Elsevier

Methods in Enzymology

Volume 386, 2004, Pages 378-418
Methods in Enzymology

Measuring Changes in Tumor Oxygenation

https://doi.org/10.1016/S0076-6879(04)86018-XGet rights and content

Publisher Summary

This chapter discusses the measurement of changes in tumor oxygenation. The oxygen pressure determinations could be of great clinical value and they are also vital to many laboratory investigations of new drugs and studies of tumor development. Blood oxygen level dependent (BOLD) contrast proton nuclear magnetic resonance (NMR) facilitates rapid interrogation of vascular oxygenation, and is particularly appropriate for examining dynamic responses to interventions. Both spectroscopic and imaging approaches have been applied to tissue oxygen pressure measurements depending on the available signal to noise. It appears that uptake and distribution efficiency vary with tumor type, but in general, maximum signal is detected from the tumor periphery corresponding with regions of greater perfusion. The various aspects of fluorocarbon relaxometry using echo planar imaging for dynamic oxygen mapping (FREDOM) are elaborated. The results suggested FREDOM as a valuable tool for assessing the dynamic time course of interventions to provide clear insight into the mode of action of therapeutic approaches and aid in the high-throughput screening of new drugs, such as vascular targeting and antiangiogenic agents.

Introduction

It has long been appreciated that hypoxic tumor cells are more resistant to radiotherapy.1 Indeed, a 3-fold increase in radio resistance may occur when cells are irradiated under hypoxic conditions compared with oxygen pressure pO2 > 15 torr for a given single radiation dose. However, recent modeling has indicated that the proportion of cells in the range 0–20 torr may be most significant in terms of surviving a course of fractionated radiotherapy.2 Certain chemotherapeutic drugs also present differential efficacy, depending on hypoxia.3, 4 Increasingly, there is evidence that hypoxia also influences such critical characteristics as angiogenesis, tumor invasion, and metastasis.5, 6, 7, 8 Moreover, repeated bouts of intermittent hypoxic stress may be important in stimulating tumor progression.9 Thus the ability to measure pO2 noninvasively and repeatedly, with respect to acute or chronic interventions, becomes increasingly important.

Early work examined cells in vitro, where ambient oxygen concentrations are readily controlled. In vivo, hypoxia may be achieved by clamping the blood supply to a tumor,10 but other levels of oxygenation reflect the interplay of supply and consumption.11, 12 Robust fine-needle polarographic electrodes opened the possibility of measuring pO2 in tumors in situ and in vivo to define local pO2 under baseline conditions or with respect to interventions. In early work, Cater and Silver13 showed the ability to monitor pO2 at individual locations in patients' tumors with respect to breathing oxygen. Later, Gatenby et al.14 showed that pO2 in a tumor was correlated with clinical outcome. Tumor oximetry received its greatest boost with the development of the Eppendorf Histograph polarographic needle electrode system.15 This computer-controlled device equipped with a stepper motor can reveal distributions of tumor oxygenation and has been applied extensively to clinical trials. Many reports have now shown that tumors are highly heterogeneous and have extensive hypoxia; furthermore, strong correlations have been shown in cervix and head and neck tumors between median pO2 or hypoxic fraction and survival or disease-free survival.5, 16, 17, 18, 19, 20 Extensive hypoxia also has been found in tumors of the prostate and breast.21, 22, 23 Thus tumor oxygenation is now recognized as a strong prognostic indicator, and this device has laid a convincing foundation for the value of measuring pO2 in patients. However, the Histograph is highly invasive, and it is not possible to make repeated measurements at individual locations, precluding dynamic studies to assess the influence of interventions on tumor pO2.

Given that hypoxic tumors are more resistant to certain therapies, it becomes important to assess tumor oxygenation as part of therapeutic planning. Patients could be stratified according to baseline hypoxia to receive adjuvant interventions designed to modulate pO2, or more intense therapy as facilitated by intensity modulated radiation therapy (IMRT). Tumors, which do not respond to interventions, may be ideal candidates for hypoxia-selective cytotoxins (e.g., tirapazamine24). Noting that any therapy and intervention may have side effects or simply add to clinical costs, it is vital that efficacy be established and therapy be optimized for an individual patient. Whether initially hypoxic regions of a tumor can be modified to become better oxygenated has long been considered a key to improving outcome of irradiation. However, many attempts to improve therapeutic outcome by manipulation of tumor oxygenation have shown only modest success in the clinic,25 and it is thought that lack of success may have resulted from inability to identify those patients who would benefit from adjuvant interventions.

