Mathematical
Modeling of Brain Cancer
to Identify Promising Combination Treatments
Background
Last Updated: June 6,2000
For
aggressive brain cancers such as glioblastoma multiforme (gbm), much of the
discussion on this web site and others are on clinical trials for new agents. This is largely because the existing arsenal
of treatments is so weak. The clinical
trials take drugs that seem promising and test them for safety and efficacy. The trials have prevented widespread use of
agents that were dangerous, and have led to some improvements in brain tumor
treatments. Life has been marginally
extended. Newer treatments generally
have fewer side effects than older ones for a similar level of effectiveness.
However,
taken in the broader context of the disease, the pace of progress through the
conventional clinical trial approach has been arduously slow. The standard treatment (radiation with or
without gross tumor resection) offers a median survival time for patients with
gbm of only 8-12 months. With this
prognosis, how valuable are trials which compare drug A that is not very
effective with a newer drug B that may be slightly more effective, but still
not very good? Consider that a highly
effective new drug, which increases survival time by 50 percent, adds only 4-6
months to the median life of a gbm patient.
The extra time is good, but hardly a cure. And, given the years it can take to get a trial approved,
conducted, and reviewed, advances come excruciatingly slowly for those
afflicted.
This
paper demonstrates the use of mathematical modeling to design improved
treatments for gbm. The approach may be
able to accelerate the pace of innovation in brain cancer treatment. While clinical trials will always be needed,
even relatively simple mathematical models can identify more complicated,
multiple-agent clinical trials that can potentially come much closer to a
cure. The modeling can also demonstrate
important weaknesses in single agents that appear promising but in reality may
have critical flaws that will always impede their efficacy. Identifying trials with a low chance of
success is as important as structuring better multi-agent trials. This is because many brain cancer patients
have an opportunity to be enrolled in only one or two trials during the course
of their disease; choosing badly can be a serious mistake.
The
use of mathematical modeling to accelerate medical breakthroughs is not
fantasy. HIV was brought under control
only through the use of multiple drugs at once. Which drugs to combine, and how to do so effectively, was done
primarily through the use of mathematical models that did not require every
single drug permutation to be tested in clinical trials first. The same types of breakthroughs may be
possible with brain cancers such as glioblastoma, but only with some changes in
the way things are done. There needs to
be much better cooperation and coordination between mathematical modelers and
neuro-oncologists, groups that currently seem to have little interaction. There needs to be a willingness on the part
of the National Cancer Institute to initiate some more aggressive multi-agent
trials, at least for people with recurrent, late stage gbm who have little to
lose from trying a higher risk treatment protocol. And there needs to be an improved mechanism for centralized
reporting of brain cancer treatments and outcomes.
Authorship
and Caveats
The
analytic portion of this paper was written by Lawrence Wein, a Professor at
MIT's Sloan School of Management. (The
introductory material was written by Doug Koplow, who is responsible for any
remaining errors or omissions in those sections). Professor Wein is a mathematician who models complex
systems. While his appointment is at a
leading business school, and he does model complex systems at factories, much
of his time over the past five years or so has been spent modeling
disease. He worked with Alan Perelson
of the Los Alamos National Laboratory on the multi-drug cocktails for HIV that
have proven so successful. He is
currently working on various aspects of improved treatment protocols for
cancer, including fractionation regimens for radiotherapy; the scheduling of
chemotherapy, radiation, and surgery for breast cancer; the phenomenon of
prolonged dormancy after antiangiogenic treatment; and the design and
administration of replication-competent viruses.
In
his own words, some important caveats are important to keep in mind when using
this paper:
"I
am a mathematician who has spent much of the last few years developing and
analyzing mathematical models for cancer. However, I am not a clinical
researcher and I have no clinical experience with cancer patients. Although I
have read over 1,000 (clinical and mathematical) papers on many aspects of
cancer, I do not pretend to have the depth of knowledge or the clinical
experience that a medical researcher possesses. Also, I have not studied
gliomas in my previous work. I have spent about two weeks preparing this
report." Thus you should:
·
Treat
this analysis as a first step, not a recipe. Treat this paper as a preliminary
demonstration of a promising new approach.
The proposed treatments are suggestive, based on their mechanism
of action and likely efficacy. However,
they are not exact and should not be treated as such.
·
Follow
your own doctor.
