A Model-Based Personalized Cancer Screening Strategy for ... · Strategy for Detecting Early-Stage Tumors Using Blood-Borne Biomarkers Sharon Seiko Hori1, Amelie M. Lutz1, Ramasamy

Integrated Systems and Technologies: Mathematical Oncology

A Model-Based Personalized Cancer ScreeningStrategy for Detecting Early-Stage Tumors UsingBlood-Borne BiomarkersSharon Seiko Hori1, Amelie M. Lutz1, Ramasamy Paulmurugan1,and Sanjiv Sam Gambhir1,2

Abstract

An effective cancer blood biomarker screening strategy mustdistinguish aggressive from nonaggressive tumors at an early,intervenable time. However, for blood-based strategies to beuseful, the quantity of biomarker shed into the blood and itsrelationship to tumor growth or progression must be validat-ed. To study how blood biomarker levels correlate with early-stage viable tumor growth in a mouse model of human cancer,we monitored early tumor growth of engineered human ovar-ian cancer cells (A2780) implanted orthotopically into nudemice. Biomarker shedding was monitored by serial bloodsampling, whereas tumor viability and volume were moni-tored by bioluminescence imaging and ultrasound imaging.From these metrics, we developed a mathematical modelof cancer biomarker kinetics that accounts for biomarkershedding from tumor and healthy cells, biomarker entry intovasculature, biomarker elimination from plasma, and subject-

specific tumor growth. We validated the model in a separateset of mice in which subject-specific tumor growth rateswere accurately predicted. To illustrate clinical translation ofthis strategy, we allometrically scaled model parametersfrom mouse to human and used parameters for PSA sheddingand prostate cancer. In this manner, we found that bloodbiomarker sampling data alone were capable of enablingthe detection and discrimination of simulated aggressive (2-month tumor doubling time) and nonaggressive (18-monthtumor doubling time) tumors as early as 7.2 months and8.9 years before clinical imaging, respectively. Our modeland screening strategy offers broad impact in their applica-bility to any solid cancer and associated biomarkers shed,thereby allowing a distinction between aggressive and nonaggres-sive tumors using blood biomarker sampling data alone.Cancer Res; 77(10); 2570–84. �2017 AACR.

IntroductionIn cancer screening, early and accurate diagnoses are essen-

tial. It is critical to intercept aggressive tumors and effectivelytreat them while they are likely still localized to their primaryorgan of origin, before they become more heterogeneous,unmanageable, and ultimately lethal. It is also important tominimize intervention on slow-growing tumors that may neverpose a threat during the patient's lifetime, to reduce unneces-sary stress and side effects of overtreatment. The health andwell-being of a patient therefore depend on a medical team'sability to make timely and well-informed decisions regarding apatient's disease status.

Frequentmonitoring of a patient's disease status is nowbecom-ing possible with inexpensive blood assays that measure levels ofcancer biomarkers "shed" or released into the blood from newlydeveloped tumors. However, even with repeated blood samplingto look for abnormal changes in cancer biomarker levels, amedical team still cannot make early, accurate decisions aboutdisease outcome; a deeper quantitative understanding betweenthe state of a tumor and the amount of biomarker in blood isneeded. This correlation should include factors influencing bloodmeasurements, such as biomarker pharmacokinetics (arrival intoand eliminationof biomarker fromblood), theunknownnumberand aggressiveness of viable (live) tumor cells, and the accuracy ofthe blood assay.

Deriving and validating this mathematical relationship is fur-ther complicated by the lack of in vivo measurements for cancer

1Department of Radiology, Molecular Imaging Program at Stanford (MIPS),Stanford University School of Medicine, Stanford, California. 2Departments ofBioengineering and Materials Science & Engineering, Stanford University, Stan-ford, California.

Note: Supplementary data for this article are available at Cancer ResearchOnline (http://cancerres.aacrjournals.org/).

Corresponding Author: Sanjiv Sam Gambhir, Stanford University, 318 CampusDrive, The James H. Clark Center, Room E150, Stanford, CA 94305. Phone: 650-725-2309; Fax: 650-724-4948; E-mail: [email protected]

doi: 10.1158/0008-5472.CAN-16-2904

�2017 American Association for Cancer Research.

Major FindingsWe showed that blood biomarkers highly shed from

early-stage cancers in living subjects may serve as feasiblereporters of tumor cell viability and disease aggressiveness.We developed a new mathematical modeling–based per-sonalized cancer screening strategy to aid in early clinicaldecision making to determine when to intervene on apotentially aggressive cancer, when to proceed with activesurveillance of a nonaggressive cancer, and how to optimal-ly continue blood sampling in a patient whose disease stateis unknown.

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Quick Guide to Equations and AssumptionsBiomarker shedding model

We model biomarker shed (secreted or released) from tumor (cancerous) and healthy (noncancerous) cells using acompartmental modeling approach based on the fundamental principles of mass balance. The model, biologically depictedin Fig. 3A, can be reduced to two compartments (Fig. 3C) in which qpl(t) is the amount (mass) of biomarker in whole-bodyplasma and qperiph(t) is the amount (mass) of biomarker in a generalized "periphery" that accounts for all biomarker notmeasureable in a plasma sample. The peripheral compartment may either represent uptake or storage of biomarker into aphysical region (e.g., interstitial or extravascular space) or a nonphysical means of sequestering biomarker (e.g., binding orinteraction with other proteins in plasma or extravascular space.)

The change in the amount of biomarker in a compartment with respect to time is the summation of the influx of biomarker fromother sources (tumor cells, healthy cells, periphery)minus the elimination or efflux of biomarker from the compartment. For the2-compartment model, the equations are:

dqpl tð Þdt

¼ ut tð Þ þ uh tð Þ � kel þ kperiph;pl� �

qpl tð Þ þ kpl;periphqperiph tð Þdqperiph tð Þ

dt¼ kperiph;plqpl tð Þ � kpl;periphqperiph tð Þ;

where the influx of plasma biomarker from tumor cells is

ut tð Þ ¼ RtNt tð Þand the influx of plasma biomarker from healthy cells is

uh tð Þ ¼ RhNh tð Þ ¼ uh;SS ¼ kelqpl;SS;

and by definition of mass, qpl;SS � cpl;SSVpl:

Model parameters are described below. The derivation of the model steady-state conditions in the absence of cancer is fullydescribed in the Supplementary Material.

Biomarker shedding model parameters* kel is the (irreversible) elimination rate of biomarker from plasma (day�1);* kpl,periph is the rate of biomarker movement from periphery to plasma (day�1);* kperiph,pl is the rate of biomarker movement from plasma to periphery (day�1);* Rt is the tumor cell biomarker shedding rate (ng/day/cell);* cpl,SS is the steady-state plasma biomarker concentration in a healthy subject (ng/mL);* Vpl is the plasma volume of distribution (mL).

Tumor growth modelIn cases for simulating early growth of subcentimeter-sized tumors, we used the monoexponential tumor growth model

NtðtÞ ¼ Nt0ekgr t

with model parameters described below.