Although pO2 determinations could be of great clinical value, they are also vital to many laboratory investigations of new drugs and studies of tumor development. Given the potential importance of measuring pO2, many diverse techniques have been developed, as reviewed by others previously,26, 27, 28, 29 and here, in the next section.

Table I lists various techniques that have been reported to provide quantitative estimates of pO2. Historically, polarographic needle oxygen electrodes have been considered a “gold standard,” and they have been applied in the clinic since the 1950s. One or more electrodes may be placed in a tumor, facilitating measurement of baseline pO2 and dynamic response to interventions.13, 30, 31, 32 Initially, the focus was on generating finer needles, which would be less invasive, and tips as fine as a few microns have been applied to animal tissues.33 However, such needles are progressively brittle and generate such small current that stray electromagnetic fields can interfere. Stationary electrodes sample limited volumes, and recognizing tumor heterogeneity, the Eppendorf Histograph was developed to generate multiple measurements along tracks in tumors.15, 34, 35 Following extensive studies in animals, the Histograph has found widespread application in the clinical setting and has unequivocally revealed hypoxia in many tumor types, for example, head and neck,36, 37 cervix,19, 38 breast,21, 22 and prostate.23 Moreover, pO2 distributions have been found to have prognostic value. Disease-free survival is significantly worse for patients with hypoxic tumors, though the optimal prognostic parameter has variously been median pO2 or percent measurements <5 torr (HF5).

Although the Eppendorf Histograph uses a large invasive needle (size = 26 G or about 0.35 mm), it has provided great impetus for further investigations. One aspect is the application of less invasive probes. Fiber-optic probes are typically finer and do not consume oxygen during measurement. Typically, only two or four locations are sampled simultaneously, but as with the earlier electrodes, these optical probes facilitate observation of dynamic changes in pO2 in response to interventions.39, 40, 41, 42, 43 Both the current commercial systems, the OxyLite (http:⧸⧸www.oxford-optronix.com⧸tissmon⧸oxylite⧸oxylite.htm) and FOXY (http:⧸⧸www.oceanoptics.com⧸Products⧸foxyfaqs.asp), exploit the fluorescent quenching by oxygen of a ruthenium complex coating. OxyLite measures fluorescent lifetime, whereas FOXY uses a simple intensity integration and is correspondingly much cheaper. Fibers are fragile, and coatings have a limited lifetime.

Reporter molecules have been developed for use with electron spin resonance (ESR or EPR), where the line width is highly sensitive to oxygen.28, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55 Two primary approaches are used: (1) direct intratumoral (IT) injection of char crystals,49, 56 phthalocyanine,57 or India ink58 into a tissue or (2) intravenous (IV) infusion of water-soluble agents which disseminate throughout the tumor vasculature.47, 53 Direct IT injection is invasive and has generally been applied as a spectroscopic approach to report pO2 at single locations only. Nonetheless, significant data have been achieved demonstrating hypoxiation and reoxygenation with respect to irradiation, and the importance of timing successive radiation doses to coincide with reoxygenation.59 Char particles may be stable in tissue for weeks to years, allowing measurements of chronic changes in tissues (e.g., accompanying tumor growth).28 The IV approach is noninvasive, but reporter molecules may predominately distribute in the well-perfused vasculature, potentially biasing measurements toward the well-oxygenated tumor regions. Progressive uptake and clearance of agents produces variable concentrations, and some agents degrade in tissue requiring appropriate correction factors.47 Nonetheless, images of tumor oxygen distribution have been reported, including three-dimensional representations.53 Spin radicals also may be applied to a combined ESR–NMR (nuclear magnetic resonance) approach, Overhauser-enhanced magnetic resonance imaging (OMRI), exploiting the Overhauser enhancement in the tissue water proton MRI signal that occurs by polarization transfer from free radicals upon electromagnetic irradiation.60

Vascular oxygenation has been probed by fluorescence or phosphorescence imaging based on reporter complexes delivered IV.61, 62 Historically, the approach was limited to superficial tissues due to limited light penetration. The latest molecules are active in the near-infrared, permitting greater depth of signal penetration.63

NMR facilitates interrogation of deep tissues noninvasively, and 19F NMR approaches will be reviewed in detail in the following section. The methods discussed earlier provide direct quantitative measurements of pO2 based on various physiochemical parameters, such as electric current, fluorescent lifetime, magnetic resonance linewidth, or relaxation. Other approaches are less direct, but can reveal hypoxia or correlates of pO2.

