specific regions of interest (ROIs), characterizedby uniform properties (temperature, density andconcentration). Biological processes occurring into thedifferent body regions can be explicitly accountedfor in terms of kinetic models, allowing to considereach compartment as a perfectly mixed tank reactor[continuous stirred-tank reactor (CSTR)]: The under-lying assumption of negligible mass transfer resistancewithin the ROI (compartment) is justified by the densevessel network feeding a single tissue or organ, atuniform plasma concentration of any component.Dynamic contrast enhancement (DCE) post-

contrastographic images are recorded upon a specificmolecule [contrast agent (CA)] injection; this moleculeshould be able to enhance the backscattered signalintensity in a given biomedical imaging technique.The average signal intensity of an ROI is thenregistered along time, providing the enhancementcurve that profiles the time evolution of the CAperfusion in the ROI.DCE data are generally interpreted in an empirical,

model-free way, based on the computation of the areaunder curve of the enhancement curve that is supposedto be related to the vascularization degree of the tissueunder analysis.[9,10] On the other hand, PBPK modelstry to establish a general method to compare clinicaldata with reference values so that the clinicalassessment can be fixed on established ranges of modelparameters.[11,12]

In this context, here, we present a PBPK model aimedat interpreting DCE-magnetic resonance imaging (MRI)data: In this technique, the commonest CAs are gado-linium compounds[13] characterized by a high molecularvolume: They change the relaxation times T1 of thedifferent tissues and give enhanced signal intensity forregions entertaining CAs. They flow throughout thebody via the vascular network, permeating out of themacross the vascular walls. If these walls are modifiedby specific pathologies[14–21] (such as inflammatorydiseases or neoplasias), the spatio-temporal pattern ofCA diffusion is altered, with respect to the correspondingsane tissue.In this work, we applied the PBPK method on DCE-

MRI data from patients affected by Crohn’s disease(CD),[16,22,23] an inflammatory idiopathic bowel diseaseproducing in the connective tissues (extravascular extra-cellular space) an anomalous pattern for blood vessels.Recently, microvasculature neoangiogenesis has beenintroduced as a novel component of inflammatory boweldisease pathogenesis,[20,24–27] whereas local vascula-rization is well known to increase with the activity ofthe disease.Results are provided in terms of characteristic times

that are useful to establish a priority list of concurrentprocesses, thus becoming a valuable tool for complexsystems dynamics elucidation. The application ofchemical engineering fundamentals to the biomedical

imaging is therefore a clear example of their generalvalidity in the biological systems modelling. As amatter of fact, the transport phenomena and chemicalreactor engineering give universal tools for the inter-pretation of dynamic evolution of biological systems,in fact, being one of the pillars of biomedical engi-neering applications.[1]

MATERIALS AND METHODS

Biomedical DCE images registration andanalysis

Spatial MR images have been acquired over time frompatients upon intravenous administration of gadodiamide(Gd-DTPA-BMA, 0.1mmol/kg body weight); DCE-MRI has been performed at 1.5 T (Magnetom Simphony;Siemens Medical Systems, Erlangen, Germany) using30mT/m gradients with a phased array multicoil for thebody to permit entire coverage of the ROI. The protocolincluded dynamic Fast Low Angle SHot (FLASH)acquisition on axial plane after CA injection in a timelapse between 15 and 400 s. In Fig. 1, it is possible toappreciate the MR image enhancement in the case ofCD before and after CA administration. Once acquired,the image time series has been analysed by PK analysis,a suitable Graphic User Interface (GUI) designed by ourgroup for the PBPK DCE analysis (Fig. 2).With respect to the backscattered signal intensity, the

contrast enhancement (CE), for each pixel in any imageof the sequence, is defined as

I tk; x; yð Þ ¼ i tk; x; yð Þ � io x; yð Þ½ � (1)

where I(tk; x; y) is the signal intensity at the spatialposition (x; y), at the time tk, and i0(x; y) is the corres-ponding basal value of intensity recorded before theCA injection.The ROI average intensity IROI(tk), at a given time tk,

has been computed as the CE signal intensity averagedover the whole ROI:[28,29]