Tumor growth model parameters* Nt0 is the initial number of tumor cells at time t ¼ 0;* kgr is the rate of growth of the tumor cell population (day�1).

Summary of Major Assumptions1. Biomarker in each compartment is assumed well mixed and homogeneous, thereby obeying compartmental model kinetics.2. Tumor biomarker shedding rateRt is the average shedding rate for all tumor cells of a given subject and is constantwith respect to

time and cell number. Rt is not a cell-specific shedding rate. It is assumed that Rt is initially characterized from an initialpopulation of subjects (to determine a specific population mean and SD) when the biomarker is being validated for earlydetection of a specific clinically relevant cancer(s).

Personalized Early Cancer Screening Using Blood Biomarkers

www.aacrjournals.org Cancer Res; 77(10) May 15, 2017 2571




blood biomarker shedding and early-stage tumor growth inhuman patient or animal models. Clinical data do not existbecause: (i) for ethical, financial, and practical reasons, patientswith lethal cancers cannot be serially monitored via blood andimaging over many years of untreated tumor growth; (ii) manyaggressive cancers are not discovered until they reach advancedstages, when early-stage biomarker shedding processes can nolonger be properly studied; (iii) to date, clinical cancer bloodbiomarkers are primarily utilized tomonitor disease recurrence ortreatment efficacy and are still being fully validated for early-stagediagnosis. Without an understanding of the link between cancerblood biomarker levels and tumor growth in living subjects, it isnot surprising that so far, no one has been able to truly improveexisting blood-based early cancer detection and screening strat-egies in patients.

Here, we demonstrate that the relationship between cancerblood biomarkers and tumor state may be exploited to screen forand monitor early cancers. We first establish that cancer biomar-kers may serve as reporters of early tumor state in early cancermouse models. We then develop a generalized mathematicalmodel to map the link between a growing tumor and the bio-marker levels shed into blood. Following validation of the math-ematical model in mice, we then allometrically scale the modelparameters from preclinical subjects (mice) to human patients toillustrate a new blood-based screening paradigm in which apatient's current blood biomarker sampling history can be usedto classify the presence and aggressiveness of the disease (Sup-plementary Fig. S1). This yields a new personalized cancer screen-ing methodology, one that leverages all existing blood data for agiven patient and determines whether the patient's blood historycan cumulatively provide a useful prediction regarding thatpatient's cancer state or progression. The general mathematicalmodel can be applied to any solid cancer and associated bio-marker(s) shed. Importantly, the model can best be utilized inearly clinical decisionmaking todeterminewhen to interveneonapotentially aggressive cancer, when to proceed with active sur-veillance of a nonaggressive cancer, and how to optimally con-tinue blood sampling in a specific patient whose disease state isunknown.

Materials and MethodsCloning

We constructed a vector using a dual ubiquitin promoterapproach to obtain high expression levels of both secretedalkaline phosphatase (SEAP; ref. 1) and the bifusion optical

imaging reporter firefly luciferase-enhanced GFP (FL-eGFP;refs. 2, 3). First, the gene SEAP was PCR amplified using aforward primer containing an NheI restriction enzyme site anda reverse primer with a FLAG tag sequence, stop codon, andXhoI restriction enzyme site. The restriction enzyme–digestedproduct was cloned into a corresponding enzyme–digestedmammalian expression vector [pcDNA 3.1(þ)] downstreamof a constitutive ubiquitin promoter (Ubi). The FLAG tag wasincorporated, but not used here, to allow more sensitive pull-down analyses (4) in future studies. The gene FL-eGFP wascloned into a separate mammalian expression vector [pcDNA3.1(þ)] under a constitutive Ubi promoter and then reclonedinto the Ubi-SEAP-FLAG plasmid by PCR cloning using aforward primer flanking the 50 end of the ubiquitin promoterand a reverse primer flanking the 30 end of SV40-PolA, bothwith a BglII restriction enzyme site. The final plasmid (pcPur-Ubi-SEAP-FLAG-Ubi-FL-eGFP) was sequence confirmed(Sequetech) and then used in further experiments.

Cell cultureAll cells were cultured under sterile conditions, maintained in a

5% CO2–humidified incubator at 37�C, and tested regularly forthe absence of mycoplasma contamination. Ovarian cancer cellline A2780 (epithelial ovarian carcinoma) was received in 2010,cultured in RPMI1640 (Invitrogen), and authenticated via shorttandem repeat profiling most recently in 2014 (Genetica DNALaboratories). Human embryonic kidney cells (293T) wereobtained from ATCC in 2010 and cultured in DMEM (Invitro-gen). All cells were used within 6 months of authentication orresuscitation. All media were supplemented with 10% FBS (Invi-trogen) and 1% penicillin (10,000 U/mL) and streptomycin(10,000 mg/mL) solution (Invitrogen). Cells were transfectedusing Lipofectamine 2000 transfection reagent (Invitrogen)according to themanufacturer's instructions. Stable cell lines wereobtained by antibiotic selection using 300 ng/mL puromycin(InvivoGen) in cell culture media. A2780 and 293T cells stablytransfected with a single vector expressing SEAP-FLAG andFL-eGFP are denoted A2780-SEAP-FL-eGFP and 293T-SEAP-FL-eGFP, respectively.

The highest 1% to 5% of eGFP-expressing stable A2780-SEAP-FL-eGFP and 293T-SEAP-FL-eGFP cells were collected on the basisof FACSusing the FACSAria (BDBiosciences). Collected cells wereexpanded and re-sorted twomore times, and thehighest SEAPandFL expressing single-cell clone was selected. These single-cellclones were used for all cell culture and animal experimentsdescribed in the article.

3. The influx of tumor-shed biomarker is assumed proportional to the rate of tumor biomarker shedding Rt and the number oftumor cells Nt(t), that is, ut(t) ¼ RtNt(t).

4. Healthy cells are defined to be any noncancerous cells in any organ shedding the biomarker of interest. The number ofbiomarker-shedding healthy cells, Nh(t), is generally unknown but assumed constant (i.e., cell proliferation and deathrates are equal). The healthy cell biomarker shedding rate is assumed to be constant with respect to time and cellnumber, and therefore, the influx of healthy-shed biomarker is assumed constant and at steady state, that is, uh(t) ¼RhNh(t) ¼ uh,SS.

5. Biomarker may reversibly enter peripheral space and whole-body plasma.

A more detailed description of the model and its assumptions, validations, and applications is provided in the SupplementaryMaterial.

Hori et al.

Cancer Res; 77(10) May 15, 2017 Cancer Research2572




SEAP and FL correlation in cell cultureSEAP activity was measured and converted to concentration

(ng/mL) using the Great EscAPe SEAP Chemiluminescence Assay2.0 (Clontech). Cell culture shedding rates were calculated on thebasis of themass of SEAP shed into 1mLofmedia in 24 hours andnormalized by the number of plated cells. To show that non-transfected cells do not shed detectable levels of SEAP, SEAP levelswere compared in 10% FBS media (without cells) and 10% FBSmedia collected from plated nontransfected cells. Both sampleslacked cellular production of reporter proteins (SEAP and FL), butexhibited a minimal background signal attributed to the assayitself (i.e., background optical signal).

