0
Research Papers

Parametric Study of the Design Variables of an Arborizing Catheter on Dispersal Volume Using a Biphasic Computational Model

[+] Author and Article Information
Egleide Y. Elenes

Department of Biomedical Engineering,
University of Texas at Austin,
107 W. Dean Keeton Street, Stop C0800,
Austin, TX 78712
e-mail: eelenes@utexas.edu

Manuel K. Rausch

Department of Aerospace Engineering and
Engineering Mechanics,
University of Texas at Austin,
2617 Wichita Street, Stop C0600,
Austin, TX 78712-1221;
Department of Biomedical Engineering,
University of Texas at Austin,
107 W. Dean Keeton Street, Stop C0800,
Austin, TX 78712
e-mail: manuel.rausch@utexas.edu

Christopher G. Rylander

Department of Mechanical Engineering,
University of Texas at Austin,
204 E. Dean Keeton Street, Stop C2200,
Austin, TX 78712-1591;
Department of Biomedical Engineering,
University of Texas at Austin,
107 W. Dean Keeton Street, Stop C0800,
Austin, TX 78712
e-mail: cgr@austin.utexas.edu

1Corresponding author.

Manuscript received December 20, 2018; final manuscript received January 28, 2019; published online April 1, 2019. Assoc. Editor: Linxia Gu.

ASME J of Medical Diagnostics 2(3), 031002 (Apr 01, 2019) (9 pages) Paper No: JESMDT-18-1066; doi: 10.1115/1.4042874 History: Received December 20, 2018; Revised January 28, 2019

