• Aucun résultat trouvé

Design, characterization, and In vivo evaluation of a magnetorheological fluid as a hemostatic agent

N/A
N/A
Protected

Academic year: 2021

Partager "Design, characterization, and In vivo evaluation of a magnetorheological fluid as a hemostatic agent"

Copied!
315
0
0

Texte intégral

(1)

Design, Characterization, and

In Vivo Evaluation of

a Magnetorheological Fluid as a Hemostatic Agent

by

Yonatan Tekleab

Submitted to the Department of Aeronautics and Astronautics

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy in Materials and Structures

at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

February 2021

c

○ Massachusetts Institute of Technology 2021. All rights reserved.

Author . . . .

Department of Aeronautics and Astronautics

December 31, 2020

Certified by . . . .

Wesley L. Harris

Charles Stark Draper Professor of Aeronautics and Astronautics

Thesis Supervisor

Certified by . . . .

Gareth H. McKinley

School of Engineering Professor of Teaching Innovation

Thesis Supervisor

Certified by . . . .

George C. Velmahos

John F. Burke Professor of Surgery, Harvard Medical School

Thesis Supervisor

Certified by . . . .

Roger D. Kamm

Cecil and Ida Green Distinguished Prof of Biological & Mechanical Eng

Thesis Supervisor

Accepted by . . . .

Zoltan Spakovszky

Professor of Aeronautics and Astronautics

Chair, Graduate Program Committee

(2)
(3)

Design, Characterization, and In Vivo Evaluation of a

Magnetorheological Fluid as a Hemostatic Agent

by

Yonatan Tekleab

Submitted to the Department of Aeronautics and Astronautics on December 31, 2020, in partial fulfillment of the

requirements for the degree of

Doctor of Philosophy in Materials and Structures

Abstract

Magnetorheological (MR) fluids and elastomers have been shown to be effective in sys-tems requiring responsive materials with fast-acting, tunable properties. Recently, use of MR fluids (MRFs) has risen with improvements in quality and cost of raw materials and manufacturing processes. Traditionally used in automotive and manufacturing industries, these applications have recently extended into healthcare, improving pros-thetics and exoskeleton designs. Inspired by such applications, we have developed a magnetically-actuated fluidic valve using a biocompatible MRF suspension for use in the human body, to slow hemorrhage.

Traumatic injury is the leading cause of death in the United States and globally for people of ages 1 − 46, 30% to 40% of which are attributed to severe or prolonged hemorrhage. Furthermore, 80% of trauma-related deaths in the first hour of hospital admission are due to hemorrhagic shock. Field-responsive, biocompatible suspensions present a unique opportunity to intervene in pre- and early hospital settings to stem thoracic and abdominal bleeding. Such a hemostat would provide physicians more time to resuscitate patients upon trauma facility admission.

The MR valve comprises an injectable, biocompatible MRF suspension with ex-ternally placed permanent magnets. To produce a significant, controllable MR effect in a bleeding patient near the site of injury, the MRF was designed for biocompati-bility, rapid delivery, and spatially localized actuation within blood vessels such that bleeding can be controlled. Understanding and optimizing the particulate chaining and accumulation mechanisms by which the MRF stems bleeding in situ is critically important.

We have synthesized and characterized a novel, biocompatible, MR hemostatic agent for use with hemorrhaging patients through a minimally invasive technique. Safety and efficacy of the technique have been demonstrated through benchtop and preliminary in vivo (rat) models. Using small Neodymium magnets in 3D printed holders that can be worn by field surgeons, we demonstrate arrest of a major hemor-rhagic event over a range of physiologically-relevant flow conditions, with sustained blood pressure, dramatically reduced volumes of blood loss, and significantly increased

(4)

survival time. In future phases, safety and efficacy of the method will be demonstrated in swine models before testing in controlled surgical settings with human patients. Thesis Supervisor: Wesley L. Harris

Title: Charles Stark Draper Professor of Aeronautics and Astronautics Thesis Supervisor: Gareth H. McKinley

Title: School of Engineering Professor of Teaching Innovation Thesis Supervisor: George C. Velmahos

Title: John F. Burke Professor of Surgery, Harvard Medical School Thesis Supervisor: Roger D. Kamm

(5)

Acknowledgments

I was fortunate to have the support of many people during my time at MIT, for which I am extremely grateful. First, I would like to thank my advisors, Professors Wesley Harris and Gareth McKinley for their guidance throughout my Ph.D. Wes has provided enormous support, offering his time and energy, providing necessary resources, and dispensing sage wisdom and encouragement when needed. Gareth is truly a wonderful mentor and teacher and has been a beacon of knowledge and creativity throughout our research. I’m tremendously appreciative for all that I have learned throughout this process, and I hope that my contributions to the engineering and medical research communities can amount to a fraction of what I have gained in this time.

I am grateful to my thesis committee for helping me mold my research problem into a worthy project and primed to be successful. Thank you to Professor Kamm for your insightful expertise, deliberate comments. Thank you to Dr. Velmahos for providing the motivation, resources, and clinical perspective on addressing the tech-nical challenges in this work. Between visiting your OR and our many conversations, I’ve very much enjoyed my time working with you and your group.

I’d also like to thank the team of people who helped make the animal experiments possible. Dr. Galit Frydman was instrumental in helping design the animal exper-iments and provided critical insight into the analyses as well. Dr. Michael Duggan provided additional technical and veterinary expertise to guide our experiments. Fi-nally, these experiments would not have been possible without the surgical skills of Drs. Nikolaos Kokoroskos and Casey Luckhurst. Resources were provided by the KSRL staff, primarily John Beagle and Jess Burke. I also thank Dr. King and the Arsenal Medical for use of their data acquisition system in our experiments. Thanks to Dr. Noelle Saillant for providing access to her group’s thromboelastograph. I also appreciate the financial support provided in part by the Aero/Astro department as well as Dean Blanche Staton and the Office of the MIT Dean for Graduate Education.

(6)

Over the past several years, I have had the opportunity to work alongside some of the brightest people in the world, but also some of the most committed, compassion-ate, and gracious individuals as well. My group members in both the HRT and NNF have been wonderful colleagues, with whom I hope to cross paths in the future. I’d like to specifically thank Shabnam, Crystal, Bavand, Michela, Philippe, who helped introduce me to the horrors and delights of experimental rheology and 3D printing. Thank you to Dave Roberts and Todd Billings for their assistance with designing and manufacturing some of our experimental arrangements.

I’d like to thank three groups at MIT who’ve helped me get away from the lab and maintain my sanity. MIT AeroAfro was established a few years ago, and I’m so happy to have met these amazing people. I will fondly remember our lunches, socials, and organized community events when I reflect my graduate work. The second is Noonball, an informal group of students, postdocs, and professors that have been meeting in the Z-Center to play basketball at noon for the past several decades. As I sit in my home during the COVID pandemic lockdown, writing my thesis, I reminisce fondly on those runs and realize how necessary they were for my cardiovascular health! The third group is the Aero/Astro IM basketball team. Behind our fearless captain, Al, we came close to winning it all a few times, but never quite made it over the hump. It was enjoyable nonetheless.

Completing my Ph.D. work would not have been possible without the endless support of my friends and family, whom I love dearly. I have the most wonderful aunts, uncles, and cousins, and I’m thankful for your show of support. To my siblings, Adrian, Sarah, and Dawit, you inspire me each and every day through your words and actions. Our conversations and banter are always uplifting.

I am blessed to have two loving parents, Elsa and Tekleab. My parents overcame incredible hardships to come to America in pursuit of a better life for their children. They have long instilled in us the importance and value of education and scholarship. Mom, Dad, thank you for your hard work to help us realize our goals. I find inspiration in your story. I may not say it enough, but I love and appreciate the sacrifices you’ve made, and I hope my work can be a testament to this.

(7)

Early in my Ph.D., I married my sweetheart, Yamicia. Juggling classes, research, qualifying exam prep, and planning a wedding was not easy, but our wedding day is one that I will forever cherish. Words cannot express how much you have meant to me during this process. You have been and continue to be my source of strength and resolve. You see me at my best and my worst, yet your love and support is unwavering. For this and so much more, thank you. I’m so blessed to have you in my life. I love you deeply. Thank you, also to my in-laws, Dave, Doris, and David, Jr., for your encouragement over the years. I am so excited to meet the two new additions to our growing family in the coming months! To my expected twins, please know that you have an army of people praying and rooting for your success and that you will always be loved.

Finally, I wish to express thanks to God for my many blessings, because I know that through Him, all things are possible. My Christian faith has been important as I navigated the past several years. Now, more than ever as we all remain distanced in our homes, I recognize the importance of faith and family.