To examine the correlation between SEAP and FL expressionin cell culture, between 1 � 102 and 1 � 106 A2780-SEAP-FL-eGFP or 293T-SEAP-FL-eGFP cells were plated in 1 mL media in12-well plates. After 24 hours, media were removed and cen-trifuged at 12,000 rpm for 1 minute, and 25 mL of the mediasupernatant was stored at �80�C to be assayed for SEAP activitylater. Next, 0.5 mL of D-luciferin (10 mg/mL in PBS) was addedto each well, and FL activity was measured in the IVIS LuminaImaging System (PerkinElmer) under sequence luminescencescan mode using 5- to 300-second acquisitions. FL activity wasquantified in terms of total flux (photon/second), averageradiance (photon/s/cm2/sr), and maximum radiance (pho-ton/s/cm2/sr) using the Living Image 3.2 software (PerkinEl-mer). In wells containing at least 1 � 103 A2780-SEAP-FL-eGFPcells, the correlation between cell number and media SEAPconcentration (Fig. 1D, unpaired two-tailed P ¼ 0.005), and FLaverage radiance (Fig. 1F, unpaired two-tailed P ¼ 0.0001), wassignificantly higher relative to nontransfected A2780 cells.Notably, the correlation between media SEAP concentrationand FL activity was also high for 1 � 103 to 1 � 106 platedA2780-SEAP-FL-eGFP cells (Fig. 1G, R2 ¼ 0.99).

Tumor implantation, blood sampling, and imaging of livingmice

All animal experiments were performed in accordance with aprotocol approved by the Stanford University AdministrativePanels on Laboratory Animal Care. Female nudemice (4–5weeksold) were purchased from Charles River Laboratories. Cells werecollected by trypsinization at 70% to 80% confluence, washed inmedia, resuspended, and counted in PBS. Three extra aliquots ofcellswere prepared tomanually validate approximate cell numberusing a hemocytometer.

Mice were anesthetized with 2% isoflurane in oxygen at 2 l/minute. For orthotopic implantation of ovarian cancer cells in theovary, surgery was performed under aseptic conditions. A longi-tudinal paramedian skin incision was made on the left flank,followed by a small incision in the abdominal muscle that wasenlarged by blunt dissection. The left ovarian fat pad and ovarywere retracted through the incision, and a small tear was made inthe bursal membrane to expose the infundibulum. Bleeding wasminimized by preemptively applying a small drop (<10 mL) ofepinephrine (1:100,000) to the bursal membrane. A single injec-tion of either 3� 106, 3� 105, 3� 104, 3� 103, or 3� 102 A2780-SEAP-FL-eGFP cells or 3� 105 A2780 cells in a volume of <15 mLPBS was delivered into the ovarian bursa under a dissectionmicroscope using a 31.5-gauge insulin syringe. The needle wasinserted into the oviduct near the infundibulum, toward the bursaand ovary. The incision was stitched with absorbable sutures, andthe skin was stapled closed with autoclips. We chose a 15-day

preclinical endpoint for "early" detectable ovarian tumors basedon the in vivo ultrasound measurements [2–4 mm diameter (5),which includes healthy ovarian tissue].

For subcutaneous implantation of 293T cells, either 1 � 105

293T cells or 1�105, 5�104, 1� 104, 5�103, 1�103, or 5�102

293T-SEAP-FL-eGFP cells were prepared in 25 mL PBS and 25 mLgrowth factor–reduced Matrigel (BD Biosciences) and implanteddorsally and 1 cm anterior to the tail.

Tumor dimensions were measured by digital caliper (FisherScientific) and/or using the Vevo 2100 high-resolution ultra-sound micro-imaging system (VisualSonics). Mice bearing fewerthan 3 � 103 A2780-SEAP-FL-eGFP cells did not develop SEAP-detectable or FL-detectable tumors (Fig. 1I and J), and no tumorswere found in these animals using in vivo ultrasound imaging orduring postexperiment dissection.

Plasma samples (25–30 mL) were obtained by submandibularbleeding at various times after tumor implantation using 5-mmGoldenrod Animal Lancets (Medipoint, Inc.) and BD LithiumHeparin-Coated Microtainer plasma separation tubes (FisherScientific) following themanufacturers' recommended protocols.All plasma samples were stored at �80�C until assayed.

To quantify FL bioluminescence activity, mice were anesthe-tized with 2% isoflurane in oxygen at 2 l/minute, and D-luciferin(3 mg in 100 mL PBS per mouse) was administered intraperito-neally. Mice were imaged in the IVIS Spectrum (PerkinElmer)under sequence luminescence scan mode using 5- to 300-secondacquisitions. Living Image 3.2 software was used to quantifytumor FL in terms of average radiance (photon/s/cm2/sr).

To measure the degradation (or irreversible elimination) ofSEAP frommouse plasma, we injected either 900 ng or 5 ng SEAPintravenously via the tail vein, and SEAP concentration wasmeasured in plasma samples taken at various times ranging from1 minute to 10 days postinjection.

Mathematical model of cancer biomarker shedding andtumor growth

We developed a series of compartmental models (Figs. 3B andC) that account for biomarker shedding by tumor and healthycells, based on the biological depiction shown in Fig. 3A. Here,healthy cells are defined to be any noncancerous cells in any organshedding the biomarker of interest. Biomarker produced in tumorcells and healthy cells is shed into whole-body plasma (qpl) andmay reversibly enter the tumor extravascular space (qtPeriph) orhealthy extravascular space (qhPeriph). Biomarker in each com-partment is assumedwell-mixed and homogenous, thereby obey-ing compartmental model kinetics. The influx, ut(t), of tumor-shed biomarker is assumed proportional to the rate of tumorbiomarker shedding, Rt (ng/day/cell), and the number of tumorcells, Nt(t), that is, ut(t) ¼ RtNt(t).

Healthy cells are also assumed to shed biomarker at a constantrate, Rh (ng/day/cell). The number of biomarker-sheddinghealthy cells, Nh(t), is generally unknown but assumed constant(i.e., cell proliferation and death rates are equal). Therefore, theinflux, uh(t), of healthy-shed biomarker is constant and at steadystate, that is, uh(t) ¼ RhNh(t) ¼ uh,SS.

Biomarker movement from compartment qi to qj is representedby fractional rate constant kj,i (day

�1). Irreversible elimination ofbiomarker from plasma occurs at rate kel (day

�1), which accountsfor degradation or removal of intact biomarker from plasma.

Supplementary Tables S1 and S2 summarize the model statevariables and parameters. For additional model details and the






Hori et al.





derivation of the model equations at steady state in the absenceof cancer, see Supplementary Material.