Specific classes of reporter molecules have been developed to reveal hypoxia26, 64 (e.g., pimonidazole,65, 66 EF5,67, 68 CCl-103F,69 Cu-ATSM70, 71 galactopyranoside IAZA72). Following IV infusion, these agents become reduced in tissues and are trapped. However, in the presence of oxygen they are reoxidized and ultimately clear from the body. Histologic assessment of the distribution of these agents provides microscopic indications of local hypoxia. EF5, pimonidazole, and Cu-ATSM are currently being tested in clinical trials, and correlations have been reported with clinical outcome.66, 67, 70 Many variants have been proposed over the past 20 years, and incorporation of radionuclides has facilitated noninvasive investigations using positron emission tomography (PET) or single photon emission computed tomography (SPECT), while 19F labels permitted NMR spectroscopy.72, 73, 74 Generally, only a single time point is investigated, but dynamic variations in hypoxia may be assessed, even in biopsy specimens, by applying pairs of hypoxia reporters in a pulse-chase fashion with respect to an intervention, as shown by Ljungkvist et al.69

Several studies have shown a lack of correlation between hypoxic marker binding and pO2 assessed using the Eppendorf Histograph, which may be related to chronic versus acute hypoxia, or the extent of necrosis.75, 76, 77 The ultimate value of the techniques is evidenced by correlations between uptake and outcome.66, 70, 71, 78 Recent data also indicate that EF5 fluorescence may be correlated with pO2.79

The techniques discussed so far all depend on exogenous reporter molecules or probes. Ideally, oxygenation could be related to endogenous characteristics. Because many biochemical pathways are under oxygen regulation, they can provide an elegant window on hypoxia, for example, induction of hypoxia-inducible factor 1 (HIF-1) and glucose transporter 1 (Glut-1) together with secondary responses, such as increased production of vascular endothelial growth factor (VEGF), NIP3 and tumor-associated macrophage activity.8 Such molecules indicate hypoxia, though they may be induced by other factors. Intrinsic radiation sensitivity also may be assessed using the Comet assay.80 These assays each require biopsy. Other markers potentially associated with hypoxia may be found in the plasma or urine and have been correlated with clinical outcome.81 An attractive alternative is the introduction of transgenes with hypoxic response elements (HREs) as promoter sequences coupled to reporter genes such as GFP (green fluorescent protein)82, 83 or luciferase.84, 85 GFP synthesis is an energetic process, which could be hindered under hypoxia conditions. Likewise, bioluminescence accompanying action of luciferase on luciferin requires adenosine triphosphate (ATP) and O2, but reports suggest that even under exceedingly low pO2, sufficient oxygen remains to reveal hypoxia.

Many practical considerations govern clinical application of oximetry methods. Proton MRI is routinely applied for anatomic evaluation of tumors and would provide an ideal conduit for prognostic investigations. Application of contrast agents may reveal tumor boundaries to enhance detectability, and the dynamic contrast enhancement (DCE) changes provide insight into vascular perfusion and surface permeability area.86 Specific studies have shown a correlation between DCE and pO2,87 and indeed, a theoretical underpinning has been provided based on the Krogh cylinder model.88 However, the correlation is unlikely to be widely applicable, since DCE is sensitive to vascular flow, perfusion, and permeability, where pO2 depends on oxygen consumption as well as delivery.