(8)
(9)

Contents

1 Introduction 35 1.1 Motivation . . . 36 1.2 Background . . . 38 1.2.1 Hypovolemic shock . . . 38 1.2.2 Magnetorheological fluids . . . 39

1.2.3 Magnetization and the MR effect . . . 41

1.3 Thesis Objectives . . . 47

2 Literature Review 49 2.1 Magnetization of Materials . . . 49

2.2 Magnetic Particles: Size, Shape, Dispersity . . . 51

2.3 Rheological Models for MR Fluids . . . 54

2.4 MR Devices and Applications . . . 57

2.5 Biocompatibility of Magnetic Fields and Magnetized Materials . . . . 61

2.5.1 Magnetic fields inside the body and susceptibilities of human tissues . . . 61

2.5.2 Physical properties of blood . . . 63

2.5.3 Biomedical applications of magnetic materials . . . 71

2.6 Magnetic Embolization In Vivo . . . 74

3 Design of a Magnetorheological Hemostatic Agent 77 3.1 Operational environment: The hemorrhaging systemic circulation . . 78

(10)

3.2.1 MR effect in the circulation . . . 81

3.3 Biocompatibility . . . 87

3.4 Usability . . . 91

3.4.1 Externally applied field . . . 91

3.4.2 MRF stability . . . 92 3.4.3 Injectability . . . 95 3.5 Constituents . . . 98 3.5.1 Solid phase . . . 98 3.5.2 Carrier fluid . . . 104 3.6 MRF design . . . 118 3.7 Conclusion . . . 120

4 Magnetorheological Fluid Synthesis and Characterization 121 4.1 Constituent characteristics . . . 122

4.1.1 Solid phase: carbonyl iron powder . . . 122

4.1.2 Carrier fluid: sodium carboxymethyl cellulose aqueous solution 132 4.2 MRF formulation . . . 135

4.2.1 Synthesis and characterization . . . 135

4.3 Final MRF characterization . . . 155

4.4 Biological response to MRF . . . 158

4.4.1 Blood-MRF interaction . . . 158

4.4.2 Coagulative response . . . 161

4.5 Conclusion . . . 168

5 In Vitro Testing of Hemostatic MRF 169 5.1 A fluidic system modeling intravascular blood flow . . . 169

5.1.1 Human blood substitute . . . 170

5.1.2 Fluidic system design . . . 173

5.1.3 Testing conditions . . . 179

5.1.4 System calibration and validation . . . 180

(11)

5.2 Flow-occlusion experiments . . . 189

5.2.1 Aqueous glycerol experiments . . . 191

5.2.2 Swine blood experiments . . . 200

5.3 Conclusion . . . 206

6 In Vivo Testing of Hemostatic MRF 209 6.1 In Vivo Efficacy Model . . . 210

6.1.1 Data capture: vital signs and MRF placement . . . 211

6.1.2 Death criterion . . . 213

6.1.3 Coagulation response . . . 214

6.1.4 Injury and MRF infusion . . . 215

6.1.5 Magnet holder assembly . . . 217

6.1.6 Optimal loading . . . 219

6.1.7 Therapeutic dose . . . 221

6.1.8 Experimental protocol . . . 222

6.2 In Vitro Model of Rat Vascular Injury and MRF Intervention . . . . 224

6.2.1 Rat IVC flow . . . 224

6.2.2 MRF intervention . . . 226

6.2.3 In vitro model analysis . . . 227

6.3 MRF Efficacy In Vivo . . . 231

6.3.1 Experimental Results . . . 233

6.3.2 Discussion . . . 239

6.4 MRF safety . . . 247

6.4.1 Preliminary safety study . . . 248

6.4.2 Histopathology analysis . . . 249

6.5 Conclusion . . . 254

7 Conclusions and Future Work 257 7.1 A Magnetorheological Hemostatic Agent . . . 257

(12)

A Quantity Definitions 263

A.1 Magnetic Quantities . . . 263

A.2 Rheology Quantities . . . 264

B Experimental Equipment 265 B.1 Magnetorheology Fixture Description . . . 265

B.2 Syringe holder . . . 271

C Data Tables 273 C.1 Fluidic System: Aqueous Glycerol Data . . . 273

C.2 Fluidic System: Swine Blood Data . . . 274

D Calculations 277 D.1 Calibration for In Vitro Rat Circulation Experiments . . . 277

E Procedures and Data Capture Examples 279 E.1 In Vivo Efficacy Protocols . . . 279

E.1.1 Hemodilution . . . 279

E.1.2 Heparin anticoagulation . . . 282

E.1.3 Necropsy . . . 285

E.2 In Vivo experiment data collection examples . . . 287

E.2.1 Event times and biomarker data . . . 287

(13)

List of Figures

1-1 2014: [22] The leading causes of death in the United States, ages 1 – 46 years . . . 37 1-2 2015: [87, 86] Annual economic burden attributed to trauma is $671

bil-lion, significantly higher than that of many other diseases . . . 37 1-3 Magnetic particles with external magnetic field (a) off, (b) on [2].

With magnetic field off, magnetic dipole moments (arrows) of the par-ticle domains are randomly oriented. When field is turned on, the dipole moments of the particle domains align with the externally ap-plied magnetic field, changing the field locally near the particle surface and producing attractive forces between particles parallel to the field lines and repulsive force orthogonally. . . 44 1-4 Illustration of the coordinate system for two magnetic particles of size

2𝑎, 𝑖 and 𝑗, interacting in a uniform external field, H0 [66]. 𝑟𝑖𝑗 = ‖rj − ri‖ denotes the distance between 𝑖 and 𝑗, while 𝜃𝑖𝑗 is the angle between the uniform field vector, and rij. . . 45

2-1 Left: magnetic domain orientation of materials under the influence of an applied magnetic field. Right: M-H relationship of these materi-als. Note that paramagnetic and diamagnetic materials have linear M-H relationships, while ferrimagnetic and ferromagnetic materials have nonlinear, path dependent M-H relationships [10, 256, 130] . . . 50

(14)

2-2 Optical micrographs (120x) showing the microstructure of MR fluid suspensions in a uniform magnetic field [280]. (a) Micron-sized, monodis-perse. (b) Nanometer-sized monodismonodis-perse. (c) Bidisperse MR fluid. The bidisperse structures formed are evenly spaced and less porous than the monodisperse structures. . . 53 2-3 MR fluids exhibit 𝐻2

0 scaling with storage modulus, 𝐺

[279] . . . . . 55

2-4 MRF devices generally operate in one of three modes: shear, squeeze, and flow [191]. The MR fluid (orange) is positioned between two sur-faces (gray) to resist a moving boundary (shear mode), a compressing or oscillating surface (squeeze mode), or a pressure gradient (flow or valve mode). . . 58

2-5 Magnetic field gradients choke the flow in the region between the two poles of the permanent magnets [98]. The effective diameter of the channel will decrease as the magnetic gradient grows larger. . . 60 2-6 The range of magnetic susceptibilities is illustrated in the top chart on

two logarithmic scales, one for negative susceptibilities (diamagnetic) and another for positive susceptibilities (paramagnetic/ferromagnetic). The bottom chart indicates the magnetic susceptibilities of some com-mon materials and biological tissues [235]. . . 62

2-7 Whole human blood composition by volume. . . 63

2-8 SEM images show red blood cells in (A) random and (B) rouleaux formations. . . 66

2-9 Capillary breakup extensional rheometry produces a uniaxial exten-sional flow within a necked region. The exponential decay of the neck diameter is characteristic of a viscoelastic fluid. The data (circles) fit well with the upper convected Maxwell constitutive model (line) [144]. 69

(15)

2-10 Blood viscosity increases with oxygen concentration in both male (a) and female (b) blood. This is demonstrated by the fully oxygen sat-urated blood (blue) having higher a higher measured viscosity than freshly drawn blood blood (red), which has a higher measured viscos-ity than oxygen depleted blood (green) [270]. . . 70

2-11 Tunneling electron microscope (TEM) image of a magnetotactic bac-terium [44]. The dark nodules are magnetosomes of magnetite crystals in a chain formation. This chain acts as a dipole that can orient the bacterium with magnetic field lines. . . 72

2-12 Clearance of foreign particles from the circulation is dependent on (a) size, (b) shape, and (c) surface charge [25]. . . 73

3-1 The blood vessels of the human body were plastinated and all other tissue removed to illustrate the spanning complexity of the body’s vas-cular network. Source: https://imgur.com/M3msR3S . . . 80

3-2 The body tightly regulates systemic circulation pressure. Blood flow is pulsatile in the arteries, but the flow resistance of the arterioles and capillaries drops the pressure and dampens the oscillations. Short-term, immediate regulation occurs through constriction and dilation of the vessels. [164] . . . 81

3-3 Model of the obstructed blood vessel. The velocity profile, v(𝑟), and downstream pressure, 𝑃 , go to zero once the vessel is fully obstructed. The upstream systolic pressure, 𝑃𝑠𝑦𝑠, maintains it’s value. . . 82

(16)

3-4 Red and blue solid lines show magnetic field strength decay along the center axis from the surface (𝑧 = 0) of a cylinder and a block magnet, respectively. Both magnets are modeled as N52 neodymium perma-nent magnets. Dashed lines represent the magnetic field produced by magnetic dipoles placed at the center of the solid magnets with equiv-alent magnetic dipole moments as the solid magnets. For distances greater than 3ℎ from the surface, the solid magnet field strength (solid lines) converge to the dipole solution (dashed lines). . . 86 3-5 Vessel wall shear rates [271], ˙𝛾𝑤𝑎𝑙𝑙 ∈ [102, 104] 𝑠−1 . . . 90 3-6 Segments of a syringe. Plunger is depressed by thumb with index and

middle fingers on either side of the barrel just below the flange. The plunger pushes fluid through the barrel, which has the widest diame-ter, into the nozzle and through the narrowest portion, the needle bore.