Reducing the 3-compartmentmodel to a 2-compartmentmodelThe 3-compartment model has "tumor peripheral" (qtPeriph)

and "healthy peripheral" (qhPeriph) compartments to account forbiomarker unavailable for measurement from plasma (Fig. 3B).Becausewe aimed tomodel the growthof early tumors prior to thedevelopment of an established vascular network andwell-definedtumor microenvironment (6), the 3-compartment model can befurther reduced to two compartments (Fig. 3C), in which ageneralized "periphery" (qperiph) accounts for all biomarker notmeasureable in a plasma sample. The peripheral compartmentaccounts for the uptake or storage of biomarker into nonplasmaspace. We note that while the peripheral compartments mayrepresent a physical region (e.g., interstitial or extravascularspace), they may also represent a nonphysical means of seques-tering biomarker (e.g., binding or interaction with other proteinsin plasma or extravascular space).

Model fitting and parameter estimation methodologyAll plasma SEAP data were log10-transformed so that the

rescaled data measurements appeared uniformly on the sameaxes and could be uniformly weighted (i.e., each data point diwasassigned a weight wi ¼ 1) during the fitting. We used the simu-lation, analysis, and modeling software SAAM II (The EpsilonGroup; ref. 7) for all model fitting and sensitivity analyses. Modelfits were compared using the Akaike information criterion (AIC)and the Bayesian information criterion (BIC), with lower AIC andBIC values indicating a better fit (8, 9).

FL average radiance [FL(t)] was converted to viable tumor cellnumber [Nt(t)] using the equation, log10[Nt(t)] ¼ (log10[FL(t)] –0.80)/1.06, which is the equation of the line fitted through theA2780-SEAP-FL-eGFP data in Fig. 1L. For each tumor-bearingmouse, the calculated Nt(t) was used as a linearly interpolatedforcing function in the tumor biomarker input function, ut(t) ¼RtNt(t). The 2-compartment model (Fig. 3C) was simultaneouslyfitted to individual tumor-bearing mouse plasma SEAP data (Fig.3E–G) and to the mean plasma SEAP levels in healthy micefollowing intravenous injection of 900 ng or 4 ng SEAP (Fig.3D) to estimate the following parameters: (i) Rt, the tumor cellbiomarker shedding rate (ng/day/cell); (ii) kel, the eliminationrate of biomarker from plasma (day�1); (iii) kpl,periph, the rate of

movement of biomarker from periphery to plasma (day�1); (iv)kperiph,pl, the rate of movement of biomarker from plasma toperiphery (day�1); (v) cpl,SS, the steady-state plasma biomarkerconcentration in a healthy subject (ng/mL); and (vi) Vpl, theplasma volume of distribution (mL).

Validation of the 2-compartment model using training andprediction datasets

Any blood biomarker being advocated for cancer detectionutility in the clinic must first be evaluated in a given populationof patients; once the biomarker pharmacokinetics have beendetermined in this "training set," the ability of the biomarker topredict cancer progression may be determined in a separatepatient population, the "prediction set." The utility of themathematical model was established by showing that theestimated training set parameters can provide decent predic-tions of cancer progression in the prediction set. Here, we usedin vivo preclinical data obtained for plasma SEAP levels andtumor volume determined by bioluminescence imaging (BLI)to explicitly validate the model's predictive capability by suc-cessfully estimating tumor growth parameters in a predictionsubset of subjects. An analogous study can be performed forother cancers and biomarkers of interest, once such databecome available; this is of particular interest and need in theclinical setting.

Mice were randomized into training and prediction subsets(n ¼ 9 mice/subset). Randomization trials were repeated10 times. For each randomization trial, the 2-compartmentmodel was fitted simultaneously to all plasma SEAP data inthe training subset to obtain population parameter estimatesfor Rt, Vpl, cpl,SS, kel, kpl,periph, and kperiph,pl, which define SEAPshedding rates and pharmacokinetics (SupplementaryTable S4). These population parameter estimates were thenused to predict individualized tumor growth parameters Nt0

and kgr in individual mice in the prediction subset (Supple-mentary Fig. S5). In this simplified example, early-stage tumorgrowth was estimated using the monoexponential equation,

Nt tð Þ ¼ Nt0ekgr t ;

whereNt0 is the initial number of tumor cells implanted, and kgris the growth rate of the tumor cell population. We used themonoexponential equation here to obtain, in the simplest sense,

Figure 1.Plasma biomarker levels correlate with tumor viability in vivo in an orthotopic early ovarian cancer mouse model. A, Plasmid pcPur-Ubi-SEAP-FLAG-Ubi-FL-eGFP used to highly coexpress correlated levels of tumor-specific biomarker SEAP and BLI bifusion reporter FL-eGFP. B and C, Comparison of shedSEAP levels (B) and FL activity [C; total flux, p/s (red); average radiance, p/s/cm2/sr (blue); maximum radiance, p/s/cm2/sr (green)] in stablytransfected A2780-SEAP-FL-eGFP single-cell clones in cell culture 24 hours after plating (mean � SEM shown for n ¼ 3 wells per clone). D–F, MediaSEAP concentration and FL activity (E and F) were assessed 24 hours after plating A2780-SEAP-FL-eGFP clone 1 cells (closed circles) or nontransfectedA2780 cells (open circles; mean � SEM shown for n ¼ 4 wells per cell number). G, The correlation between FL average radiance and media SEAPconcentration for the indicated number of plated cells (n ¼ 4 wells per cell number). Dashed lines indicate signal due to media alone (in absence of cells),indicating inherent assay background signal not due to production of reporter proteins (SEAP or FL). H, Detection of ovarian tumors via in vivoultrasound imaging in one representative mouse with 3 � 104 A2780-SEAP-FL-eGFP cells implanted in the left ovary. I–K, Plasma SEAP (I) and in vivo FLaverage radiance (J and K) were monitored in mice inoculated with 3 � 106 (red; n ¼ 6 mice), 3 � 105 (yellow; n ¼ 6 mice), 3 � 104 (blue; n ¼ 6 mice), 3 � 103

(green; n ¼ 4 mice), 3 � 102 (purple; n ¼ 4 mice) A2780-SEAP-FL-eGFP cells, or 3 � 105 nontransfected A2780 cells (white; n ¼ 3 mice). PlasmaSEAP concentration and FL average radiance were indistinguishable from baseline (healthy) mouse levels for 3 � 102 and 3 � 103 A2780-SEAP-FL-eGFPcells and 3 � 105 A2780 cells. L, In vivo FL activity measured within 4 hours of cell implantation correlated well with implanted cell number for theindicated n replicates. M, The correlation between plasma SEAP and in vivo FL activity was plotted at each time point for mice bearing 3 � 106 (red;n ¼ 6 mice), 3 � 105 (yellow; n ¼ 6 mice), or 3 � 104 (blue; n ¼ 6 mice) A2780-SEAP-FL-eGFP cells. Solid black line, overall correlation in all measurementsfor n ¼ 18 A2780-SEAP-FL-eGFP tumor-bearing mice.






a basic generalization of tumor presence and progression (e.g.,Nt0 > 0, kgr > 0). This is not unreasonable, as early-stagepreclinical xenograft models have been shown to follow mono-exponential (or variants such as Gompertzian) growth (10, 11).We do not attempt to model tumor growth or cancer develop-ment on a multiscale level, as has been done in other mathe-matical models incorporating several tumor cell states (hypoxic,dormant, etc.) and biological processes (angiogenesis, apopto-sis, senescence, etc.; ref. 12), although these models may theo-retically be substituted in place of the monoexponential equa-tion in future studies.