Convection-enhanced delivery (CED) is an investigational therapy developed to circumvent the limitations of drug delivery to the brain. Catheters are used in CED to locally infuse therapeutic agents into brain tissue. CED has demonstrated clinical utility for treatment of malignant brain tumors; however, CED has been limited by lack of CED-specific catheters. Therefore, we developed a multiport, arborizing catheter to maximize drug distribution for CED. Using a multiphasic finite element (FE) framework, we parametrically determined the influence of design variables of the catheter on the dispersal volume of the infusion. We predicted dispersal volume of a solute infused in a permeable hyperelastic solid matrix, as a function of separation distance (ranging from 0.5 to 2.0 cm) of imbedded infusion cavities that represented individual ports in a multiport catheter. To validate the model, we compared FE solutions of pressure-controlled infusions to experimental data of indigo carmine dye infused in agarose tissue phantoms. The Tc50, defined as the infusion time required for the normalized solute concentration between two sources to equal 50% of the prescribed concentration, was determined for simulations with infusion pressures ranging from 1 to 4 kPa. In our validated model, we demonstrate that multiple ports increase dispersal volume with increasing port distance but are associated with a significant increase in infusion time. Tc50 increases approximately tenfold when doubling the port distance. Increasing the infusion flow rate (from 0.7 μL/min to 8.48 μL/min) can mitigate the increased infusion time. In conclusion, a compromise of port distance and flow rate could improve infusion duration and dispersal volume.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Ostrom, Q. T. , Gittleman, H. , Xu, J. , Kromer, C. , Wolinsky, Y. , Kruchko, C. , and Barnholtz-Sloan, J. S. , 2016, “ CBTRUS Statistical Report: Primary Brain and Other Central Nervous System Tumors Diagnosed in the United States in 2009-2013,” Neuro-Oncology, 18(Suppl. 5), pp. v1–v75. [CrossRef] [PubMed]
Berger, M. S. , 1994, “ Malignant Astrocytomas: Surgical Aspects,” Semin. Oncol., 21(2), pp. 172–185. http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=8153663 [PubMed]
Lesser, G. J. , and Grossman, S. , 1994, “ The Chemotherapy of High-Grade Astrocytomas,” Semin. Oncol., 21(2), pp. 220–235. http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=8153666 [PubMed]
Shaw, E. J. , 2000, “ Central Nervous System Overview,” Clinical Radiation Oncology, L. L. Gunderson , and J. E. Tepper , eds., Churchill-Livingstone, Philadelphia, PA, pp. 314–354.
Galanis, E. , and Bucker, J. , 2000, “ Chemotherapy for High-Grade Gliomas,” Br. J. Cancer, 82(8), pp. 1371–1380. [CrossRef] [PubMed]
Grossman, S. A. , and Batara, J. F. , 2004, “ Current Management of Glioblastoma Multiforme,” Semin. Oncol., 31(5), pp. 635–644. [CrossRef] [PubMed]
Bart, J. , Groen, H. J. M. , Hendrikse, N. H. , van der Graaf, W. T. A. , Vaalburg, W. , and de Vries, E. G. E. , 2000, “ The Blood-Brain Barrier and Oncology: New Insights Into Function and Modulation,” Cancer Treat. Rev., 26(6), pp. 449–462. [CrossRef] [PubMed]
Kemper, E. M. , Boogerd, W. , Thuis, I. , Beijnen, J. H. , and van Tellingen, O. , 2004, “ Modulation of the Blood-Brain Barrier in Oncology: Therapeutic Opportunities for the Treatment of Brain Tumours?,” Cancer Treat. Rev., 30(5), pp. 415–423. [CrossRef] [PubMed]
Ostrom, Q. T. , Gittleman, H. , Fulop, J. , Liu, M. , Blanda, R. , Kromer, C. , Wolinsky, Y. , Kruchko, C. , and Barnholtz-Sloan, J. S. , 2015, “ CBTRUS Statistical Report: Primary Brain and Central Nervous System Tumors Diagnosed in the United States in 2008–2012,” Neuro-Oncology, 17(Suppl. 4), pp. iv1–iv62. [CrossRef] [PubMed]
Morrison, P. F. , Laske, D. W. , Bobo, H. , Oldfield, E. H. , and Dedrick, R. L. , 1994, “ High-Flow Microinfusion: Tissue Penetration and Pharmacodynamics,” Am. J. Physiol., 266(1 Pt. 2), pp. R292–R305. [PubMed]
Morrison, P. F. , Chen, M. Y. , Chadwick, R. S. , Lonser, R. R. , and Oldfield, E. H. , 1999, “ Focal Delivery During Direct Infusion to Brain: Role of Flow Rate, Catheter Diameter, and Tissue Mechanics,” Am. J. Physiol., 277(4), pp. R1218–R1229. [PubMed]