Source: https://www.nationwidechildrens.org/-/media/nch/family-resources/ helping-hands/images/hhv60_photo6.ashx . . . 96

3-7 The sedimentation rate normalized by the particle diameter is plotted as a function of zero shear viscosity of the carrier fluid. Sedimentation rates for CIP SM, HF, HQ, and HS are all well within the same order of magnitude. Reference values of sedimentation rate are listed for zero shear viscosity of water, blood and honey. . . 101 3-8 Casson models are plotted for blood (red) and an ideal carrier fluid(black).

The shear stress (𝜏 ) is plotted with solid lines on the left axis, and the viscosity (𝜂) with dashed lines on the right axis. Our ideal fluid is shear thinning with a yield stress of about 50 𝑚𝑃 𝑎. . . 105 3-9 After 5 weeks, CIP suspended in 5.5%wt Carbopol○ 934 polymer so-R

lution has been oxidized, destabilizing the suspension. . . 108 3-10 Shown above are flow curves of three polymeric solutions that are

(17)

3-11 An illustration of the chemical structure of carboxymethyl cellulose. Each monomer contains three functional groups (𝑅), where 𝑅 = 𝐻 or 𝑅 = 𝐶𝐻2𝐶𝑂𝑂𝑁 𝑎. The monomer length, 𝑏 = 0.515 𝑛𝑚 [156] . . . 111

3-12 (A) Benchabane (left) and Lopez (right) show shear thinning behavior of NaCMC over a variety of concentrations. At very low concentra-tions, the solution appears to be Newtonian-like, with a constant vis-cosity. The plot on the left uses a higher MW NaCMC, which results in higher viscosity at equivalent shear rates as well as a more pronounced shear thinning. (B) Plotting the specific viscosity as a function of con-centration illustrates how the viscosity scaling changes between the concentration domains. Benchabane (left) shows a marked increase in the scaling between the semidilute unentangled and semidilute en-tangled domain. Although it is denoted 𝑐*, this is indeed the entan-glement concentration, 𝑐𝑒 and not the overlap concentration. Lopez (right) captures the semidilute unentangled, semidilute entangled and concentrated regimes [20, 158]. . . 113

3-13 (A) Increasing solvent salt concentration lowers solution shear stress. The effect is more pronounced for a divalent salt [139]. (B) Lower-ing solution pH decreases viscosity. The effect is more pronounced at higher concentrations [71]. (C) Polymer chain zeta potential decreases with increasing salt concentration [139]. (D) Below neutral pH, poly-mer chain zeta potential decreases as pH is reduced. Above neutral pH, zeta potential is largely unaffected with changing pH [39]. . . 115

3-14 Specific viscosity of NaCMC aqueous solutions. (A) Dissolved salts (NaCl in this instance) reduce the NaCMC solution viscosity. (B) Viscosity increases with polymer size across all concentration regimes. (C) Larger NaCMC DS increases solution viscosity at concentrations below the entanglement transition. . . 116

(18)

3-15 Viscosity of CMC solutions at polymer concentrations of 1.0%wt, 1.5%wt, and 2.0%wt NaCMC (𝑀 𝑊 = 250 𝑘𝐷𝑎, 𝐷𝑆 ≈ 0.95)are plotted across shear rates observed in blood vessels. The flow curve profiles are similar to those observed in literature. . . 117

4-1 Carbonyl iron powders, HS (left) and SM (right) grades at different magnifications. Green length scales indicate lengths of 10 𝜇𝑚 (top panel), 2 𝜇𝑚 (middle panel), and 200 𝑛𝑚 (bottom panel). The SM particles have softer and rougher, less round surfaces than HS particles because they undergo additional annealing under hydrogen to remove impurities. This also results in a higher purity of iron and therefore a higher 𝑀𝑆. Photo credit: Crystal Owens . . . 124

4-2 M-H curves for SM and HS grades of BASF carbonyl iron powders. There is very little hysteresis in CIP, as the lower (H) and upper (N) data sit nearly on top of one another. Dashed lines represent the fitting function (Equation 4.1). A magnified inset shows the slight offset in the hysteresis curves. The coercivity and remanence can be seen in the magnified inset, labeled 𝐻𝐶 and 𝑀𝑟, respectively. Though we were not able to achieve saturation experimentally, the fitted curves allow us to estimate 𝑀𝑆. . . 126

4-3 Top panel: Specific susceptibility as a function of applied field. At low applied fields, this quantity is larger for the SM particles, indicating that they will produce an overall larger magnetic response. This gap between SM and HS diminishes with increasing applied field strength. Bottom panel: The magnetic susceptibility is plotted against the total magnetic field strength, 𝐻. . . 128

(19)

4-4 Bingham (black dashed line) and Casson (red dashed line) viscosity models for 1%vol CIP in S60 calibration oil at moderately high field strengths show a clear difference. Especially at higher shear rates, the Casson model shows a greater degree of accuracy with experimental data (blue filled circles). . . 131 4-5 Top panel: Rate-controlled flow curves of 1%vol CIP in S60 viscosity

standard. Dashed lines represent the fitted Casson functions, and the color of the circles/lines correspond to the magnetic field strength. Lower panel: An increase in yield stress is observed with increasing applied field strength. . . 132 4-6 Viscosity flow curves are plotted across a large range of shear rates

for 1.5%wt and 2.0%wt aqueous CMC along with fits to Cross (dashed lines) and Carreau (solid lines) constitutive models. At low shear rates, the difference in viscosity is nearly an order of magnitude. Due to shear thinning, the curves begin to converge toward the solvent viscosity at high shear rates. Cross model appears to provide a closer fit. . . 134 4-7 Flow curves show consistent viscosity for the carrier fluid (2%wt CMC

solution) over a 2 month span (left), but the MRF shows aging as the viscosity changes over time. . . 136 4-8 The MRF flow curves (right plot) shift downward as the it ages. The

presence of an increasing yield stress can also be seen from the data and the modified Cross fits (dashed lines) for the aged MRF, leveling off at low shear rates. For comparison, the shear stress of the carrier fluid (left plot) shows little to no effect of aging. . . 137 4-9 Viscosity (left) and shear stress (right) flow curves for CMC (blue),

MRFv1 (red), and MRFv2 (green) at the 3 week time point. There is a dramatic difference between the older and revised versions of the MRF. The CMC data is fit to the Cross model, MRFv1 is fit to the modified Cross model, and MRFv2 is fit to both, for comparison. . . . 142

(20)

4-10 Observing sedimentation of MRFv1 at 3 weeks and MRFv2 1 week. Snapshots were taken as soon as the cuvettes are filled (𝑡 = 0 hours), at 𝑡 = 24 hours, and at 𝑡 = 48 hours. MRFv2 does not show evi-dence of sedimentation until about 48 hours, while the CIP in MRFv1 precipitates much more rapidly. . . 143

4-11 A TA.XTplus texture analyzer measures the force needed to extrude the MRFv2 at 0.25 𝑚𝐿, 0.50 𝑚𝐿/𝑠, 0.75 𝑚𝐿/𝑠, and 1.00 𝑚𝐿/𝑠 flow rates in a syringe with an 18G catheter. The measurements are wildly inconsistent, with several exceeding the capacity of the load cell, lead-ing to the conclusion agglomerates jammlead-ing the catheter. . . 146

4-12 Left panel: The CIP particles in MRFv2 form large agglomerates. Top-right panel: A histogram and fitted Weibull PDF (red line) of the CIP agglomerate size distribution. Bottom-right panel: Empirical (solid line with black dot) and Weibull (dahsed line) CDFs for CIP agglom-erate (blue) and CIP particle (red) distributions. . . 148