ResultsCancer-specific blood biomarkers correlate with early-stagetumor viability

Because no clinical biomarker has yet proven successful forearly cancer screening purposes (13, 14), and as the potential ofblood biomarker screening for early cancers has not been vali-dated yet in human patients (14, 15), a critical first step is to verifythat cancer biomarkers are capable of detecting small (subcenti-meter) early-stage tumors in living animals. We do this here byfirst developing tumorigenic cell lines distinguishable fromendogenous healthy cells based on their ability to be highlydetectable via the blood and imaging. We stably transfectedhuman epithelial ovarian cancer cell line A2780 with twotumor-specific reporter genes: (i) SEAP (1), a truncated form ofhuman placental alkaline phosphatase not normally produced inany cell and thus shed only from transfected tumor cells; and (ii)the bifusion optical imaging reporter, FL-eGFP (2, 3), whichenables both sensitive detection of cell viability via BLI and cellsorting capabilities via fluorescence imaging (Fig. 1A). Use of atumor-specific biomarker and sensitive imaging modality neces-sarily reduces a biologically complicated biomarker sheddingsystem into an ideal one in which biomarker is knowinglyreleased only from imageable (quantifiable) tumor cells. Here,the stably transfected A2780-SEAP-FL-eGFP clone highly expres-sing SEAP and FL-eGFP shed 1,600-fold more SEAP (Fig. 1B) andexpressed 42,000-fold higher FL average radiance (Fig. 1C) rela-tive to nontransfected A2780 cells in culture. This enabled simul-taneous and highly sensitive detection via shed biomarker(Fig. 1D) and cellular imaging (Figs. 1E and F), with both bio-marker and imaging reporters correlating well with respect to cellnumber and each other, over at least 3 log-orders of magnitude,for as few as 1 � 103 cells (R2 ¼ 0.99, Fig. 1G).

It has been reported that BLI signal correlates well with viabletransfected cell number in culture and with large tumor burdenin various subcutaneous cancer xenograft models (16–20), butnot for submillimeter early-stage solid tumors implantedorthotopically, let alone for deep-tissue cancers, such as ovariancarcinoma, which are even more difficult to detect via opticalmethods due to increased light attenuation. To examine howblood biomarker kinetics change over the course of early viabletumor growth in vivo, we surgically implanted a range of A2780-SEAP-FL-eGFP cells (from 3 � 102 to 3 � 106 cells) orthoto-pically in the nude mouse ovary and monitored tumor growthvia ultrasound imaging (Fig. 1H), blood SEAP (Fig. 1I), and BLIsignal (Figs. 1J and K; Supplementary Fig. S2) for at least15 days of "early" tumor growth, while the ultrasound imagesshowed that the healthy and tumor tissue in the ovary was lessthan 5 mm in diameter. FL activity correlated well with

implanted cell number as early as 4 hours postimplantationfor a range of 3 � 104 to 3 � 106 implanted cells (R2 ¼ 0.98,Fig. 1L). We observed a high correlation between FL averageradiance and plasma SEAP concentration for groups of micebearing 3 � 104, 3 � 105, or 3 � 106 A2780-SEAP-FL-eGFP cells(R2 ¼ 0.62–0.79, Fig. 1M), and a higher correlation for thecombined data of all replicate mice (R2 ¼ 0.86, Fig. 1M). Notsurprisingly, these overall correlative trends were also observedin individual mice (Fig. 2), even in mice that remained healthyfor observation up to 25 days. This indicates that withoutconfounding background biomarker shedding from healthycells, the correlation between tumor-shed biomarker and tumorcell viability is notably high and remains so possibly beyondthe 15-day "early growth" period. Finally, to examine thecorrelation in other cell lines and xenograft models, we repeat-ed the transfection and SEAP-FL correlation analyses in thehuman embryonic kidney cell line 293T in culture and in asubcutaneous xenograft mouse model using a stably transfected293T-SEAP-FL-eGFP clone. The correlation between plasmabiomarker levels and tumor viability was also consistently highin vivo (R2 ¼ 0.91, Supplementary Fig. S3).

We found that as few as 3 � 104 ovarian cancer cells weredetectable by SEAP shed into the 2-mL mouse blood volume. Arough extrapolation to patients suggests that 9 � 107 cells maylead to detectable biomarker levels in 6 Lof patient blood volume,assuming equivalent biomarker shedding rates and a linear scale-up for humans.Given a1�106 cells/mm3 tumordensity (21, 22),this corresponds to a tumor volume of about 90 mm3 (or 4.53

mm3), which may be detectable by a clinical biomarker such asCA125, if CA125were shed at 500-fold higher rates than currentlymeasured (21).

Because frequent blood- and imaging-based early cancer mon-itoring cannot practically be performed in human patients, thismanipulatable living mouse model of early cancer growth isadvantageous because (i) a known, low number of cancer cellscan bemonitoredwith high sensitivity and specificity via a tumor-specific secreted biomarker; and (ii) tumor growth and viabilitycan be easily localized and quantified via noninvasive imagingmethods in a living subject, over the natural course of cancerprogression. Although an in vivo biological correlation existsbetween cancer blood biomarker levels and tumor size in bothorthotopic (Fig. 1M) and subcutaneous xenograft mouse models(Supplementary Fig. S3J), themathematical relationship betweenthese blood and tumor measurements has not yet been estab-lished and validated in vivo. This quantitative link is important forunderstanding why SEAP exemplifies an ideal early cancer bio-marker, and for evaluating how endogenous clinically relevantbiomarkers may be better exploited to detect aggressive tumorsearlier.

In vivo cancer biomarker shedding rate measurable forindividual subjects

Most clinical cancer blood biomarkers are shed not only fromtumor cells, but from healthy (noncancerous) cells in benignconditions as well. Therefore, although an exclusively tumor-shedbiomarker, such as SEAP, may be used to detect an early-stagetumor, twonatural follow-up questions are: (i) what are the in vivoshedding rates of an ideal, exclusively tumor-shed biomarker thatenable early tumor detectability; and (ii) how does backgroundbiomarker shedding from healthy cells interfere with tumordetection in vivo?

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Figure 2.

Correlation between plasma SEAP concentration and FL average radiance for individual mice. Mice bearing either 3 � 106 (red; n ¼ 6 mice), 3 � 105 (yellow; n ¼ 6mice), or 3 � 104 (blue; n ¼ 6 mice) A2780-SEAP-FL-eGFP cells in the ovary.






Figure 3.