Bobo, R. H. , Laske, D. W. , Akbasak, A. , Morrison, P. F. , Dedrick, R. L. , and Oldfield, E. H. , 1994, “ Convection-Enhanced Delivery of Macromolecules in the Brain,” Proc. Natl. Acad. Sci. USA, 91(6), pp. 2076–2080. [CrossRef]
Laske, D. W. , Youle, R. J. , and Oldfield, E. H. , 1997, “ Tumor Regression With Regional Distribution of the Targeted Toxin TF-CRM107 in Patients With Malignant Brain Tumors,” Nat. Med., 3(12), pp. 1362–1368. [CrossRef] [PubMed]
Vogelbaum, M. A. , and Aghi, M. K. , 2015, “ Convection-Enhanced Delivery for the Treatment of Glioblastoma,” Neuro-Oncology, 17(Suppl. 2), pp. ii3–ii8. [CrossRef] [PubMed]
Vandergrift, W. A. , Patel, S. J. , Nicholas, J. S. , and Varma, A. K. , 2006, “ Convection-Enhanced Delivery of Immunotoxins and Radioisotopes for Treatment of Malignant Gliomas,” Neurosurg. Focus, 20(4), p. E13. [CrossRef] [PubMed]
Patel, S. J. , Shapiro, W. R. , Laske, D. W. , Jensen, R. L. , Asher, A. L. , Wessels, B. W. , Carpenter, S. P. , and Shan, J. S. , 2005, “ Safety and Feasibility of Convection-Enhanced Delivery of Cotara for the Treatment of Malignant Glioma: Initial Experience in 51 Patients,” Neurosurgery, 56(6), pp. 1243–1253. [CrossRef] [PubMed]
Kunwar, S. , 2003, “ Convection Enhanced Delivery of IL13-PE38QQR for Treatment of Recurrent Malignant Glioma: Presentation of Interim Findings From Ongoing Phase I Studies,” Acta Neurochir. Suppl., 88, pp. 105–111. https://www.ncbi.nlm.nih.gov/pubmed/14531568 [PubMed]
Debinski, W. , and Tatter, S. B. , 2009, “ Convection-Enhanced Delivery for the Treatment of Brain Tumors,” Expert Rev. Neurother., 9(10), pp. 1519–1527. [CrossRef] [PubMed]
Kunwar, S. , Chang, S. , Westphal, M. , Vogelbaum, M. , Sampson, J. , Barnett, G. , Shaffrey, M. , Ram, Z. , Piepmeier, J. , Prados, M. , Croteau, D. , Pedain, C. , Leland, P. , Husain, S. R. , Joshi, B. H. , Puri, R. K. , and Group, P. S. , 2010, “ Phase III Randomized Trial of CED of IL13-PE38QQR versus Gliadel Wafers for Recurrent Glioblastoma,” Neuro Oncol., 12(8), pp. 871–881. [CrossRef] [PubMed]
Sampson, J. H. , Archer, G. , Pedain, C. , Wembacher-Schroder, E. , Westphal, M. , Kunwar, S. , Vogelbaum, M. A. , Coan, A. , Herndon, J. E. , Raghavan, R. , Brady, M. L. , Reardon, D. A. , Friedman, A. H. , Friedman, H. S. , Rodriguez-Ponce, M. I. , Chang, S. M. , Mittermeyer, S. , Croteau, D. , Puri, R. K. , and Investigators, P. T. , 2010, “ Poor Drug Distribution as a Possible Explanation for the Results of the PRECISE Trial,” J. Neurosurg., 113(2), pp. 301–309. [CrossRef] [PubMed]
Brady, M. L. , Raghavan, R. , Singh, D. , Anand, P. J. , Fleisher, A. S. , Mata, J. , Broaddus, W. C. , and Olbricht, W. L. , 2014, “ In Vivo Performance of a Microfabricated Catheter for Intraparenchymal Delivery,” J. Neurosci. Methods, 229, pp. 76–83. [CrossRef] [PubMed]
Gill, T. , Barua, N. U. , Woolley, M. , Bienemann, A. S. , Johnson, D. E. , Sullivan, S. O. , Murray, G. , Fennelly, C. , Lewis, O. , Irving, C. , Wyatt, M. J. , Moore, P. , and Gill, S. S. , 2013, “ In Vitro and In Vivo Testing of a Novel Recessed-Step Catheter for Reflux-Free Convection-Enhanced Drug Delivery to the Brain,” J. Neurosci. Methods, 219(1), pp. 1–9. [CrossRef] [PubMed]
Krauze, M. T. , Saito, R. , Noble, C. , Tamas, M. , Bringas, J. , Park, J. W. , Berger, M. S. , and Bankiewicz, K. , 2005, “ Reflux-Free Cannula for Convection-Enhanced High-Speed Delivery of Therapeutic Agents,” J. Neurosurg., 103(5), pp. 923–929. [CrossRef] [PubMed]
Vazquez, L. C. , Hagel, E. , Willenberg, B. J. , Dai, W. , Casanova, F. , Batich, C. D. , and Sarntinoranont, M. , 2012, “ Polymer-Coated Cannulas for the Reduction of Backflow During Intraparenchymal Infusions,” J. Mater. Sci. Mater. Med., 23(8), pp. 2037–2046. [CrossRef] [PubMed]
Yin, D. , Forsayeth, J. , and Bankiewicz, K. S. , 2010, “ Optimized Cannula Design and Placement for Convection-Enhanced Delivery in Rat Striatum,” J. Neurosci. Methods, 187(1), pp. 46–51. [CrossRef] [PubMed]
DeAngelis, L. M. , 2001, “ Brain Tumors,” N. Engl. J. Med., 344(2), pp. 114–123. [CrossRef] [PubMed]
Vogelbaum, M. A. , 2014, “ A Pilot Trial of Intraparenchymally-Administered Topotecan Using Convection-Enhanced Delivery (CED) in Patients With Suspected Recurrent/Progressive WHO Grade III or IV (High Grade) Glioma Requiring Stereotactic Biopsy,” National Library of Medicine, Bethesda, MD, Document No. NCT02278510.