IROI tkð Þ ¼ 1N

∑x;yð Þ∈ROI

i tk; x; yð Þ � i0 x; yð Þ½ � (2)

where the summation is extended to all N pixelsenclosed into the ROI. The average intensity IROI(tk)is supposed to vary linearly with the CA concentrationin the ROI cROI (IROI(tk)∝ β � cROI): This hypothesis islargely confirmed into the CA concentration range ofclinical practice.[11]

The calibration factor β is not known a priori, and itrepresents a challenge for the clinical application ofquantitative DCE-MRI.[11] We propose a novel methodto compute β through the direct acquisition of the CA

V. RUSSO AND L. DI PAOLA Asia-Pacific Journal of Chemical Engineering

© 2014 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2014)DOI: 10.1002/apj

https://www.researchgate.net/publication/5844862_DyCoH_an_innovative_tool_to_Dynamic_Contrast_Enhancement_analysis?el=1_x_8&enrichId=rgreq-6d9d5e66-62b0-4e29-8e4b-e736dc146830&enrichSource=Y292ZXJQYWdlOzI2MjExNTA0ODtBUzoxNDI3ODMwMzc4NDE0MDhAMTQxMTA1MzUzNzQ3MA==

concentration in arterial plasma cA(t) [also known asthe arterial input function (AIF)]. Considering thepositive infusion step case, the arterial CA molar flowQP�c∞A equals the CA injection (systemic) molar flowFin=Qin � cin, being Qin as the injection flow rate andcin as the bolus concentration:

Qin�cin ¼ QPc∞A → c∞A ¼ Qincin

QP(3)

being QP as the plasma flow rate; consequently,denoting with I∞A as the signal at steady state of theaortic function, the calibration factor is derived as

β ¼ I∞Aφin�cin

(4)

where φin ¼ QinQP

represents the dilution ratio of theinfusion flow in the total plasma flow.

Intensity data are thus normalized as

yi ¼IiI∞A

¼ ciδ δ ¼ γ�τB (5)

being γ=QincinVB; in this way, β is included explicitlyin the model and can be derived through the dataregression, given the AIF cA(t).

PBPK compartmental model for DCE analysis

We applied a chemical reaction engineering approachbased on a combination of interacting tanks (exchangingflows) that represent body regions at local (ROI) andglobal (systemic) scales (Fig. 3): The resulting PBPKcompartmental model sketches the specific ROI asa membrane CSTR, the membrane representing thevascular walls, characterized by a permeabilitycoefficient PS; to describe the overall CA perfusion

Figure 1. Contrast-enhanced pathologic bowel wall in a patient with active phase of Crohn’sdisease: left, before the contrast agent injection; right, after the contrast agent injection.

Figure 2. Pharmacokinetic-analysis GUI. This figure is available in colour online at www.apjChemEng.com

Asia-Pacific Journal of Chemical Engineering METHODOLOGIES FOR POST-CONTRASTOGRAPHIC ANALYSIS


throughout the body, a systemic plasmatic compartmentis introduced in order to derive local incoming plasmaticCA molar rate eF�cA (eF is the regional blood flow feedingthe ROI), given the global CA input function FU(t):

FU tð Þ ¼ Qincinu tð Þ (6)

is the definition of FU(t) that refers to the case ofpositive infusion step (Eqn. 3). At a systemic level,the metabolic removal of the CA is accounted for alinear removal kinetics kM � cP.Generally speaking, an ROI is a tissue divided roughly

into three parts: arterial plasma (volume fraction αP),interstitial (αI) and cellular (αC). In the case of highmolecular weight CA (as gadolinium chelates), the CAmolecules are not allowed into the cellular compartmentbecause of the cell membrane barrier; thus,

cROI tð Þ ¼ αp�cP tð Þ þ αI �cI tð Þ (7)