Blood oxygen level dependent (BOLD) contrast proton NMR facilitates rapid interrogation of vascular oxygenation and is particularly appropriate for examining dynamic responses to interventions.48, 89, 90, 91 Deoxyhemoglobin is paramagnetic and induces signal loss in T2∗-weighted images. However, BOLD does not provide absolute pO2 values and is confounded by the influence of blood flow, as investigated extensively by Howe et al.,92 who termed the expression FLOOD (flow and oxygen level dependent) contrast. In addition, variation in vascular volume can introduce signal perturbation.93 Nonetheless, some studies have indicated a correlation with relative pO2, but poor indication of absolute pO2.53, 94, 95

Near-infrared spectroscopy (NIRS) offers an alternative approach based on the differential light absorption of the strong chromophores oxyhemoglobin and deoxyhemoglobin. NIRS provides a noninvasive means to monitor global tumor vascular oxygenation in real time based on endogenous molecules. Although many NIRS investigations have been conducted in the brain and breast in both laboratory and clinical settings over the past decade, there have been relatively few reports regarding solid tumors.43, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106 Most studies to date have used reflectance mode. By contrast, we have favored transmission mode, so as to interrogate deep tumor regions, and we have presented preliminary studies in rat breast and prostate tumors with respect to various interventions.43, 101, 106 NIR approaches are presented in detail in Chapter 17 of this volume.

Each technique has specific virtues and drawbacks, which must be considered for any given application, particularly the degree of invasiveness, the ability to generate maps of heterogeneity, and the ability to assess dynamic changes. In addition, the location of a measurement (e.g., vascular versus tissue compartments, the precision of measurements, and spatial and temporal resolution) must be considered. For further details of the techniques described earlier, the reader is referred to the references. In the next section, we present 19F NMR approaches in greater detail.

Nuclear magnetic resonance (NMR) is attractive because it is inherently noninvasive. Liquid-state NMR is characterized by several parameters, including signal amplitude, chemical shift (δ), spin–spin relaxation (T2), and spin–lattice relaxation (T1). Oxygen could be quantified using 17O NMR, but this is rather esoteric.107 Alternatively, it has long been recognized that the oxygen molecule (O2) is paramagnetic, causing increased spin–lattice relaxation rates (R1 = 1⧸T1). Indeed, physical and theoretical chemists must go to great lengths to rigorously remove oxygen from solutions (using freeze–thaw procedures) to achieve inherent relaxation rates for studying nuclear interactions.108 Proton NMR studies have reported changes in the water relaxation rate as a result of tissue oxygenation,109 but many other processes (metal ions, cellularity, pH, ionic strength) also cause relaxation, and thus it is not suitable for detecting pO2, except under rare circumstances, such as with the eye.110 There is also a substantial temperature response, whereas the relaxivity due to oxygen is only 0.0002 s−1⧸torr.110

However, several investigators showed that the 19F NMR spin–lattice relaxation rates for fluorocarbons are much more sensitive to pO2.111, 112 Thomas et al.113 pioneered the application of 19F NMR relaxometry to measure pO2 in tissues, in vivo, including lung, liver, and spleen; several other investigators demonstrated feasibility and applications,114, 115, 116, 117, 118, 119, 120 as reviewed some years ago by Mason.121 The 19F NMR R1 of perfluorocarbons (PFCs) varies linearly with pO2,113, 122 and each resonance is sensitive to pO2, temperature, and magnetic field, but importantly, is essentially unresponsive to pH, CO2, charged paramagnetic ions, mixing with blood, or emulsification.123, 124, 125, 126, 127

A particular PFC molecule may have multiple resonances, and each resonance has a characteristic R1 response to pO2. This is attributed to steric effects of O2, as it approaches the molecule,112 which implies that perfluorinated groups, which are both geometrically and magnetically comparable, should have similar R1 responses to oxygen tension. At a fixed temperature and magnetic-field strength, the R1 response to pO2 of any single resonance obeys the simple formulaR1 = R1a + (R1pX)where X is the mole fraction of O2 dissolved in the PFC, R1a is the anoxic relaxation rate, and R1p is the relaxation rate due to the paramagnetic contribution of oxygen. According to Henry's law, the dissolved mole fraction is related directly to the partial pressure of oxygen,pO2 = KXwhere K represents Henry's constant for a given solution of gas at a specified temperature. By substitution,R1 = R1a + (R1p/K)pO2The slope (R1pK) indicates the response of a particular resonance to pO2.