4-13 Samples of MRFv2 were placed into an ultrasonic bath (𝑓 = 40 𝑘𝐻𝑧, 𝑃 = 110 𝑊 ) for 10, 20, 30, and 60 minute periods. The evolution of the microstructure can be seen in these 30𝑋 magnified images. The ultrasonic bath breaks up agglomerates across the spectrum of sizes over the first 10 minutes. With continued sonication, we observe a reversal of this trend; the smaller particles coalesce, forming larger structures. . . 152

(21)

4-14 Images of CIP agglomerates at 30𝑋 magnification (left panel), ag-glomerate distribution histogram with Weibull PDF (middle panel), and CDFs for CIP particles and agglomerates (right panel). From top to bottom, the images and plots correspond to filtered CIP in N10 oil, filtered and sonicated CIP in N10 oil, filtered CIP in 2%wt CMC, and filtered and sonicated CIP in 2%wt CIP in CMC. This data suggests that filtration removes the very large agglomerates, sonication helps to further break down agglomerates, and CMC adsorption stabilizes the suspension, preventing agglomerate formation. . . 154 4-15 Viscosity (left) and shear stress (right) flow curves for the MRF

formu-lated with unmodified CIP (blue) and CIP that has been both filtered and sonicated (green). Though the two MRFs have an equal CIP vol-ume fraction (𝜑 = 5%), MRFv3 exhibits a slightly lower viscosity. . . 155 4-16 Flow curves for the MRF with uniform applied fields up to 810 𝑘𝐴/𝑚

are plotted (left). The yield stress is captured from each flow curve by fitting the data to the modified Cross model, and plotted against the applied field strength (right). At low field strengths, the data is slightly below the low field approximation (dashed straight line). . . . 157 4-17 Blood from donor #3 was incubated with saline (control), CMC, CIP,

and MRF for 90 minutes at 37∘𝐶. 60𝑋 images of blood smears show erythrocytes, leukocytes, platelets as well as the CI particles. . . 160 4-18 Mean clotting time of the whole blood after mixing with additives

(blue) is plotted with ± 𝜎 error bars (black). Dotted orange lines cor-respond to the evolution of the control sample (mean ± 𝜎) as it ages. 163 4-19 (A) The cup-pin system in the TEG analyzer is illustrated. The cup

is loaded with the blood sample and raised to the suspended pin. The attached torsion wire measures the pin displacement while the cup is rotated at a fixed amplitude and frequency during the coagulation process. (B) An example TEG tracing, labeled with the characteristic parameters to describing the evolution of coagulation [57]. . . 164

(22)

4-20 TEG parameters 𝑅, 𝐾, 𝛼, and 𝑀 𝐴 are plotted for Native TEG tests using citrated blood. The recommended time window for testing cit-rated blood is highlighted (green box). For whole blood, we observe a shift in parameters towards a hypercoagulable state. The blood+MRF data indicates hypercoagulation in reaction time and rate of clot growth, but a weaker clot formed. . . 167

5-1 Swine blood was drawn and anticoagulated with Lithium Heparin. The viscosity (𝑇 = 37∘𝐶) was captured 2 hours after drawing (blue) and again 16 hours after drawing (red). We observe a slight increase in vis-cosity with age. From about ˙𝛾 = 25 𝑠−1, both swine blood curves have reasonably good agreement with the Casson model fit for human blood (purple). The Newtonian model provides a reasonable approximation at high shear rates (green). Vessel wall shear stress is indicated along the x-axis by vessel type. . . 171

5-2 Top panel: the blood (or blood substitute) flows from the pressurized tank (station 0) through the tubing, exiting at station 18. The flow rate is calculated by collecting the runoff into a container and mea-suring the rate of accumulation. The segment between station 14 and 15 represents the artery. Center panel: MRF is infused between sta-tions 12 and 13. Lower panel: the fluidic system can be modeled as an electrical system with electrical current, potential, and resistance respectively representing the flow rate (𝑄), hydraulic head (ℎ), and flow resistance as head loss per unit flow rate (𝑅𝑖 ≡ ∆ℎ𝑖/𝑄𝑖). When the switch is closed, MRF flow rate is fixed at 𝑄𝑀, and zero when it is open. . . 174

(23)

5-3 Flow rates were measured across a range of tank pressures (∘) using water. The fluidic system was calibrated by fitting the data measured using water to tune the minor loss coefficients, shifting the theoreti-cal P-Q curve (dashed blue line) right, creating a theoreti-calibrated P-Q flow curve (solid blue line). The calibrated model was validated by compar-ing the calibrated flow curve for 37% glycerol (solid black line) with experimental measurements (∘) (𝑅2 = 0.9959). The major losses for water and 37% glycerol (dotted blue/black lines) are plotted to illus-trate the relative impact of the minor loss terms on the total pressure loss. . . 182

5-4 The fluidic system was calibrated by fitting the flow rate-pressure data (∘) measured using 37% glycerol to tune the minor loss coefficients, yielding in only minor shift of the theoretical P-Q curve (dashed black line) left, creating a calibrated P-Q flow curve (solid black line). The calibrated model was validated by comparing the calibrated flow curve for swine blood (solid red line) with experimental measurements (∘) (𝑅2 = 0.9837). The major losses for 37% glycerol and swine blood (dotted black/red lines) are plotted to illustrate the relative impact of the minor loss terms on the total pressure loss. . . 183

5-5 N52 neodymium permanent magnet fit inside holders that were 3D printed to hold the axially magnetized cylindrical magnets. The holder ensures the magnets maintain a fixed separation so that the field is static, and also that the tubing remains fixed in place and cannot move in response to the flow of MRF through the field. The orientation of the magnets creates a field that is symmetric about the vessel and also almost completely orthogonal to the flow for the segment within the holder. A viewing window was also included in the design to monitor the evolution of the obstruction. . . 185

(24)

5-6 Axially magnetized, cylindrical N52-grade neodymium magnets (19.1 𝑚𝑚 diameter, 9.5 𝑚𝑚 thickness) are arranged in magnet holders, produc-ing a field that was modelled usproduc-ing an axisymmetric mesh in FEMM. Top panel: A pair of the magnets are arranged such that their surfaces are separated by 12.7 𝑚𝑚, with their magnetic moments both pointing in the ˆz direction. A heat map and field lines for the double pair (left) and single pair (right) show the field produced by the magnets. Blue lines parallel to, and slightly above and below the r-axis represent the vessel walls. Bottom panel: The field strength is plotted along the vessel centerline axis (𝑧 = 0) for the double (black line) and single (orange line) magnet pairs (left plot). For reference, the magnet ra-dius is indicated in grey. The field strength is also plotted along the magnet axis (𝑟 = 0) for both magnet pairs (right, inset plot). The field strength increases moving away from the vessel centerline approaching the vessel wall. The field strength is largest at (𝑟 = 0 , 𝑧 = 12𝐷15). . . 186 5-7 Aqueous glycerol solution flows through the tubing and MRF infusion

begins at 𝑡 = 0. As the MRF approaches the magnetic field (orange arrows), the CI particles become magnetized and are attracted to the regions of highest field strength near the walls. Trapped particles resist and attract more particles eventually forming chains that span the vessel and densify until an occlusion is formed. Some CI particles break off and escape the magnetic trap, as seen in the two lower images. The blood flow (green arrows) diminishes as the obstruction takes place, while the MRF infusion rate is constant until the flow is stopped. . . 193 5-8 An image of the CIP chains formed in the tubing following an

experi-ment. The pressure has been turned off and the system is at rest, but the magnetic field is still active. The image is overlayed on a plot of the magnetic field strength. In the region of the particles, the field is below 40, 𝑘𝐴/𝑚, and the particles are still able to form chains that nearly span the tube. . . 194

(25)

5-9 The test cases are color coded with solid circles marking the data points and linear interpolants connecting the data to estimate flow rates within the intervals. The total flow-through volumes are indi-cated beside each data set. . . 195 5-10 Upper panel: Flow rate measurements were repeated for TC 3 (low

𝐻0,𝑚𝑎𝑥, low 𝑃14) and 5 (high 𝐻0,𝑚𝑎𝑥, high 𝑃14), both of which have the low MRF infusion rate. Center panel: The repeated measurements were averaged (blue line) and fit to a 7th degree polynomial (red line) to produce mean flow curves. Lower panel: The volume of fluid that has flown through the vessel is (𝑉𝐵) plotted as a function of time. A larger 𝑉𝐵 was collected in TC 5 than TC 3 although TC 5 has a shorter 𝑡𝑂𝑐𝑐. . . 199 5-11 Flow rate data using swine blood is displayed for test cases 5–8. The

raw data for each trial (upper panel), the mean flow curve (center panel), and flow-through volume (bottom panel) are plotted over time. TC 8 has the shortest average occlusion time and lowest flow-through volume. . . 205