Therefore, the mass balances in the ROI interstitialand arterial plasma compartments are respectively

dcPdt

¼ 1τB

cA tð Þ � cP tð Þ½ � � 1τP

cP tð Þ � cI tð Þ½ � (8)

dcIdt

¼ αPαI �τP cP tð Þ � cI tð Þ½ � (9)

whereas the AIF cA(t) is derived from the CA massbalance in the systemic compartment (VB blood volume):

dcAdt

¼ � 1τA

þ 1τM

� �cA tð Þ þ 1

τAcP þ FU tð Þ

VB(10)

being

• the global characteristic times:1. the residence time in the systemic blood compartment:

τA ¼ VB

QB(11)

2. the metabolic removal time:

τM ¼ 1kR

(12)

• the residence time in the ROI vascular volumefraction:

τB ¼ VPeF (13)

• the permeation characteristic time:

τP ¼ VP

PS(14)

• volume ratio in the ROI, respectively, of the arterialplasma and interstitial part:

αP ¼ VP

VROI(15)

αI ¼ VI

VROI(16)

The dynamic evolution of the system is recast in acompact manner as

x ¼ Ax tð Þ þ Bu tð Þx 0ð Þ ¼ 0

�(17)

where x(t) is the state vector that collects theconcentration functions in the three compartments:

x tð Þ ¼cA tð ÞcP tð ÞcI tð Þ

264

375 (18)

and the A and B matrices are respectively

A ¼

� 1τA

þ 1τM

� �1τA

0

1τB

� 1τB

þ 1τP

� �1τP

0αPαI �τP � αP

αI �τP

266666664

377777775

(19)

B ¼Qin�cinVB

0

0

2664

3775 (20)

Figure 3. Three compartments of physiologically basedpharmacokinetic model.



The A matrix is invertible (det(A)≠ 0), so the solutionis in closed form; with the initial condition x(0) = 0 inEqn. 17, it is

x t;Θð Þ ¼ c tð Þ ¼ eAt�x 0ð Þ þ A�1� exp Atð Þ � I½ �B (21)

being Θ the parameter vectors, as

Θ ¼ τA τB τM τP αI αP β½ �T (22)

Thus, parameters can be extracted by a least-squareslinear regression of concentration data.Reminding the normalization procedure previously

stated, the concentration variables are recorded as yAfor the systemic blood compartment and yROI = αP � yP +αI � yI for the ROI overall compartment. Finally, in acompact form, the dynamic system can be written as

yi ¼ A�yi þ B

Moreover, the properties of the Amatrix also influencethe behaviour of the system itself: It is a diagonalizablematrix and has only real negative eigenvalues(Eqn. 19), for any positive value of the parameters τA,τB, τP, τM, αP and αI (all the parameters are positive bydefinition); this property not only ensures that the systemis asymptotically stable, but also the state’s evolutiondoes not contain oscillating terms but is possiblydamped, because each component of the state is a linearcombination of exponential terms.

Classical DCE analysis vs pharmacokineticapproach

The classical DCE analysis, as stated previously, relieson the ROI backscattered intensity signal measurementover time.[28] This methodology is demonstrated tosuffer from some limitations because of the acquisitionmethod: MR is an imaging technique whose peculiarityis to be scalable with respect to the specific patient and/or the specific exam; hence, the correspondingbackscattered signal intensity may vary widely itsrange. This intrinsic characteristic presents thedrawback of not to be objective, an aspect that arisesspontaneously when one wants to compare differentpatients with a same degree of disease’s morbidity orto compare different stages of a disease in order tofollow up the efficacy of a therapy (Fig. 4).To overcome this drawback, the first strategy has

gone in the direction of improving the ROI detectionmethod by applying the deformable models of theactive contours framework[30] or the optimal masstransfer methodology[31–33] and by extending theDCE analysis to the three-dimensional case[34]; evenif all these approaches improve the ROI detection andmake it more refinished (Fig. 5) by removing the

average effect induced by dirty data (i.e. data thatcontain portions of tissue not belonging to the ROI,hence not affected by the disease and thehypervascularization phenomenon), it remainsunsolved the issue of the objectiveness of analysis.In this sense, the PBPK compartmental approach

overcomes this limitation, because all the ROImeasurements are referred to the arterial CAconcentration, taken as the maximum CAconcentration related to the maximum backscatteredsignal intensity (as it is evident in Fig. 4(B)). Thepower of the PBPK approach relies on providingresults whose goodness is based not on ROI detectionimprovements but on the reinterpretation in a physicaland physiological key of the DCE analysis.