Mathematical model of cancer biomarker shedding and tumor growth. A, Biological schematic illustrating biomarker influx from tumor cells, ut(t), and fromhealthy cells, uh(t). Fractional rate constants ki,j represent transfer of biomarker from compartment j to compartment i. See Supplementary Tables S1 andS2 for a description of all model state variables, parameters, and units. B and C, Mathematical schematic of the general 3-compartment model (B),which reduces to a 2-compartment submodel (C). D, Plasma SEAP concentration was measured at various times following intravenous injection of 900 ng(solid line) or 5 ng SEAP (dashed line) in healthy mice (without tumor). Model fits from all replicate mice are similar and therefore appear superimposed.E–G, For tumor-bearing mice, plasma SEAP levels were monitored following implantation of 3 � 106 (E), 3 � 105 (F), or 3 � 104 (G) A2780-SEAP-FL-eGFPcells in the ovary in n ¼ 6 replicate mice per group. Solid lines in E–G indicate model fits to each mouse replicate, fitted simultaneously with data in D.

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To derive the dynamic in vivo relationships between bio-marker shedding, plasma biomarker kinetics, and tumorgrowth, we next developed a general mathematical model todescribe biomarker rates of change in three in vivo compart-ments: tumor extravascular space, healthy extravascular space,and whole-body plasma (Fig. 3A and B; Supplementary TablesS1 and S2). The general 3-compartment model can be extendedto virtually any solid tumor and associated biomarkers shedand is intended to be further tailored for a specific cancer andbiomarker or biomarker panel. During early tumor growth,before leaky tumor vasculature has been established and bio-marker is still entering healthy vasculature, the 3-compartmentmodel reduces to 2 compartments (Fig. 3C). To our knowledge,these models are the first to characterize the in vivo sheddingrates, vascular permeabilities, and blood pharmacokinetics of agiven biomarker of interest, relative to the presence of early-stage cancer in vivo.

For example, to characterize SEAP in the mice bearing ortho-topic A2780-SEAP-FL-eGFP ovarian tumors, we first measuredthe half-life of SEAP in blood in healthy mice followingintravenous injection of purified SEAP (Fig. 3D) and thensimultaneously fitted the 2-compartment model equations(Supplementary Materials) to these data and to each tumor-bearing mouse's 15-day blood SEAP profile (Fig. 3E–G). Themodel provides in vivo estimates for the following parameters(Supplementary Table S3): (i) Rt, the tumor cell biomarkershedding rate (ng/day/cell); (ii) kel, the elimination rate ofbiomarker from plasma (day�1); (iii) kpl,periph, the rate ofmovement of biomarker from periphery to plasma (day�1);(iv) kperiph,pl, the rate of movement of biomarker from plasmato periphery (day�1); (v) cpl,SS, the steady-state plasma bio-marker concentration in a healthy animal (ng/mL); and (vi)Vpl, the plasma volume of distribution (mL).

A major advance of this mathematical modeling analysisis that an in vivo biomarker shedding rate, Rt, can now bequantified for an individual living subject, relative to any earlytumor burden present. This rate represents an average rate for agiven time period and inherently takes into account anysubject-specific biological differences in tumor cell biomarkerexpression and tumor growth rate. For the ovarian cancermouse model, SEAP shedding rate Rt values ranged from2 � 10�5 to 8 � 10�5 ng/cell/day, consistent with the sheddingrate measured in cell culture conditions (6 � 10�5 ng/cell/day,Supplementary Fig. S4). Interestingly, mice implanted with3 � 104 A2780-SEAP-FL cells exhibited roughly 4-fold lowershedding rates compared with mice in the 3 � 105 and 3 � 106

cell groups; this is consistent with the higher probability ofinitial cell death (or limited cell survival) for these extremelyfew implanted cells.

The mathematical model is intended to predict subject-specific (personalized) tumor growth rates based on a subject'scancer blood biomarker profile alone. To validate the modelstructure, we used biomarker and tumor growth data from arandomized initial population of mice to train the model andestimate biomarker shedding rates and other pharmacokineticparameters (Supplementary Fig. S5; Supplementary Table S4).These parameters were then used to make subject-specificpredictions about tumor growth in a separate population ofmice (Supplementary Fig. S6). Using SEAP as an examplebiomarker, the model was used to accurately predict the tumorgrowth profiles of individual mice based on their plasma SEAP

data alone. Similar integrative experimental and mathematicalmodeling studies can be performed for validation of cancerbiomarkers in the clinic, once the appropriate serial blood andtumor data become readily available.

Model extends to clinical cancer biomarkers shed from tumorand healthy cells

SEAP was chosen as an ideal cancer biomarker because it isexclusively tumor-shed and therefore enabled gold-standardin vivo blood detectability. To determine how backgroundbiomarker shedding from healthy cells may interfere withtumor detection for other biomarkers in vivo, as is commonfor clinical cancer biomarkers, and to mimic other biologicalinfluences on plasma biomarker levels (e.g., autoantibodies thatdecrease biomarker levels, changes in vascular permeability,etc.), we next examined a range of parameter values that maybe exhibited by more realistic clinical biomarkers. We per-formed a one-way sensitivity analysis by resimulating plasmaSEAP levels following a 10-, 100-, or 1,000-fold increase ordecrease in a single population parameter estimate (Fig. 4).Clearly, increasing Rt would increase the predicted plasmaSEAP levels (Fig. 4A) and prompt earlier detectability. Alteringkel, kpl,periph, and kperiph,pl, however, have little impact on plasmaSEAP levels (Fig. 4B–D). Decreasing Vpl, the apparent plasmavolume of distribution, would theoretically increase plasmaSEAP levels, although physically this may not be feasible(Fig. 4E). Interestingly, model simulations showed that increas-ing cpl,SS 1,000-fold, as may be expected if SEAP were producedendogenously by healthy cells, would obscure detectability ofthis early ovarian tumor even beyond 15 days (Fig. 4F).

Mathematical model establishes blood-based personalizedearly cancer screening paradigm

Previous cancer biomarker mathematical models have usedblood biomarker levels to estimate tumor size, which is onemeasure of the state of a tumor (21, 22). A more useful metric isthe aggressiveness of the cancer, which may indicate howquickly the disease is progressing. To illustrate the translationalimpact of the model on patient screening and early diagnosis ofaggressive and nonaggressive cancers in the clinic, we nextpresent a simulated scenario in which asymptomatic patientsare actively monitored for a specific blood biomarker indicativeof the presence of a potentially lethal cancer (SupplementaryMaterial). Here, we aim to identify patients who unknowinglyhave aggressive primary tumors, using their plasma biomarkermeasurements alone, at an early, intervenable time before thecancer becomes large enough (>53 mm3) to be likely detectableby current clinical imaging modalities, such as MRI, PET, CT, orultrasound. We also aim to identify patients that have nonag-gressive or slow-growing cancers that may not pose a threat forseveral decades (if at all), to minimize their risk of beingovertreated.