PFCs essentially act as molecular amplifiers, since the solubility of oxygen is greater than in water, but thermodynamics require that the pO2 in the PFC will rapidly equilibrate with the surrounding medium, and estimates of diffusion suggest the equilibration can occur within seconds. Because relaxation is proportional to oxygen concentration, the effect will be greater at a given pO2 than for water. Importantly, ions do not enter the hydrophobic PFC phase, and thus do not affect the bulk relaxation. Indeed, PFCs are typically exceedingly hydrophobic and do not mix with the aqueous phases, but rather form droplets or emulsions. Based on these principles, PFCs have been applied to in vivo pO2 measurements. Characteristics of many diverse PFCs are summarized in Table II.

At any given magnetic field (Bo) and temperature (T), sensitivity to changes in pO2 is given by R1 = a + bpO2. Thus a greater slope is important, and the ratio η = b/a has been proposed as a sensitivity index.128 Generally, a small “a” value (intercept) represents greater sensitivity, but it also generates longer T1 values under hypoxic conditions, potentially increasing data acquisition times. Indeed, the T1 of hexafluorobenzene (HFB) at 4.7 T may reach 12 s, potentially creating long imaging cycles, but this is readily overcome by applying single-shot (echo planar) imaging techniques, as presented in a later section.

Many PFCs, such as perfluorotributylamine (PFTB), perflubron (formerly referred to as perfluorooctyl bromide; PFOB), and Therox (F44-E), have several 19F NMR resonances, which can be exploited to provide additional information in spectroscopic studies, but seriously hamper effective imaging. Multiple resonances can lead to chemical shift artifacts in images, which compromise the integrity of relaxation time measurements, though they can be avoided by selective excitation, or detection, chemical shift imaging, deconvolution, or sophisticated tricks of NMR spin physics.116, 119, 129, 130, 131, 132, 133 These approaches add to experimental complexity and are generally associated with lost signal to noise ratio (SNR). Thus we strongly favor PFCs with a single resonance, and we will describe the use of HFB,27, 32, 42, 106, 134, 135, 136, 137 though some research groups favor 5-crown-5-ether (15C5).88, 117, 138, 139

R1 is sensitive to temperature, although the response varies greatly between PFCs and between individual resonances of each individual PFC. Over small temperature ranges, a linear correction to calibration curves is appropriate, but over larger temperature ranges, the response can be complex, as investigated extensively by Shukla et al.140 for several PFCs. Differential sensitivity of pairs of resonances to pO2 and temperature allowed Mason et al.141 to simultaneously determine both parameters by solving simultaneous equations. However, generally it is preferable for a pO2 sensor to exhibit minimal response to temperature, since this is not always known precisely in vivo and temperature gradients may occur across tumors. As shown in Table II, even a relatively small error in temperature estimate can introduce a sizable discrepancy into the apparent pO2; for example, the relative error introduced into a pO2 determination by a 1° error in temperature estimate ranges from 8 torr⧸° for PFTB141 to 3 torr⧸° for PFOB (perflubron)142 or 15C5117 and 0.1 torr⧸° for HFB,143 when pO2 is actually 5 torr. It must be noted that error depends on actual pO2 and the error varies with magnetic field and temperature. R1 response does depend on magnetic field, necessitating calibration curves for each type of magnet system (e.g., 1.5, 4.7, or 7 T). Thus comparison of PFC utility for pO2 measurements is complicated by the field used for specific published investigations, and in Table II, we consider sensitivity as presented.

Choice of PFC may be governed by practical considerations, such as cost and availability, since several products, particularly proprietary emulsions, may be difficult to obtain. HFB and 15C5 offer the immediate advantage of a high symmetry and a single 19F NMR resonance. This offers maximum SNR and simplifies imaging, which may otherwise require frequency selective excitation, deconvolution, or other NMR tricks to avoid chemical shift artifacts.

The most popular route for the delivery of PFCs is as emulsions injected intravenously. Given the extremely hydrophobic nature of PFCs, they do not dissolve in blood directly, but may be formulated as biocompatible emulsions. Much effort has been applied to formulate stable homogenous emulsions, as reviewed elsewhere.144 Following IV infusion, the emulsion circulates in the vasculature with a typical half-life of 12 h, (depending on the nature of the emulsion) providing substantial clearance within 2 days.145, 146 Primary clearance is by macrophage activity, leading to extensive accumulation in the liver, spleen, and bone marrow.113, 147 Indeed, this is a major shortcoming of IV delivery, since animals may exhibit extensive hepatomegaly or splenomegaly.148 The emulsions are not toxic, and other than causing swelling, appear not to cause health problems. PFC clearance occurs from the liver with a typical half-life of 60 days for perfluorotripropylamine and 3 days for perflubron, with primary clearance by migration to the lungs and exhalation.149