RESULTS AND DISCUSSION

One of the limits of the classical DCE analysis is thateach patient presents his or her own CE profile,depending on different factors, such as the patient state,the tissue MR response, that are not linked to the MRtechnique (see section on Conclusions). Thus, it isalmost impossible to compare different degrees ofmorbidity even if related to the same patient, withouta proper quantitative reference. To overcome thisdrawback, the cROI has to be normalized and comparedwith the AIF that represents the maximum CAconcentration in the body: In this way, it is possibleto compare different pathological stages as well as

0 50 100 150 200 250 300 350 4000

50100150200250300350400450

time (sec)

Enh

ance

men

t

(A)

0 50 100 150 200 250 300 350 4000

0.2

0.4

0.6

0.8

1

1.2

1.4

time (sec)

Yi

(B)

Figure 4. Comparison between patients with same degreeof disease morbidity: classic dynamic contrast enhancementapproach (A) and physiologically based pharmacokineticsdynamic contrast enhancement approach (B). This figure isavailable in colour online at www.apjChemEng.com



different tissues. Further, the compartmental-DCEanalysis is a valuable tool to follow up the evolutionof the disease and assess the efficacy of a therapy.The model computes the AIF and the ROI’s enhance-

ment data in the temporal image series, providing, asexplained previously, the concentration–time curve andthe characteristic times.In this work, we applied the model to the analysis of

images from patients affected by CD; specifically, wedeal with clinical data related to patients, respectively,in the inactive and active phases, and the correspondingestimated parameters are reported in Tables 1 and 2; forcomparison, the procedure is applied also consideringas ROI different tissues.From the data collected in Tables 1 and 2, it is possible

to state parameters related to the systemic description,namely τA and τM have similar values for all tissues inthe patients; moreover, for each patient, the type of tissueand his or her health condition influence the values of αP

and τP. Indeed, τP for the pathological tissue is lowerthan for the healthy one of the same kind (in the caseof inherent, intestinal wall), and, as for the ill case, it islower in the active case with respect to the inactiveone; therefore, the increased blood vessel leakage,known to be linked to the morbidity degree, is correctlyand quantitatively registered by the model.This behaviour emerges also in Fig. 6, where we

report the normalized CE curves for the same typeof tissue in three representative patients: one healthyand the others affected by CD in the inactive andactive phases, respectively. Normalization refers tothe asymptotic value (as t→∞) of the cA(t) curveassociated with each patient (the cA(t) curve of thepatient affected by active CD is reported as reference).The ill tissue curve relative to the active phase hadthe highest asymptotic value, and it is close to thereference curve cA(t), corresponding to the arterialcompartment evolution.

Figure 5. Different region of interest detection methods in classical dynamiccontrast enhancement approach. This figure is available in colour online atwww.apjChemEng.com

Table 2. Model parameters for different tissues in Crohn’s disease (active phase).

τA (s) τB (ms) τM (s) τP (s) αP αI

Ill 18.34 2.6 18.57 17.22 0.2731 0.6568Sane 11.98 1.1 13.03 257.7 0.0965 0.2558Muscular 13.08 2.1 13.70 185.9 0.0791 0.8996Adipose 9.504 3.4 9.929 160.2 0.0548 0.8999

Table 1. Model parameters for different tissues in Crohn’s disease (inactive phase).