6-1 The image shows cannulation of the rat IVC with a 22G IV catheter, which is later pulled to inflict the IVC injury. The state of the rat’s condition is monitored through pressure tracings, blood analysis, and core temperature through catheters in the left and right femoral arter-ies (24G) and a thermocouple probe in the rectum. A catheter is also placed in the left femoral vein for MRF/saline infusion. . . 216 6-2 The magnet assembly comprises a tripod with the upper magnet holder

mounted on a lead screw and a triangular base with slots to fit the tripod legs. Both magnet holders can be quickly removed and replaced with magnets/holders appropriate for the injury. Magnet spacing is adjusted by turning the lead screw. . . 218

(26)

6-3 Major vessels of the rat’s venous circulation are annotated. The injury location is marked with a red cross and the magnet (drawn to scale) placement is shaded in blue. Catheter insertion point in the left femoral vein is also noted. . . 223

6-4 The fluidic system simulating rat IVC flow uses gravitational head to drives the flow (right). The aqueous glycerol solution flows from the tubing, above station 1, through the system and out at station 8. Fluid-filled pressure catheters are placed at stations 2 and 7 to monitor/record pressure tracings. The segment between stations 3 and 4 has increased resistance to represent capillary flow. The 22G catheter inside the tubing at station 5 (inset image) is withdrawn to produce the injury. MRF is infused at station 4. Magnets in 3D printed holders (lower left) are placed above and below station 5. The schematic of the systemic circulation (upper left) is labeled with the corresponding stations [165]. . . 225

6-5 The baseline experiment (i.e., no injury) illustrates that the raw (hol-low marker) and corrected (solid marker) measurements for both 𝑃2 (red triangle) and 𝑃7 (blue triangle) agree with Equation 6.8 (red/blue solid lines) and Equation 6.10 (red/blue dashed lines), respectively. . 229

6-6 Left panel: Measured (hollow marker) and corrected (solid marker) pressures are plotted for control (blue) and MRF (red) experiments. At the end of the experiment, the rate of 𝑃𝑐𝑜𝑟𝑟

2 and 𝑃7𝑐𝑜𝑟𝑟 decay for control is 1.32 𝑚𝑚𝐻𝑔/𝑚𝑖𝑛, while 𝑃2𝑐𝑜𝑟𝑟 and 𝑃7𝑐𝑜𝑟𝑟 are nearly stable for the MRF test. Right panel: The Nd magnets in 3D printed holders produce a field that leads to aggregation of the CI particles, which obstructs the vessel and occludes the fluid flow. The dark blue oval represents the surface of the cross-sectional rat abdomen. . . 230

(27)

6-7 This image captures the experiment arrangement for one of the MRF efficacy experiments at 𝑡 = +20 𝑚𝑖𝑛 (after injury). The rat is posi-tioned in the assembly between the upper and lower magnet holders with the IVC injury aligned with the center of the pair. Anesthesia from the isoflurane vaporizer is delivered through a nose cone. The PowerLab DAQ monitors BP measurements from the right femoral artery catheter and sends the tracing to recording software. The lower right image shows the discolored IVC between the magnet holders, containing activated MRF. . . 232

6-8 MAP tracings of control (blue) and MRF (red) rats are plotted for all experiment from injury (red line at 𝑡 = 0) to completion, which is when MAP drops below 15 𝑚𝑚𝐻𝑔 or when 𝑡 = +60 𝑚𝑖𝑛. Following injury, MAP falls rapidly in all cases and never recovers or stabilizes for five of six controls and half of MRF experiments. For the remaining half of the MRF rats and the sixth control, MAP recovers above at least 52 𝑚𝑚𝐻𝑔 before experiment completion. Green ellipses indicate MAP decline preceded by flushing the arterial line (dashed) or a biomarker draw (solid). . . 235

6-9 Survival time and injury blood loss are shown for the 6 control (blue) and 10 MRF (red) experiments as bar charts (upper panels) and rel-ative frequency histograms (middle panels). Most of the control data (rats 1-5) have a narrow distribution, while the MRF data is very much bimodal. A scatter plot (lower panel) illustrates the dependence of survival time on blood loss. . . 237

(28)

6-10 The survival function presents the survival proportion over time. This representation more clearly shows a rather uniformly distributed sur-vival time (almost linear) for 5 of the 6 rats. The MRF curve shows a rapid descent; 40% of the MRF group expires within a few minutes. Another 40% survive the duration, and the remaining 20% lie some-where in between. The median MRF survival time (]𝑡𝑠) is nearly 2.7 times the median control group survival time. . . 240 6-11 Radiopauqe CI particles are visible inside the infusion catheter, the

il-iac vein and the abdominal IVC. A dense region of particles is observed near the injury and more sparsely concentrated particles slightly down-stream in the IVC. The cluster of particles surrounding the magnet and injury form a plug 1.9 𝑐𝑚 in length. . . 242 6-12 Purple arrows show atypical blood flowing produced by the pressure

at the IVC injury falling to atmospheric pressure. Anastomoses (pur-ple, bi-directional arrows) allow venous blood to circumvent the MRF obstruction; redirected blood flows from veins in the pelvic region to the portal veins. This blood can then make its way to the IVC, joining blood from other branches (purple, uni-directional arrows). . . 244 6-13 There appears to be a negative association between the magnet

separa-tion height and percentage of blood volume lost for ℎ𝑠𝑒𝑝 ∈ [3.9, 5.2] 𝑐𝑚. The association is characterized by the Spearman correlation coeffi-cient, 𝜌 = −0.720. . . 246 6-14 A black residue is visible throughout the lungs of Safety Rat 1 (left

image) following IV infusion of the MRF at 4% 𝐵𝑉 (0.20%𝐵𝑉 CIP). The heart and lungs are also engorged, appearing to still be filled with blood/fluid after removal. For comparison, the lungs and heart of a rat from the efficacy control group is shown on the right. The lungs maintain their bright pink color and the heart and lungs have collapsed, which is typical once the lungs have been removed. . . 249

(29)

6-15 Following the experiment, a necropsy is performed to harvest and pre-serve the liver, kidneys, spleen, a toe, the heart and lungs, the brain as well as the IVC. The MRF is visible inside the IVC. . . 250 B-1 3D printed syringe holder . . . 271 D-1 Pressure measurements taken at stations 2 and 7 provide MAP and

CVP. A calibration test without injury was performed, yielding the 𝑃2 (red line) and 𝑃7 (blue line) curves above, while the dashed lines rep-resent expected curves for a closed circulation system. These measure-ments are adjusted for the flow-through volume to provide corrected head loss (ℎ𝑐𝑜𝑟𝑟

(30)
(31)

List of Tables

2.1 Estimated values for Reynolds number (𝑅𝑒), Womersley number (𝛼), and wall shear rate ( ˙𝛾𝑤), taken from Robertson et al. [219]. . . 65 2.2 Commonly used blood viscosity models. Model parameters for blood

are taken from Robertson et al., which were calculated from blood from a healthy, 25 year old female donor with 𝐻𝑡 = 0.4, and measured at 𝑇 = 23∘𝐶 [219]. . . 68

3.1 Properties of select carbonyl iron powder grades produced by BASF. BASF produces some particles that have undergone annealing in hy-drogen gas to further extract impurities and reduce the hardness of the particles. Product undergoing this treatment are designated soft ; otherwise, they are considered hard [239]. Note: this hard/soft desig-nation is not related to the qualitative degree of magnetic coercivity and remanence occasionally used to describe magnetic materials. . . . 100 3.2 Commonly used rheological modifiers in pharmaceutical applications.