Some investigators have examined pO2 of tissues, while PFC remained in the blood, providing a vascular pO2.114, 118, 150 Flow can generate artifacts, and correction algorithms have been proposed.151 Many investigators have measured pO2 in liver, spleen, and tumors following clearance from the blood, thus providing measurement of tissue pO2.95, 100, 115, 117, 118, 119, 152, 153, 154, 155, 156, 157

Both spectroscopic and imaging approaches have been applied to tissue pO2 measurements depending on the available SNR. It appears that uptake and distribution efficiency vary with tumor type, but in general, maximum signal is detected from the tumor periphery corresponding with regions of greater perfusion.100, 117, 138, 154, 158, 159 Several reports have examined changes in tumor pO2 in response to acute interventions such as vasoactive drugs and hyperoxic gases.32, 95, 100, 135, 136, 137, 153, 160 Spectroscopic time resolution has ranged from seconds to minutes,161, 162 whereas imaging often takes longer.160

Long tissue retention facilitates chronic studies during tumor development, and progressive tumor hypoxiation has been observed over extended time periods of many days.154, 156 Correlated 19F and proton MRI suggest that PFC does not redistribute, but remains associated with specific tissues, analogous to tree rings.154, 156 Thus in principle, a whole tumor can be investigated by administering successive doses of PFC emulsion during growth.

PFC emulsions may also be administered intraperitoneally (IP), resulting in similar distribution to IV administration (unpublished observations). Given the volatile nature of many PFCs, they could be inhaled, but although this is a popular route for delivery of anesthetics and blood flow tracers, it does not appear to have been widely exploited for oximetry. Nonetheless, aerosols have been delivered to the lungs by inhalation to facilitate pO2 measurements.163

Two approaches have been applied to circumvent reticuloendothelial uptake. PFC has been incorporated in polyalginate beads for direct implantation at a site of interest.164, 165 We favor direct IT injection of neat PFC, allowing any region of interest in a tumor to be interrogated immediately. Use of a fine needle ensures minimal tissue damage, as described in detail in a later section. Others have used direct injection of emulsions into tumors, but this increases the volume considerably, making it more invasive.88 Investigators have suggested that emulsification improves retention at the site of injection. Direct injection of neat PFC also has been used to investigate retinal oxygenation166, 167, 168 and cerebral oxygenation in the interstitial and ventricular spaces.139

As described in the following section we favor direct intratumoral injection of neat HFB followed by echo planar imaging to generate pO2 maps in tumors.

Section snippets

FREDOM (Fluorocarbon Relaxometry using Echo Planar Imaging for Dynamic Oxygen Mapping)

Recognizing that tumors are heterogeneous and that pO2 may fluctuate, we developed a procedure, which allows repeated quantitative maps of regional pO2 to be achieved with multiple individual locations simultaneously in 6.5 min with a precision of 1–3 torr, when pO2 is in the range 0–10 torr.160 We have applied FREDOM to diverse tumor types and interventions, as reviewed in a later section.

MRI is attractive because it is readily available at many institutions. For small animal work, 19F NMR is

Future

Ultimately, the value of a technique depends on its robustness, ease of use, and widespread implementation. To date, few laboratories had adopted the FREDOM approach because efficient investigation of HFB requires an unusual NMR pulse sequence. With the recent upgrade of our own instrumentation to the Varian Unity INOVA, the software is now available on this popular platform, facilitating ready implementation elsewhere. In terms of research applications, it is known that tumor tissue pO2 varies

Acknowledgements

This work was supported in part by NIH R01 CA79515 (NCl)⧸EB002762 (NIBIB), DOD Breast Cancer Initiative IDEA Award (DAMD 17–03–1–0363) (DZ) and predoctoral scholarship (DAMD 17–02–1–0592) (LJ) in conjunction with Cancer Imaging Program P20 CA 86354 and NIH BRTP Facility P41-RR02584. We are grateful to Dr. Anca Constantinescu for facilitating all the tumor investigations, Ms. Soon-Hee Sul for undertaking the Monte Carlo simulations, and Professor Eric Hahn for mentoring us in tumor biology.

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