τA (s) τB (ms) τM (s) τP (s) αP αI

Ill 29.98 52.6 29.85 94.68 0.6449 0.0002Sane 25.28 21.1 25.91 263.5 0.2846 0.0620Muscular 24.96 469.8 24.49 205.6 0.2094 0.3242Adipose 22.51 1 22.31 254.6 0.1098 0.1849



Figure 6. Activity comparison of the sane tissue with similar tissues affected byCrohn’s disease, in the inactive and active phases. This figure is available incolour online at www.apjChemEng.com

Figure 7. Tissue comparison: the concentration curves refer to different tissues(ill, sane, muscle and fat tissue). This figure is available in colour online atwww.apjChemEng.com

Figure 8. Radial analysis for ill tissue in Crohn’s disease active phase. This figure isavailable in colour online at www.apjChemEng.com



Finally, Fig. 7 reports the normalized CE curves fordifferent tissues, and it refers to the same patient affectedby CD in the active phase; CE curve corresponding to thehighest degree of the vascularization (active phase ofCD) presents the highest asymptotic values, with regardto the corresponding curves associated with the musculartissue (well vascularized) and the adipose tissue (lessvascularized). This result is consistent with the behaviourof the τP and αP in Table 2, where the ill tissue presents asmaller τP and a larger αP, because of the large spreadingof leaking vessels. Clinical data show a high compliancewith respect to the proposed model, as witnessed by thestatistics results: correlation coefficient R is always largerthan 0.9, with the corresponding p-value lower than 0.02,for both ROI and test tissues in all clinical data under ouranalysis.These results foster the application of the model to

other hypervascularization pathologies (such as cancer)

in order to derive normalized model parameter withphysiological meaning, to be adopted in the clinicalassessment.In this direction, we have recorded the vessel para-

meters τP and αP distribution in the tissue surroundingthe lesions (i.e. in space), performing what we namedthe radial analysis of the lesion (Fig. 8).The idea of this approach is based on the fact that the

region surrounding the lesion is affected by the hypervas-cularization phenomenon due to the microvasculatureneoangiogenesis; this effect tends to fade to the physio-logical value at large distance from the lesion; hence,the aim of the radial analysis is to evaluate the amplitudeof the neovessel region. In Fig. 8, αP is larger within thelesion, decreasing to physiological values well far fromthe lesions; conversely, τP is smaller inside the lesion(hypervascularization) and increases to physiologicalvalues outside the lesion. The radial analysis is

Figure 10. Radial analysis results of the healthy tissue of the intestine wall. This figureis available in colour online at www.apjChemEng.com

Figure 9. Radial analysis for ill tissue in Crohn’s disease inactive phase. This figure isavailable in colour online at www.apjChemEng.com



performed on the ROI (tumour or flogistic area) sche-matized as a spherical volume of radius R.

CONCLUSIONS

This work presents a typical application of chemicalreaction fundamentals to the biological systemsmodelling. As a matter of fact, we built up a chemicalreaction engineering model able to represent drugperfusion: The representation has been applied to realclinical data, and it demonstrated to match the keyfeatures of different clinical cases.The model is demonstrated to comply well with

clinical data, referred to CD, and can be considered as astarting point for the clinical assessment of thispathology and other flogistic and neoplastic diseases(Figs 9 and 10). The application of the radial analysis,henceforth, demonstrated the power of the method notonly to assess clinical diagnoses but also to follow upthe course of anti-angiogenic therapies.The ability of the model to discriminate between sane

and ill (active and inactive phases) clinical cases is ademonstration of the power of chemical engineeringapproach in quantitative physiological modelling, as wellas the universality of chemical engineering fundamentalsin the interpretation of physical phenomena and systems.We described all results in terms of characteristic

times: This approach, typical of chemical engineeringmodelling, is straight yet effective in describingconcurrent transport phenomena. Indeed, in our work,the different tissues have been easily discriminatedthrough the permeation characteristic times.

This example can be extended to other similarapplications, because of the high multidisciplinarynature of chemical engineering fundamentals that canbe applied on a large scale of length (from moleculesto large size plants) and fields (from classical chemistryto biomedicine).