The pH listed is for the range of typical formulations used in pharma-ceuticals. . . 106

4.1 BASF’s inspection test results are listed for the specific lots of CIP SM and HS received along with the sales specifications for these products. 122 4.2 The ferromagnetic hysteresis loops for BASF SM and HS grade

car-bonyl iron powders were measured using a VSM. These characteristic properties were extracted from the fitting function in Equation 4.1. . 127

(32)

4.3 Fitting parameters and RMSE for Cross and Carreau models of 1.5%wt CMC and 2.0%wt CMC. In each cell of the table the Cross and Carreau fit-ting parameters are listed to the left and right of the vertical bar, respectively. The lower bound for 𝜂∞ was set equal to the viscosity of water. With this bound, all fitting solutions converged to this value. With the bound removed, high shear viscosity converged around 10−10, however the RMSE values for fits with and without the lower bound 𝜂∞ were within 2% of each other. . . 133 4.4 Modified Cross model parameters. The yield stress is fixed to zero

through 48 hours because the measured flow points do not go to low enough shear rates for model to capture the yielding transition behavior.138 4.5 𝑑10, 𝑑50, and 𝑑90 values for CIP agglomerates in MRFv2 before

sonica-tion and after sonicating samples for 10, 20, 30, and 60 minutes. The percentage difference in agglomerate size from baseline (i.e., 0 𝑚𝑖𝑛) is in parentheses. . . 151 4.6 𝑑10, 𝑑50, and 𝑑90 values for CIP agglomerates after only filtering and

after filtering and sonicating the particles, suspended in N10 oil and 2%wt CMC. 𝜑 = 5% for all samples. The filtered and sonicated CIP in CMC exhibits with best dispersibility, having the smallest size dis-tribution. . . 153 4.7 Yield stress, zero-shear viscosity, relaxation time, and flow index

pa-rameters are captured by fitting the MRF Magnetorheological data to the modified Cross Model (Equation 4.9) for flow curves with applied magnetic fields up to 810 𝑘𝐴/𝑚. . . 157 4.8 The additives are prepared by diluting with normal saline. The MRF

dilution is 1 : 1 by volume, and the CIP and CMC are diluted to reflect the same concentrations as in the MRF. . . 159 4.9 Clotting time was tested using whole blood from three healthy, adult

donors (A, B, & C) after mixing with additives, CMC, CIP, MRF, or saline (control) to determine the impact on clotting time. . . 163

(33)

5.1 Experimental conditions for the eight test cases assessing the impact of the MR effect on blood flow through the fluidic system. . . 180 5.2 Dimensionless numbers for blood and MRF immediately following

in-fusion and after flow occlusion to the left and right of the arrow, re-spectively. 𝑀 𝑛 is calculated using 𝐻𝑅𝑀 𝑆 and paramagnetic volume susceptibility of 𝜒 = 10−5 for blood. A maximum 𝐵𝑖 for the MRF is calculated using the maximum packing density of CIP with double magnet pairs. . . 190 5.3 The key metrics from the fluidic system experiments using aqueous

glycerol are presented for a single iteration for each test case and also for repeated measurements of TC 3 and 5. 𝑡𝑂𝑐𝑐 represents the duration between the start of MRF infusion and a complete obstruction in the vessel. 𝑉𝐵 is the total volume of blood passing through the vessel during this period. Υ30 𝑠 is the 30-second obstruction index, indicates the effectiveness of the MRF over a 30 second interval. . . 201 5.4 The key metrics from the fluidic system experiments using swine blood

are presented for each iteration, with mean and standard deviations below in boldface for test cases 5–8. . . 203 6.1 Obstruction indices, Υ, are provided for the MRF rat experiments. . 247 6.2 Safety was assessed by infusing MRF at different doses in three rats. . 248 A.1 Definition of some quantities used in magnetodynamics. Vector and

vector field quantities are presented in boldface type. . . 263 A.2 Definition of some quantities used in rheology. . . 264 C.1 Key metrics from the fluidic system experiments using aqueous glycerol

are presented for each iteration, with mean and standard deviations below in boldface. Color coding the test cases and sorting by Υ30 𝑠, we see that TC 5 (yellow rows) iterations tend to have larger obstruction indices than TC 3 iterations. . . 274

(34)

C.2 Key metrics from the fluidic system experiments using swine blood are presented for each iteration, with mean and standard deviations below in boldface. Color coding the test cases and sorting by Υ30 𝑠, we see TC 8 (gray) clustered near the top and TC 5 (yellow) clustered at the bottom. TC 7 (pink) have a much wider distribution, overlapping with most of TC 6 and 5 as well as a small portion of Tc 8. TC 6 (brown) appears to be mostly clustered below TC 8 and above TC 5 and 7, with a single iteration much further below. The mean values, similarly indicate TC 8 and 5 have distinctly low and high values, respectively, of 𝑡𝑂𝑐𝑐 and 𝑉𝐵, while TC 6 and 7 have more overlap within one standard deviation. . . 275

(35)

Chapter 1

Introduction

This thesis investigates the characterization, design, and implementation of a mag-netorheological fluid (MRF) in a biological setting for the purpose of reducing and possibly controlling the rate of blood loss in a human patient. Although the work focuses on controlling bleeding in a traumatic situation, similar strategies may po-tentially be used in controlled operating environments in which bleeding is difficult to manage. For example, unexpected intraoperative bleeding [172], routine medical procedure for individuals with clotting disorders, and postpartum hemorrhage caused by abnormal detachment of the placenta (placenta accreta) [72, 79] are procedures that require extreme care due to the high risk of significant bleeding.

Magnetorheological fluids belong to a class of materials described as smart ma-terials due to their ability to change their material properties quickly in response to external stimuli. Smart materials include fluids and solids that alter their properties (e.g., shape, viscosity, strength, thermal or electrical conductivity, refractive index) through energy conversion [85, 173, 272]. Specifically, magnetorheological (MR) fluids along with electrorheological (ER) fluids belong to a subset called smart fluids. In the presence of an applied magnetic fields, MR fluids can quickly and dramatically alter their bulk properties by converting magnetic energy from the external field into mechanical energy. The ability to manipulate the intrinsic properties of a fluid in real time can be advantageous in a wide spectrum of cases. Since the 1990s, MR and ER fluids have replaced common working fluids in many mechanical systems that

(36)

require dynamic fluid behavior for several purposes including lubrication, damping, heat transfer/insulation, and pressure transmission [111, 112]. Note that external and applied are used interchangeably to describe a magnetic field produced by an external source such as a permanent magnet or electromagnet. The external magnetic field is denoted by H0 and has no contribution from any magnetic moment induced within, or produced by, the MRF.

MR fluids are typically designed for use in mechanical systems, presenting unique challenges in using conventional MR fluids in the human body, and more so, under traumatic stress conditions. Nevertheless, the ability to dramatically and reversibly change rheological properties by controlling magnetic fields externally can provide great benefits for medics and first responders in reducing blood loss and lowering mortality due to hemorrhaging.

1.1

Motivation

Traumatic injury is the leading cause of death in people between the ages of 1 and 46, both in the United States and worldwide (Figure 1-1) [22]. In 2013, there were 192, 945 trauma related deaths in the United States and over 30 million patients treated for non-fatal injuries.

The economic impact of trauma in the United States is also extremely costly. The Center for Disease Control (CDC) estimates the total annual cost of trauma in the US to be $671 billion, more than double the cost due to heart disease, cancer, or diabetes (Figure 1-2) [87, 86].

The World Health Organization estimates that injury accounted for 5 million deaths (9% of global mortality) in the year 2000 [68]. Furthermore, hemorrhage accounts for 30 to 40% of trauma deaths, second only to traumatic brain injury, and of these, 33 − 56% occur before the patient can be taken to a trauma care center [1]. Once inside a trauma care center, hemorrhage also accounts for over 80% of deaths occurring in the first hour and nearly 50% of deaths in the first 24 hours, but very few after 24 hours [136]. By the time hemorrhaging patients reach trauma centers, a

(37)

Figure 1-1: 2014: [22] The leading causes of death in the United States, ages 1 – 46 years

Figure 1-2: 2015: [87, 86] Annual economic burden attributed to trauma is $671 bil-lion, significantly higher than that of many other diseases

(38)

significant quantity of blood volume has already been lost, leading to irreversible tissue damage and eventually organ system failure before a physician has the opportunity to intervene.

Injury severity, site of injury, first response intervention, and time to reach a trauma care facility are significant factors in increasing the survival probability. This presents an opportunity for intervention in the pre-hospital phase. If hemorrhaging can be reduced or halted altogether, this could potentially give first responders more time to reach a trauma facility, thereby reducing mortality rate due to traumatic hemorrhage.

1.2

Background

1.2.1

Hypovolemic shock

If an injury is severe or left untreated long enough, a bleeding patient may enter into a state of hypovolemic (or hemorrhagic) shock. This is a state in which the body is deprived of oxygen due to a sudden and precipitous decrease in blood volume, causing a sympathetic reflexive response to prompt compensatory mechanisms. In an attempt to maintain oxygen perfusion to the most critical organs, the body will shunt blood from the extremities by constricting arterioles and venous reservoirs, while increasing cardiac output and arterial blood pressure (BP) by elevating heart rate [108]. If the shock is severe enough, these mechanisms will fail to maintain adequate circulation, decreasing arterial pressure and leading to a cascade of system failures that deteriorate steadily, known as progressive shock. In this shock state, the body is unable to maintain compensatory responses; metabolic byproducts remaining in the blood and tissue lead to acidosis and blood clotting is hampered, thereby further exacerbating the bleed. At this point, without medical intervention, the body will not be able to recover [108, 116].