Barua, N. U. , Hopkins, K. , Woolley, M. , O'Sullivan, K. , Harrison, R. , Edwards, R. J. , Bienemann, A. , Wyatt, M. J. , Arshad, A. , and Gill, S. , 2016, “ A Novel Implantable Catheter System With Transcutaneous Port for Intermittent Convection-Enhanced Delivery of Carboplatin for Recurrent Glioblastoma,” Drug Delivery, 23(1), pp. 17–173. [CrossRef]
Elenes, E. Y. , and Rylander, C. G. , 2017, “ Maximizing Local Access to Therapeutic Deliveries in Glioblastoma—Part II: Arborizing Catheter for Convection-Enhanced Delivery in Tissue Phantoms,” Glioblastoma, S. De Vleeschouwer , ed., Codon Publications, Brisbane, QLD.
Mauck, R. L. , Hung, C. T. , and Ateshian, G. A. , 2003, “ Modeling of Neutral Solute Transport in a Dynamically Loaded Porous Permeable Gel: Implications for Articular Cartilage Biosynthesis and Tissue Engineering,” ASME J. Biomech. Eng., 125(5), pp. 602–614. [CrossRef]
Ateshian, G. A. , Likhitpanichkul, M. , and Hung, C. T. , 2006, “ A Mixture Theory Analysis for Passive Transport in Osmotic Loading of Cells,” J. Biomech., 39(3), pp. 464–475. [CrossRef] [PubMed]
Ateshian, G. A. , Albro, M. B. , Maas, S. , and Weiss, J. A. , 2011, “ Finite Element Implementation of Mechanochemical Phenomena in Neutral Deformable Porous Media Under Finite Deformation,” ASME J. Biomech. Eng., 133(8), p. 081005. [CrossRef]
Maas, S. , Rawlins, D. , Weiss, J. A. , and Ateshian, G. A. , 2015, “ FEBio: Finite Elements for Biomechanics Theory Manual,” accessed Feb. 27, 2019, http://mrl.sci.utah.edu/software/febio
Gu, W. Y. , Lai, W. M. , and Mow, V. C. , 1998, “ A Mixture Theory for Charged-Hydrated Soft Tissues Containing Multi-Electrolytes: Passive Transport and Swelling Behaviors,” ASME J. Biomech. Eng., 120(2), pp. 169–180. [CrossRef]
Normand, V. , Lootens, D. L. , Amici, E. , Plucknett, K. P. , and Aymard, P. , 2000, “ New Insights Into Agarose Gel Mechanical Properties,” Biomacromolecules, 1(4), pp. 730–738. [CrossRef] [PubMed]
Pluen, A. , Netti, P. A. , Jain, R. K. , and Berk, D. A. , 1999, “ Diffusion of Macromolecules in Agarose Gels: Comparison of Linear and Globular Configurations,” Biophys. J., 77(1), pp. 542–552. [CrossRef] [PubMed]
Holmes, M. H. , and Mow, V. C. , 1990, “ The Nonlinear Characteristics of Soft Gels and Hydrated Connective Tissues in Ultrafiltration,” J. Biomech., 23(11), pp. 1145–1156. [CrossRef] [PubMed]
Lai, W. M. , and Mow, V. C. , 1980, “ Drag-Induced Compression of Articular Cartilage During a Permeation Experiment,” Biorheology, 17(1–2), pp. 111–123. [CrossRef] [PubMed]
Garcia, J. J. , and Smith, J. H. , 2009, “ A Biphasic Hyperelastic Model for the Analysis of Fluid and Mass Transport in Brain Tissue,” Ann. Biomed. Eng., 37(2), pp. 375–386. [CrossRef] [PubMed]
Chen, X. , and Sarntinoranont, M. , 2007, “ Biphasic Finite Element Model of Solute Transport for Direct Infusion Into Nervous Tissue,” Ann. Biomed. Eng., 35(12), pp. 2145–2158. [CrossRef] [PubMed]
Sobey, I. , and Wirth, B. , 2006, “ Effect of Non-Linear Permeability in a Spherically Symmetric Model of Hydrocephalus,” Math. Med. Biol., 23(4), pp. 339–361. [CrossRef] [PubMed]
Cheng, S. , and Bilston, L. E. , 2007, “ Unconfined Compression of White Matter,” J. Biomech., 40(1), pp. 117–124. [CrossRef] [PubMed]
Muralidharan, P. , 2006, “ Finite Deformation Biphasic Material Characterization and Modeling of Agarose Gel for Functional Tissue Engineering Applications,” Master's thesis, University of Cincinnati, Cincinnati, OH.
Tao, L. , and Nicholson, C. , 1996, “ Diffusion of Albumins in Rat Cortical Slices and Relevance to Volume Transmission,” Neuroscience, 75(3), pp. 839–847. [CrossRef] [PubMed]
Rausch, M. K. , and Humphrey, J. D. , 2017, “ A Computational Model of the Biochemomechanics of an Evolving Occlusive Thrombus,” J. Elasticity, 129(1–2), pp. 125–144. [CrossRef]
Chen, M. Y. , Lonser, R. R. , Morrison, P. F. , Governale, L. S. , and Oldfield, E. H. , 1999, “ Variables Affecting Convection-Enhanced Delivery to the Striatum: A Systematic Examination of Rate of Infusion, Cannula Size, Infusate Concentration, and Tissue–Cannula Sealing Time,” J. Neurosurg., 90(2), pp. 315–320. [CrossRef] [PubMed]
Netti, P. A. , and Travascio, F. , 2003, “ Coupled Macromolecular Transport and Gel Mechanics: Poroviscoelastic Approach,” Bioeng. Food Nat. Prod., 49(6), pp. 1580–1596.