APPENDIX

Algorithm

The PBPK DCE analysis framework is wrapped with asuitable GUI, named PK_analysis, that allows tomanage and analyse MRI data and PBPK DCE results.The PK-analysis GUI collects and handles different

elements, such as axes, to show Digital Imaging andCommunications in Medicine (DICOM) images andplot the results, panels with check boxes, pop-upmenus and push buttons to select the specific routineof analysis. All these elements are managed by theso-called event-driven (or event-based) programmingparadigm, in which the flow of the program isdetermined by events: for example, outputs or useractions (mouse clicks and key presses), or messages/inputs from other programs, functions or threads.In Table 3 are listed the GUI functions and routines

jointly with a brief description of their behaviour.The GUI and their ancillary functions have been

developed through the MATLAB programming languageand the specific GUIDE tool for the GUI design; moreover,the application has been compiled as an executable(deployable) file for Windows and Macintosh platforms.

Table 3. Pharmacokinetic-analysis functions and routines.

Function name Description

PK_Analysis.m It is the main function devoted to the GUI’s creation and initialization; it collects a series of ancillaryfunctions for loading and opening the DICOM images, for scrolling and zooming actions inside the imagesseries, for starting of routines and subfunctions, for plotting results (both graphical and numerical) and forobtaining and setting inputs/parameters.

F_Brix_Plus.m It is the function committed to the PBPK analysis through amodified (improved) Brix method; it relies on atwo-compartment model, with a systemic blood compartment description for the arterial concentrationdetection.

F_3_Compt.m It is the function committed to the PBPK analysis through the so-called three-compartment methodology; itrelies on a three-compartment model with a systemic blood compartment description for the arterialconcentration detection and a metabolic term that considers the contrast agent consumption and itsremoval.

F_3_Compt_Delay.m It is the function committed to the PBPK analysis through the so-called three-compartment methodologywith delay; it relies on a three-compartment model with a systemic blood compartment description for thearterial concentration detection, a metabolic term that considers the contrast agent consumption and itsremoval and a two-phase kinetic that takes into account the effects induced by the time gap between thecontrast agent injection and the achievement of the perfect mixing condition in the EES compartment.

Concentration.m It is the function dedicated to the PBPKDCE analysis that yields the concentration curve over time, startingfrom a suitable cropped ROI image series. It computes both the arterial and tissue concentration, and theseoutputs are the inputs for the fitting routine that is parametric with respect to the specific model(F_Brix_Plus, F_3_Compt and F_3_Compt_Delay), the parameters initialization and their variation’srange.

PBPK, physiologically based pharmacokinetics; EES, extravascular extracellular space; DCE, dynamic contrast enhancement; ROI, regionsof interest



REFERENCES

[1] N. Peppas, R. Langer. AIChE J., 2004; 50, 536–546.[2] F. Cacace, V. Cusimano, L. Di Paola, A. Germani. Math.

Biosci., 2011; 234, 147–153.[3] S. Ferreira, M. Martins, M. Vilela. Phys. Rev. E., 2002; 65,

021907.[4] S. Feng, S. Chien. Chem. Eng. Sci., 2003; 58, 4087–4114.[5] K. Bisch, R. Dedrick. J. Pharm. Sci., 1968; 57, 1346–1351.[6] K. Bischoff, R. Dedrick, D. Zaharko, J. Longstreth. J. Pharm.

Sci., 1971; 60, 1128–1133.[7] K. Bischoff. Bull. Math. Biol., 1986; 48, 309–322.[8] M. Di Muria, G. Lamberti, G. Titomanlio. Heat Mass.

Transfer, 2009; 45, 579–589.[9] X. Yang, J. Liang, J.T. Heverhagen, G. Jia, P. Schmalbrock,

S. Sammet, R. Koch, M.V. Knopp. Magn. Reson. Med.,2008; 59(6), 1448–1456.

[10] S. De Bruyne, N. Van Damme, P. Smeets, L. Ferdinande,W. Ceelen, J. Mertens, C. Van de Wiele, R. Troisi, L. Libbrecht,S. Laurent, K. Geboes, M. Peeters. Brit. J. Cancer, 2012;106(12), 1926–1933.