Internal bleeding is particularly dangerous for several reasons: 1. the individual may be unaware of bleeding;

(39)

2. symptoms may not arise until a significant quantity of blood is lost; 3. the source of internal bleeds are often difficult to target;

4. internal bleeds are generally noncompressible (i.e., cannot be treated by com-pression of the wound).

First responders are trained to focus on stopping or stemming bleeding when pos-sible, and restoring circulation volume. Certainly, whole blood replacement is ideal, but it is unavailable and often impractical in a pre-hospital setting, depending on environmental and/or infrastructural limitations. There is no standard resuscitation fluid; generally, an isotonic crystalloid (salt solution) such as 0.9% NaCl solution or Ringer’s lactate solution is administered [253]. Though administration of resuscitation fluids extends life by increasing blood volume, it also dilutes the blood, reducing the hematocrit (volume fraction of red blood cells) and concentration of blood platelets, blood proteins and other soluble factors such as fibrinogen, which are essential for coagulation. This can lead to coagulopathy (inability to form clots), thereby exacer-bating the state of shock and the body’s inability to reverse this process to achieve homeostasis [108, 137, 107].

1.2.2

Magnetorheological fluids

Physicists and mathematicians have examined the behavior of fluids that are influ-enced by magnetic fields since Michael Faraday discovered the principle of electro-magnetic induction in 1831, which was later adopted into Maxwell’s equations [216]. Maxwell’s equations along with the Navier-Stokes equations provided physicists a means to quantitatively analyze the behavior of these fluids, giving rise to the field of magnetohydrodynamics (although this name was not coined until the next century)[6]. This allowed for more rigorous understanding of magnetofluids such as liquid metals, sea water, electrolytes, ionized gases, and other conductive fluids.

Unlike plasmas and sea water however, magnetorheological fluids are not natu-rally occurring and have different fluid properties. MR fluids are suspensions of solid

(40)

magnetizable particles suspended in a nonmagnetizable liquid medium. First devel-oped in the late 1940s by the National Bureau of Standards (now National Institute of Standards and Technology), MR fluids were rapidly identified as potentially ideal for use in mechanical systems for their unique properties. Early studies showed these newly created fluids could be used for clutches, hydraulic systems, shock absorbers, dashpots, and form casting molds [213, 185].

Today, MR fluids are commercially available from industrial chemical manufac-turers for use in common applications [133]. However, in order to achieve a desired behavior for a specific application, a uniquely designed fluid may be necessary. The design of an MR fluid is largely dependent on its constituents:

1. solid magnetic particles; 2. liquid carrier medium; 3. additives.

The interaction between these constituents in the presence of an external magnetic field governs the rheological properties of the fluid [67].

The solid phase of an MR fluid must possess a magnetic susceptibility large enough to be manipulated by the externally applied magnetic field. Ferromagnetic materials are ideal because they tend to have very high non-linear magnetic susceptibilities, but ferrimagnetic materials (e.g., magnetite) are also used in some cases [159, 126, 31, 274]. Generally, a sensitive MRF is desired to elicit a large response in magnetization of the solid phase both quickly and with a relatively small applied field. To achieve such a design, we evaluate the magnetic properties of the solid particles. A high mag-netic saturation (𝑀𝑆), low magnetic coercivity (𝐻𝐶), and low magnetic remanence (𝑀𝑟) are generally considered desirable in MRF synthesis. Magnetic saturation is the maximum magnetization a material can reach. Magnetic coercivity is a measure of a material’s resistance to an applied external field. Magnetic remanence indicates the residual magnetization within a previously saturated material after it has been removed from the external field. Materials with low coercivity and remanence will

(41)

have a faster and more dramatic response to changes in the applied field [100]. Com-mon magnetic materials used in MR fluid suspensions include carbonyl iron (CI), magnetite, alloys of iron, iron oxides and some steels [97]. The material selected must balance the desired chemical and magnetic properties with an acceptable density to prevent particle sedimentation if that may be a concern in the operating environment. Particle size, shape, and dispersity are also important factors in the MRF design, as they impact the behavior of the fluid in both the energized and resting states. These factors will also dictate the maximum volume (packing) fraction [181] of the magnetic material, which limits the magnetic moment of the fluid. More recent work also investigates incorporating nonmagnetic particles and the effect on yield stress properties in both energized and non-energized states, as well as sedimentation sta-bility [207, 284, 223]. Most conventional MR fluids are intentionally produced with near spherically shaped particles to reduce anisotropic effects of particle magnetiza-tion.

The nonmagnetic carrier fluid is also selected based on the application, consider-ing variables such as operatconsider-ing temperature range, surface tension, shear and normal stresses, and chemical compatibility with system components. With operational vari-ables in mind, a fluid may be selected based on its behavior (e.g., viscosity, thermal conductivity, polarity) within these operational bounds. Commercially available MR fluids generally use water-, hydrocarbon-, or silicone-based carrier fluids [40].

Finally, additives may be used to improve the functional use of the MR fluid. There have been many studies investigating particle coatings, surfactants and other additives to improve chemical stability, inhibit particle agglomeration, limit oxidation rate, as well as prevent sedimentation while maintaining desired yield strength [9].

1.2.3

Magnetization and the MR effect

Magnetic fields are produced in two ways. Ampère’s Law relates magnetic field (B) to current density (J). From this relation we know that electric currents produce magnetic fields.

(42)

∇ × B = 𝜇0 (︂ J + 𝜀0 𝜕E 𝜕𝑡 )︂ (1.1) 𝜕E

𝜕𝑡 is the time derivative of the electric field, and 𝜇0 and 𝜀0 are constants known as the permeability and permittivity of free space respectively (𝜇0 = 4𝜋 × 10−7𝑁 𝐴−2, 𝜀0 = 8.854 𝐹 𝑚−1).

Magnetized materials also have magnetic fields, but without having a bulk current flow. This behavior is due motion of the charged subatomic particles in the material, essentially creating small currents. Electron spin and electron orbit about the nucleus produce an atomic magnetic moment. In most materials, atomic magnetic moments are randomly ordered, thereby canceling one another, producing no magnetic field at a macro-scale. However, some materials exhibit ordering of their magnetic moments. Depending on the type of ordering, these magnetic materials may be ferromagnetic, ferrimagnetic, or antiferromagnetic. Regions of uniformly ordered structures of mag-netic moments, called magmag-netic domains, produce magmag-netic fields, contributing to the overall field for the material. In the presence of external magnetic fields, a ferri-magnetic or ferroferri-magnetic material will align its domains with the field, creating its own magnetization. When the domains are fixed in alignment in the absence of an external field, the material has a permanent magnetization, and we call the material a magnet [101, 130].

The MR effect describes the changes in rheological properties of the MR fluid due to an applied field. This effect is explained by de Vicente et al. in their particle magnetization model, which attributes the MR effect to the relative magnetic perme-ability mismatch between the carrier fluid (𝜇𝑐𝑟) and the solid particles (𝜇𝑝𝑟) [67].

The MR effect holds true for MR fluids with solid magnetic particles larger than 1 𝜇𝑚. Particles above this threshold lie in the multi-domain regime (i.e., have multiple magnetic domains), and the influence of Brownian thermal energy can be neglected in comparison to the influence of magnetic interaction energy. The dipolar coupling parameter, 𝜆, is a ratio of magnetic interaction energy between two magnetic moments and their thermal energies in an external field, H0:

(43)

𝜆 = 𝜋𝜇0𝜇𝑐𝑟𝛽 2𝑎3𝐻2

0 2𝑘𝐵𝑇

, (1.2)

where 𝑎 is the particle radius, 𝜇𝑐𝑟 and 𝜇𝑝𝑟 are carrier fluid and particle relative permeabilities, and 𝛽 ≡ 𝜇𝑝𝑟−𝜇𝑐𝑟

𝜇𝑝𝑟+2𝜇𝑐𝑟 is known as the magnetic permeability contrast

fac-tor. For values of 𝜆 >> 1, thermal energy is relatively small and can be neglected. Small values of 𝜆 for magnetic colloids or suspensions generally correspond to the solid particles having a diameter less than 1𝜇𝑚. When solid particles much smaller than 1 𝜇𝑚, the relative influence of thermal energy is significant and cannot be ne-glected. Magnetic particles this small generally have only a single domain [31, 111]. This describes a separate class of magnetic fluids called ferromagnetic fluids, or fer-rofluids. Ferrofluids were first synthesized in 1963, by S. Stephen Papell of the NASA Lewis Research Center for priming pumps for liquid rockets in zero-gravity environ-ments [226, 134, 252]. Ferrofluids have the advantage of being colloidal liquids and do not sediment, however, they do not exhibit the MR effect and lack the desired yielding properties for most MR applications.