There is currently no clinical data available for trackingblood biomarker levels and tumor volume measurementsin individual patients over the course of untreated tumorgrowth. Acquisition of such data is not trivial, requiringpopulation-based screening studies spanning decades ofeffort, thousands of highly monitored cancer patients withvarying degrees of disease, and immense financial resourcesto enable frequent blood screening and imaging. To illustratethe potential of our modeling strategy, we therefore






allometrically scaled (23–25) the biomarker parameters esti-mated from our in vivo ovarian mouse model to patients andforward-simulated clinical tumor growth and correspondingplasma biomarker sampling profiles for patients undergoingregular blood draws (e.g., every 3 months, although anysampling frequency can be implemented; SupplementaryMaterial). To mimic common obstacles hindering blood-based early cancer detection, we assumed biomarker sheddingfrom both tumor and healthy cells, at rates similar to the well-studied clinical blood biomarker PSA (Supplementary Mate-rial). We also incorporated assay measurement error (technicalvariability), which would affect a clinician's ability to accu-rately interpret biological anomalies (Supplementary Materi-al). We summarize our findings here in 3 representativepatients who have either: (i) aggressive disease, requiringintervention within 12 months of detection (Fig. 5A–D; Sup-plementary Fig. S7A–S7D); (ii) moderately aggressive disease,requiring intervention within 1 to 5 years (Supplementary Fig.S8A–S8C); or (iii) nonaggressive disease, requiring interven-tion after 5 years, if at all (Fig. 6A–C).

We use the mathematical model of blood biomarker shed-ding to introduce a new modeling-based screening strategy thatintegrates the patient's blood sampling history into the deci-sion-making process for blood-based diagnosis. After eachblood draw, the biomarker shedding model is fitted to thepatient's cumulative blood biomarker data. If the patient's

blood sampling history suggests the potential presence of agrowing tumor, the model provides an estimate of the currenttumor burden volume as well as a measure of the aggressivenessof the cancer (in terms of the time required for the tumor tobecome imaging detectable), with a specified "threshold ofuncertainty" (a reflection of the model's goodness of fit, basedon the SD of the tumor growth rate estimated during the modelfitting). A screening decision can be made when the model fitsthe data within an acceptable threshold of uncertainty, whichcan be tailored for each individual patient (e.g., here, we use a20% coefficient of variation in the estimated tumor growthrate). The aim of the following simulations is to illustrate a"dynamic" mathematical modeling strategy that may beexploited to better design optimal blood sampling schedulesbased on the specific parameters of a given patient. The goal ofthis strategy is to utilize a patient's cumulative blood samplinghistory (current and past measurements) to determine whetherthe patient should proceed to imaging or other diagnosticfollow-up.

Figure 5A illustrates the simulated blood sampling history(red circles) and true but unknown tumor growth curve (bluecircles) of an example patient who unknowingly has an aggres-sive cancer (2-month doubling time). Although blood samplesare acquired every 3 months, the tumor remains small and doesnot become imaging detectable until month 49.1 at its earliest(when it reaches a volume of 53 mm3, Fig. 5A); even then, the

Figure 4.

One-way sensitivity analyses to compareSEAP to other potential cancerbiomarkers. Parameter estimates wereaveraged for the n ¼ 6 mice from the3� 104 A2780-SEAP-FL-eGFP cell group.A–F, Plasma SEAP levels were thensimulated after a 0-fold (black ––––),10-fold (blue ––––), 100-fold (blue – – –), or1,000-fold (blue ***) increase or decreasein the indicated parameter estimates: RT

(A); kel (B); kpl,periph (C); kperiph,pl (D); Vpl

(E); cpl,SS (F).

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tumor may go undetected until it becomes symptomatic orotherwise clinically apparent. Without a quantitative frame-work to link plasma biomarker levels to tumor size, thepatient's plasma biomarker are assumed "normal" through

month 51, when the tumor is 6.243 mm3 and finally largeenough to be imaging detectable. But based on the patient'sblood sampling history alone, could it have been detectedearlier, and known that it would grow aggressively?

Figure 5.

Application of the mathematical modelto personalized screening of patientswith asymptomatic aggressive disease.Simulated screening scenario in whichpatient plasma biomarker levels weresampled every 3 months during thesimulated growth of an aggressivetumor (2-month doubling time). A–D,The model was fitted (red curve, lefty-axis) to simulated patient bloodbiomarker sampling data (red circles,left y-axis) alone for the entire 51-monthblood sampling history until the tumorbecame imaging detectable (A), or upto 30 months (B), 39 months (C), or 42months (D). Themodel-predicted tumorgrowth curve (blue curve, right y-axis)was then compared with the truesimulated tumor growth data (bluecircles, right y-axis) not used in modelfitting. The model-predictedparameters (mean � SD) includedtimage, the estimated time of imagingdetectability, and dbiom, the estimatedtumor diameter at the last biomarkersample. Yellow region, lead time gainedwhen the model predicts the imaging-detectable time within a threshold of20% uncertainty; gray region, timeperiod after the tumor becomesimaging detectable. Note differences inleft y-axis scale between panels.






For the representative patient shown in Fig. 5, at least 11 bloodsamples are needed for themodel to initially detect thepresence ofa tumor (month 30, Fig. 5B). At this time, the model predicts thetumor will not become imaging detectable until month 46.0 �132.3, and as the variability in this prediction is greater than the20% threshold of uncertainty (132.3/46.0 � 100 ¼ 288%), thissuggests that more blood samples are needed to hone the modelpredictions for this patient and distinguish the cancer fromrandom fluctuations in assay measurement error. By includingat least 3 to 4more blood samples (Fig. 5C and D), the variabilityreduces to 21%bymonth 39 and then 7%bymonth 42, when themodel predicts that the tumor will become imaging detectable in

7.2months, indicative of aggressive tumor growth. In this case, themodel predicts the tumor is only 2.213� 0.743mm3 based on thepatient's blood data alone. We note that inclusion of moresamples taken every 3 months, which would require additionalwaiting time, would further improve the variability of the param-eter estimates but at the potential increased risk of the patient'shealth (Fig. 5A). Instead, an alternative patient-specific samplingschedule can be implemented in which additional blood samplesare taken immediately and more frequently (daily or weekly) assoon as the model detects the presence of cancer (e.g., starting asearly asmonth 30 for the patient in Fig. 5B); with these additionaldata, it is less likely that the blood sampling history will be a

Figure 6.

Application of the mathematical model to personalized screening of patients with asymptomatic nonaggressive disease. Simulated screening scenarioin which patient plasma biomarker levels were sampled every 3 months during the simulated growth of a nonaggressive tumor (18-month doubling time).A–C, The model was fitted (red curve, left y-axis) to simulated patient biomarker sampling data (red circles, left y-axis) alone for the entire 37-yearblood sampling history (A) until the tumor became imaging detectable or up to 27.25 years (B), or 28 years (C). The model-predicted tumor growthcurve (blue curve, right y-axis) was then compared with the true simulated tumor growth data (blue circles, right y-axis) not used in model fitting. Themodel-predicted parameters (mean � SD) included timage, the estimated time of imaging detectability, and dbiom, the estimated tumor diameter at thelast biomarker sample. Yellow region, lead time gained when the model predicts the imaging-detectable time within a threshold of 20% uncertainty;gray region, time period after the tumor becomes imaging detectable. Note differences in left y-axis scale between panels.