[11] G. Brix, M. Bahner, U. Hoffmann, A. Horvath, W. Schreiber.Radiol, 1999; 210, 269–276.

[12] P. Tofts et al. J. Magn. Reson. Imaging, 1999; 10, 223.[13] P. Caravan, J. Ellison, T. McMurry, R. Lauffer. Chem. Rev.,

1999; 99, 2293–2352.[14] C. Hayes, A. Padhani, M. Leach. NMR Biomed., 2002; 15, 154.[15] P. Hayton, M. Brady, L. Tarassenko, N. Moore. Med. Image

Anal., 1997; 1, 207–224.[16] A. Oto, X. Fan, D. Mustafi, S.A. Jansen, G.S. Karczmar,

D.T. Rubin, A. Kayhan. Acad. Radiol., 2009; 16(10),1223–1230.

[17] G. Sempere, M. Sanjuan. Am. J. Roentgenol., 2005; 184,1829–1835.

[18] M. Rijpkema, J. Kaanders, F. Joosten, A. van der Kogel, A.Heerschap. J. Magn. Reson. Imaging, 2001; 14, 457–463.

[19] A. Padhani. Brit. J. Radiol., 2003; 76, S60–S80.

[20] J. O’Connor, A. Jackson, G. Parker, G. Jayson. Br. J. Cancer,2007; 96, 189–195.

[21] J. O’Connor, Y. Watson, A. Jackson. Radiography, 2007; 13,45–53.

[22] D. Baumgart, W. Sandborg. Lancet, 2007; 369, 1641–1657.[23] J. Oommen, A. Oto. Abdom. Imaging, 2001; 36, 134–141.[24] S. Danese, M. Sans, C. De La Motte, C. Graziani, G. West,

M.H. Phillips, R. Pola, S. Rutella, J. Willis, A. Gasbarrini,C. Fiocchi. Gastroenterology, 2006; 130, 2060–2073.

[25] D.G. Binion, P. Rafiee.Gastroenterology, 2009; 136, 400–403.[26] I.D. Pousa, J. Maté, J.P. Gisbert. Eur. J. Clin. Inv., 2009; 38(2),

72–81.[27] F. Scaldaferri, S. Vetrano, M. Sans, V. Arena, G. Straface,

E. Stigliano, A. Repici, A. Strum, A. Malesci, J. Panes,S. Yla-Herttuala, C. Fiocchi, S. Danese. Gastroenterology,2009; 136(2), 585–595.

[28] V. Russo, R. Setola, R.D. Vescovo, R. Grasso, B.B. Zobel.DyCoh: an innovative tool to dynamic contrast enhancementanalysis. In Engineering in Medicine and Biology Society. 29thAnnual International Conference of the IEEE, 63–66, 2007.

[29] V. Russo, R. Setola. Handbook of Research on AdvancedTechniques in Diagnostic Imaging and BiomedicalApplications, IGI Global, 2009.

[30] R. Setola, V. Russo. Tracking motion of deformable organ inDCE framework. In Proceedings of the 18th IFAC WorldCongress, Vol. 18, The International Federation of AutomaticControl (IFAC), 2011; pp. 9627–9632.

[31] L. Ambrosio, L.A. Caffarelli, Y. Brenier, G. Buttazzio, C. Villani.Optimal Transportation and Applications, Springer-Verlag,Berlin, 2001.

[32] S. Haker, L. Zhu, A. Tannenbaum, S. Angenent. Int. J.Comput. Vision, 2004; 60, 225–240.

[33] R. Tauseef, A. Tannenbaum. Multigrid optimal mass transportfor image registration and morphing. 6498, 2007.

[34] R. Setola, V. Russo. 3D analysis in MRI-DCE post-contrastographic framework. In Third Conference of theItalian National Bioengineering Group (GNB). ItalianNational Bioengineering Group, 2012.



Documents

Chemical reaction engineering methodologies for post-contrastographic biomedical imaging analysis