Sampson, J. H. , Akabani, G. , Archer, G. E. , Bigner, D. D. , Berger, M. S. , Friedman, A. H. , Friedman, H. S. , Herndon , J. E., II , Kunwar, S. , Marcus, S. , McLendon, R. E. , Paolino, A. , Penne, K. , Provenzale, J. , Quinn, J. , Reardon, D. A. , Rich, J. , Stenzel, T. , Tourt-Uhlig, S. , Wikstrand, C. , Wong, T. , Williams, R. , Yuan, F. , Zalutsky, M. R. , and Pastan, I. , 2003, “ Progress Report of a Phase I Study of the Intracerebral Microinfusion of a Recombinant Chimeric Protein Composed of Transforming Growth Factor (TGF)-α and a Mutated Form of the Pseudomonas Exotoxin Termed PE-38 (TP-38) for the Treatment of Malignant Brain Tumors,” J. Neurooncol., 65(1), pp. 27–35. [CrossRef] [PubMed]
Rand, R. W. , Kreitman, R. J. , Patronas, N. , Varricchio, F. , Pastan, I. , and Puri, R. K. , 2000, “ Intratumoral Administration of Recombinant Circularly Permuted Interleukin-4-Pseudonomas Exotoxin in Patients With High-Grade Glioma,” Clin. Cancer Res., 6(6), pp. 2157–2165. https://www.ncbi.nlm.nih.gov/pubmed/10873064
Lonser, R. R. , Walbridge, S. , Garmestani, K. , Butman, J. A. , Walters, H. A. , Vortmeyer, A. O. , Morrison, P. F. , Brechbiel, M. W. , and Oldfield, E. H. , 2002, “ Successful and Safe Perfusion of the Primate Brainstem: In Vivo Magnetic Resonance Imaging of Macromolecular Distribution During Infusion,” J. Neurosurg., 97(4), pp. 905–913. [CrossRef] [PubMed]
Lonser, R. R. , Sarntinoranont, M. , Morrison, P. F. , and Oldfield, E. H. , 2015, “ Convection-Enhanced Delivery to the Central Nervous System,” J. Neurosurg., 122(3), pp. 697–706. [CrossRef] [PubMed]
Chittiboina, P. , Heiss, J. D. , Warren, K. E. , and Lonser, R. R. , 2014, “ Magnetic Resonance Imaging Properties of Convective Delivery in Diffuse Intrinsic Pontine Gliomas,” J. Neurosurg. Pediatr., 13(3), pp. 276–282. [CrossRef] [PubMed]
Smith, J. H. , and Garcia, J. J. , 2011, “ A Nonlinear Biphasic Model of Flow-Controlled Infusions in Brain: Mass Transport Analyses,” J. Biomech., 44(3), pp. 524–531. [CrossRef] [PubMed]
Polivka , J., Jr. , Polivka, J. , Holubec, L. , Kubikova, T. , Priban, V. , Hes, O. , Pivovarcikova, K. , and Treskova, I. , 2017, “ Advances in Experimental Targeted Therapy and Immunotherapy for Patients With Glioblastoma Multiforme,” Anticancer Res., 37(1), pp. 21–33. http://ar.iiarjournals.org/content/37/1/21.full [PubMed]
Touat, M. , Idbaih, A. , Sanson, M. , and Ligon, K. L. , 2017, “ Glioblastoma Targeted Therapy: Updated Approaches From Recent Biological Insights,” Ann. Oncol., 28(7), pp. 1457–1472. [CrossRef] [PubMed]
Xu, Y. Y. , Gao, P. , Sun, Y. , and Duan, Y. R. , 2015, “ Development of Targeted Therapies in Treatment of Glioblastoma,” Cancer Biol. Med., 12(3), pp. 223–237. [PubMed]
Chen, Z. J. , Broaddus, W. C. , Viswanathan, R. R. , Raghavan, R. , and Gillies, G. T. , 2002, “ Intraparenchymal Drug Delivery Via Positive-Pressure Infusion: Experimental and Modeling Studies of Poroelasticity in Brain Phantom Gels,” IEEE Trans. Biomed. Eng., 49(2), pp. 85–96. [CrossRef] [PubMed]
Chen, Z. J. , Gillies, G. T. , Broaddus, W. C. , Prabhu, S. S. , Fillmore, H. , Mitchell, R. M. , Corwin, F. D. , and Fatouros, P. P. , 2004, “ A Realistic Brain Tissue Phantom for Intraparenchymal Infusion Studies,” J. Neurosurg., 101(2), pp. 314–322. [CrossRef] [PubMed]
Kaczmarek, M. , Subramaniam, R. P. , and Neff, S. R. , 1997, “ The Hydromechanics of Hydrocephalus: Steady-State Solutions for Cylindrical Geometry,” Bull. Math. Biol., 59(2), pp. 295–323. [CrossRef] [PubMed]
Stewart, D. C. , Rubiano, A. , Dyson, K. , and Simmons, C. S. , 2017, “ Mechanical Characterization of Human Brain Tumors From Patients and Comparison to Potential Surgical Phantoms,” PLoS One, 12(6), p. e0177561. [CrossRef] [PubMed]
Raghavan, R. , Brady, M. L. , Rodriguez-Ponce, M. I. , Hartlep, A. , Pedain, C. , and Sampson, J. H. , 2006, “ Convection-Enhanced Delivery of Therapeutics for Brain Disease, and Its Optimization,” Neurosurg. Focus, 20(4), p. E12. [CrossRef] [PubMed]
Smith, J. H. , and Garcia, J. J. , 2009, “ A Nonlinear Biphasic Model of Flow-Controlled Infusion in Brain: Fluid Transport and Tissue Deformation Analyses,” J. Biomech., 42(13), pp. 2017–2025. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