In the presence of a magnetic field, MR fluid particles will align their domains with the external field, thereby inducing an internal magnetization. Figure 1-3 shows the dipole moment (arrows) of domains within the particles with the field off, and on. In the off state, their net dipole moment is zero, but in the energized state, their alignment of domains leads to an induced dipole moment, m. For ferromagnetic, monodisperse, spherical particles of radius 𝑎, and saturation magnetization of 𝑀𝑆, the magnetic moment is

m = ⎧ ⎪ ⎨ ⎪ ⎩ 4𝜋𝛽𝑎3H 0, 3𝛽𝐻0 << 𝑀𝑆 4 3𝜋𝑎 3M S, 3𝛽𝐻0 >> 𝑀𝑆 (1.3)

Figure 1-4 illustrates the coordinate system used to understand interparticle forces between two particles in the magnetic field. The net force on a solitary magnetic diplole due to a uniform field is zero, therefore, only interparticle forces are consid-ered. This simplification, however, is not true of non-uniform fields, as magnetic field

(44)

Figure 1-3: Magnetic particles with external magnetic field (a) off, (b) on [2]. With magnetic field off, magnetic dipole moments (arrows) of the particle domains are randomly oriented. When field is turned on, the dipole moments of the particle domains align with the externally applied magnetic field, changing the field locally near the particle surface and producing attractive forces between particles parallel to the field lines and repulsive force orthogonally.

gradients do produce forces on individual dipole moments. The force on particle 𝑖 due to the presence of particle 𝑗 is

Fmagij =(︀mi· ∇)︀Bj = 𝜇0𝜇𝑐𝑟(︀mi· ∇)︀Hj, (1.4)

where Hj and Bj are the internal magnetic field and magnetic flux density of particle i induced by particle j. The internal field is the sum of the external field and the demagnetizing field (𝐻𝐷),

(45)

Figure 1-4: Illustration of the coordinate system for two magnetic particles of size 2𝑎, 𝑖 and 𝑗, interacting in a uniform external field, H0 [66]. 𝑟𝑖𝑗 = ‖rj − ri‖ denotes the distance between 𝑖 and 𝑗, while 𝜃𝑖𝑗 is the angle between the uniform field vector, and rij.

H = H0+ HD = H0− NM, (1.5)

where N is the demagnetizing tensor. This is typically expressed as a scalar func-tion, with an average demagnetizing factor, 𝑁𝐷. For a spherical particle in a uniform external field, the demagnetizing field is also uniform, and is linearly proportional to the magnetization (M), resulting in a constant demagnetizing factor of 𝑁𝐷 = 13, expressed as,

H = H0− 𝑁𝐷M = H0− 1

3M (1.6)

For an MR fluid of spherical particles the magnitude of the magnetic field inside the particle is 𝐻 = 3𝜇𝑐𝑟𝐻0

𝜇𝑝𝑟+2𝜇𝑐𝑟, giving a magnetization of 𝑀 = 3𝛽𝐻0.

In the limit of small applied field (3𝛽𝐻0 << 𝑀𝑆), we obtain the following force expression

(46)

Fmagij = −12𝜋𝜇0𝜇𝑐𝑟𝛽2𝑎2𝐻02 (︂ 𝑎 𝑟𝑖𝑗 )︂4 [︀(3𝑐𝑜𝑠2𝜃 𝑖𝑗 − 1)^r + 𝑠𝑖𝑛(2𝜃𝑖𝑗)^𝜃]︀, (1.7)

and in the limit of large applied field (3𝛽𝐻0 >> 𝑀𝑆), we obtain

Fmagij = −4 3𝜋𝜇0𝜇𝑐𝑟𝑎 2 𝑀𝑆2(︂ 𝑎 𝑟𝑖𝑗 )︂4 [︀(3𝑐𝑜𝑠2 𝜃𝑖𝑗 − 1)^r + 𝑠𝑖𝑛(2𝜃𝑖𝑗)^𝜃]︀. (1.8)

The induced magnetization produces attractive forces between the particles along the field lines and repulsive forces orthogonally as shown in Figure 1-3 [2]. This results in the particles aggregating into columnar structures between the top and bottom surfaces. Macroscopically, the fluid appears to exhibit a large yield stress in the presence of the applied magnetic field [29, 67, 66]. In the presence of an applied field, the yielding behavior of the fluid can be characterized by a dimensionless quantity known as the Bingham number (𝐵𝑖), which is the ratio of the magnetically induced yield stress to the viscous shear stress [245].

𝐵𝑖(H, ˙𝛾) = 𝜏0(H) 𝜏 (H, ˙𝛾) =

𝜏0

𝜂 ˙𝛾 (1.9)

The microscopic behavior of a magnetizable fluid can be characterized by a di-mensionless quantity called the Mason number (𝑀 𝑛), which is the ratio of the viscous shear stress of the fluid to the interparticle magnetic stress [143, 66].

𝑀 𝑛(H, ˙𝛾) = 𝜂 ˙𝛾 |Fmagij | 𝑎2 = 16𝜂𝑐˙𝛾 𝜇0𝜇𝑐𝑟𝛽2𝐻02 (1.10)

It has been shown mathematically and validated experimentally that the micro-scopic and macromicro-scopic forces are linearly related, meaning that the product of the Bingham and Mason numbers should provide a ratio of the yield and magnetic stresses in the fluid. Also, because the yield stress is a function of the magnetization of the particles, this product, known as the critical Mason number (𝑀 𝑛*), is a constant. This is also the Mason number at which point 𝐵𝑖 = 1 (i.e., the magnetically induced yield stress equals the viscous shear stress) [245].

(47)

1.3

Thesis Objectives

This thesis work has three primary objectives.

1. Formulate and rigorously characterize an MR fluid, suitable for use inside the human body,

2. Investigate and demonstrate a method for administering the MR fluid to stop blood flow under physiological conditions, and

3. Assess the effectiveness of the MRF and technique in reducing blood loss and extending survival time in a quantifiable manner.

We intend to test and evaluate the MRF and technique through bench-top laboratory experiments as well as in vivo animal model experiments.

Magnetorheological fluids have shown much promise in many applications since their inception nearly 70 years ago, gaining momentum over that period, but most dramatically in the past decade. The unique, tunable properties of MR fluids have made them attractive to experts in commercial industries, government and military re-search, as well as academia, spanning many fields, including the medical field. Trauma related hemorrhage is a serious concern, currently lacking an adequate long-term so-lution, and we believe that MR fluids can be formulated to significantly reduce or halt noncompressible hemorrhages in patients.

(48)
(49)

Chapter 2

Literature Review

To tackle the objectives of this thesis, we seek some basic understanding of past and ongoing research related to our area of investigation. In attempting to use MR fluids to solve a problem in the realm of trauma and critical care, we merge two generally disparate fields, requiring us to have some fundamental knowledge of both. This re-search is highly cross-disciplinary, involving concepts in electromagnetics, continuum mechanics, human anatomy and physiology, pharmacology, as well as medical inter-vention methods. A comprehensive literature review covering all of these disciplines would be inordinately long and also unnecessary. Instead, we will review a limited subset of specific concepts most relevant to the analysis of this research, which we also believe will help us achieve the objectives set forth in this thesis.

2.1

Magnetization of Materials

The degree of magnetization of a material is described by a constitutive equation relating an applied magnetic field H and the corresponding magnetization inside the material M. These two terms are related by a dimensionless proportionality term called magnetic susceptibility or volume susceptibility, denoted by 𝜒.

M = 𝜒H (isotropic susceptibility) 𝑀𝑖 = 𝜒𝑖𝑗𝐻𝑗 (anisotropic susceptibility)

Références

Documents relatifs

Nous souscrivons donc aux recommandations européennes les plus récentes concernant le traitement anticoagulant et antiagrégant des patients atteints de fibrillation auriculaire (et

As early as the Mar Del Plata Conference in 1977, the Member States of the United Nations asserted that “All peoples, whatever their stage of development

The objective of this work is to characterize, in a multi-agent approach, the traffic vehicles behaviours, and to model them in a versatile traffic simulator, serving as a testing

The présentation shows how to calculate thé uncertainty attached to thé results of a calibrated AMS on thé whole measuring range and how thé uncertainty of thé référence

work carried out since these early use cases has been concerned with solutions for specific problems associated with semantic integration, such as mapping between

the main sulfate precursor, are projected to peak in the year 2020, the emissions of the carbonaceous aerosols are ex- pected to increase up to the year 2100.. Therefore, the

Please click on the blue dashed frames for access to the PDF files of the

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des