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misrepresentation of the true tumor growth. Importantly, themathematical model is intended to be refitted to all biomarkerdata after every blood sample, to assess the likelihood of aggres-sive disease relative to any new biomarker data incorporated intothe patient's blood sampling history.

Because variability of the biomarker sampling data can affectthe accuracy and confidence (certainty) of the model predic-tions, we next sought to quantify how the model predictions ofdetection time and tumor burden volume would change in theabsence of assay measurement error (Supplementary Material).Supplementary Fig. S7A–S7D illustrate the true biomarkerdata (with mb ¼ 0 and sb ¼ 0) from the representative patientin Fig. 5. We first note that measurement error does not affectthe accuracy (predicted imaging detection time ¼ month 49.1)or certainty (1%) of the model predictions when all bloodsamples are included for this patient (Supplementary Fig. S7Avs. Fig. 5A). The model's confidence in its predicted detectiontime via imaging is lower in the presence of measurement error(288% in Fig. 5B vs. 1076% in Supplementary Fig. S7B)because, in this case, the random noise incorrectly suggests thepresence of a more aggressive tumor. Again, this highlightsthe need to immediately acquire more frequent blood samples,particularly when a reasonable (20%) threshold of uncertaintyis exceeded. As noted in all cases (Fig. 5; SupplementaryFig. S7), the certainty of the model predictions improves asmore blood samples are incorporated into the fitting (from288% to 1% in Fig. 5A and B, respectively, and from 1076% to1% in Supplementary Fig. S7A–S7B, respectively).

To illustrate how this modeling-based screening strategy maybe implemented over years of blood sampling, we repeated themodeling analysis in patients representing moderately aggres-sive disease (Supplementary Fig. S8A–S8C) and nonaggressivedisease (Fig. 6A–C). In each case, respectively, the model wasable to predict the presence of disease 2.5 and 8.9 years earlierthan imaging, suggesting that these patients were not at imme-diate risk for aggressive disease (<1 year).

We note that in all cases examined, the predicted detection time(and thus the aggressiveness of disease) was estimable with agreater certainty than the predicted tumor diameter. This isimportant because although additional blood samples may beneeded to pinpoint the size of the tumor, the aggressiveness ofthe tumor can be estimated with better certainty early on.

DiscussionThis new comprehensive set of in vivo plasma biomarker

profiling data enables a more rigorous, kinetic analysis in indi-vidual living subjects, over the entire unperturbed course of earlycancer progression. Importantly, this integrative experimentalmodeling approach can be extended to characterize new classesof candidate clinical biomarkers released indirectly from tumors,including circulating nucleic acids (26), autoantibodies generatedin response to tumor-associated antigens, (27–33), and syntheticbiomarkers shed following exogenous administration of genevector (34) or nanoparticle-based agents (35), which exhibitwidely varying blood kinetics, half-lives, and assay diagnostics.Future studies may also broaden the applications of this patient-specific mathematical modeling approach beyond early cancerscreening to address other unmet clinical needs, such as moni-toring and predicting cancer treatment response. Additional stud-ies in living animals and in patients may also be pursued to better

understand biomarker shedding mechanisms during in vivotumor development. In particular, genetically engineered mousemodels can be used to mimic spontaneous cancer growth andimmune interactions within the tumor microenvironment. Thekinetics of biomarker shedding in healthy patients as a function ofage, genetics, and environmental factors may eventually be incor-porated into the mathematical model as the relevant patient-specific and population data become available.

The advancement of new technologies that minimize tech-nical (measurement) variability may further improve the accu-racy of the model predictions. More sensitive blood-basedmeasurements are now becoming possible, especially fornewer classes of biomarkers, such as circulating tumor DNA(36–38). Weekly or daily monitoring of biomarker levels isbecoming possible with the development of new wearable orimplantable diagnostics, such as the glucose-monitoring con-tact lens (39). These improvements in the accuracy and fre-quency of cancer biomarker sampling may require a decade ormore of development, but can be developed in parallel withthe validation of better early cancer biomarkers, alongside theimplementation of the personalized blood screening schedulesdeveloped here, to facilitate the modeling-based classificationof aggressive and nonaggressive cancers.

Disclosure of Potential Conflicts of InterestNo potential conflicts of interest were disclosed.

Authors' ContributionsConception and design: S.S. Hori, R. Paulmurugan, S.S. GambhirDevelopment of methodology: S.S. Hori, A.M. Lutz, R. Paulmurugan,S.S. GambhirAcquisition of data (provided animals, acquired and managed patients,provided facilities, etc.): S.S. Hori, A.M. Lutz, R. Paulmurugan, S.S. GambhirAnalysis and interpretation of data (e.g., statistical analysis, biostatistics,computational analysis): S.S. Hori, A.M. Lutz, R. Paulmurugan, S.S. GambhirWriting, review, and/or revision of the manuscript: S.S. Hori, A.M. Lutz,R. Paulmurugan, S.S. GambhirAdministrative, technical, or material support (i.e., reporting or organizingdata, constructing databases): A.M. Lutz, R. Paulmurugan, S.S. GambhirStudy supervision: S.S. Hori, S.S. GambhirOther (conception of mathematical model): S.S. Hori, S.S. GambhirOther (design and implementation of mathematical model): S.S. HoriOther (analysis and interpretation of mathematical modeling results):S.S. Hori, S.S. Gambhir

AcknowledgmentsWe thank T. Sekar for assistance with FAC sorting, C. Chan, A. Sathir-

achinda, U. Kota, and K. Foygel for insightful discussions, B. Nelson,X. Duan, R. Sahota, and E. Annandale for providing purified recombinantSEAP, J. Rosenberg for statistical support, T. Doyle for in vivo imagingsupport, C. Chan, J. Ronald, O. Ilovich, and S. Murty for reviewing themanuscript, and A. Thomas for assistance with the manuscript figures. Wealso acknowledge technical support from the Stanford Small Animal Imag-ing Facility and the Stanford Shared FACS Facility.

Grant SupportThis study was supported in part by the Canary Foundation and NCI grants

ICMIC P50 CA114747 to S.S. Gambhir and R25 CA118681 to S.S. Hori.The costs of publication of this article were defrayed in part by the

payment of page charges. This article must therefore be hereby markedadvertisement in accordance with 18 U.S.C. Section 1734 solely to indicatethis fact.

Received October 26, 2016; revised December 7, 2016; accepted March 2,2017; published OnlineFirst March 10, 2017.






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2017;77:2570-2584. Published OnlineFirst March 10, 2017.Cancer Res Sharon Seiko Hori, Amelie M. Lutz, Ramasamy Paulmurugan, et al. Detecting Early-Stage Tumors Using Blood-Borne BiomarkersA Model-Based Personalized Cancer Screening Strategy for

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A Model-Based Personalized Cancer Screening Strategy for ... · Strategy for Detecting Early-Stage Tumors Using Blood-Borne Biomarkers Sharon Seiko Hori1, Amelie M. Lutz1, Ramasamy