Schematic of the arborizing catheter, showing multiple ports or microneedles deflected from the primary cannula

Grahic Jump Location
Fig. 2

(a) FE model geometry of the biphasic solid with two embedded infusion cavities (i.e., source ports) and (b) constant infusion pressure applied at a rapid ramp time of t0 and constant effective solute concentration were applied at the inner surface boundary of the infusion cavities. Zero interstitial pressure and traction free surface boundary conditions were applied at the outer boundaries of the solid.

Grahic Jump Location
Fig. 3

(a) Indigo carmine stock solution (5% w/w) was serially diluted from 1:100 in an agarose solution and plotted as percentages versus their corresponding grayscale intensity threshold values from postprocessed images and (b) volume dispersed, Vd (milliliter), plotted versus time (minutes) for FE simulations compared to infusion experiments (Exp) for two flow rates (1 μL/min and 7 μL/min)

Grahic Jump Location
Fig. 4

Prescribed infusion pressure versus resultant average infusion flow rates. Flow rates were calculated after the pressure was applied at a rapid ramp to the boundary of the infusion cavity.

Grahic Jump Location
Fig. 5

Representative color maps for simulation with source ports (infusion cavities) spaced 1.5 cm apart for infusion pressures ranging from 1 kPa to 4 kPa. The color map shows the normalized effective solute concentration at time = 300 min.

Grahic Jump Location
Fig. 6

Time (hours) required for the normalized effective concentration between sources to reach 50% of the prescribed concentration at the sources (Tc50) versus the port separation distance, d (centimeter)

Grahic Jump Location
Fig. 7

Time to reach a concentration overlap (ranging from 0.1 to 0.5 of the normalized effective solute concentration) midway between two sources for port separation distance ranging from 0.5 to 2.0 cm

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In