Continue to rely on your own neuro-oncologists to design your individual
treatment protocol. This is especially
important because there may be debilitating side-effects from combining two or
more treatments that are not evident in this first-stage analysis.
·
Recognize
differences between your own case and the subject of this particular analysis. The paper is focused on a 65-year old male
patient with gbm who did not have any tumor removed by surgery. The suggested combinations may be less
applicable to different patient profiles.
Feedback
We want your feedback on this
approach and any data you may have that can help make the paper more accurate
and more useful to a range of patients.
Feedback from clinicians, neuro oncologists, or other mathematicians is
especially needed. The areas of
feedback that would be most helpful include: tumor cell count, growth
progression, tumor cell kill rates of various treatments, the variability in
these values across the patient population, and other brain cancer modeling
work you may be aware of. A structured
feedback form can be found on Al Musella's http://www.virtualtrials.com
website.
We
are aware of a large multi-year modeling effort underway on gbm between
Massachusetts General Hospital, the Barrows Neurologic Institute, Princeton
University, Los Alamos National Laboratory, and others. While their anticipated results are years
away, we hope to track the progress of this effort on the Virtual Trials
website. We invite any information you
may have about its status, sponsors, participants, or projected milestones.
Overview
of Tumor Modeling
A
brain tumor is a dynamic system in which bad cells grow and spread, eventually
overwhelming good cells in the brain.
Where in the brain they start, how quickly they grow, and how they
spread will all affect how quickly the cancer spreads. Additional factors of import include the
number of cells in the tumor at a given point in time and the kill rate of particular treatments
(either singularly or combined). A
brain tumor has been compared to a forest fire, because it spreads along the
outer perimeter and often dies out in the center due to a lack of fuel (or, in
the case of a tumor, oxygen and nutrients from the blood). Thus, tumor treatments must also be able to
move in the brain more quickly than the tumor spreads if the treatment is to
effectively destroy the tumor entirely.
Some
basics of cancer and the terminology that follows will be helpful. First, brain cancer cells grow extremely
fast. Second, at any point in time,
only a portion of them are replicating, and many cancer treatments only kill
cells during this active phase. Models must adjust for this constraint in
determining the net tumor cell kill rates (the Wein paper does). Third, a small fraction of tumor cells
(about one in a thousand) -- called clonogenic
cells -- are capable of regrowing the entire tumor. All of the clonogenic cells must be killed if the tumor is not to
grow back after treatment. Because a
tumor such as gbm has so many billions of cells, no single treatment available
is capable of such a high kill rate.
Table 1 in Professor Wein's analysis demonstrates this problem. Finally, the ability of a treatment to seek
out tumor cells rather than healthy cells, and to move through the brain to
reach the outer perimeter of the tumor, all affect how well a treatment works.
Wein's
paper presents treatments in terms of tumor cell "kill rates." A one log cell kill rate would kill 90
percent of the tumor cells. A two log
treatment (such as radiation) would kill 99 percent of the tumor cells. A three-log kill rate would be 99.9%;
four-log would be 99.99%, and so on.
These are rough estimates; the exact efficacy of a particular treatment
is largely patient-specific. The
combination of the expected kill rate, the ability of a new treatment to target
tumor cells, and to migrate throughout the tumor all help to quickly identify
proposed treatments that are not particularly effective when used singularly.
Another
important thing that the model does is to combine multiple treatments with
different mechanisms of action in order to greatly reduce the number of cells
surviving. Combining treatments at the same time is important. As with HIV, the small fraction that
survives any one of the drugs will tend to be resistant to that drug. If three drugs are used sequentially, the
tumor will have a chance to become resistant to each one independently. If three drugs are used together, the
likelihood of resistance developing is much, much smaller. As a result, three drugs used together will
tend to yield much better kill rates than if they are used sequentially. This general conclusion must, of course, be
tempered by the increased risk of cross-reactions among the agents.
Analysis
of Treatment Options for a 65-year old Male with Glioblastoma Multiforme
Lawrence Wein, July 1999
I. Recommendation
I
believe that the predicted median survival of 8 months is perhaps optimistic in
this patient's case, given his age (65), lack of surgery (which probably would
have only bought him a few months) and the diffuse nature of the disease at the
time of presentation (unless his tumor burden at presentation was significantly
smaller than normal). I think that the best -- and perhaps only -- hope for a
cure in this case is an aggressive combination of novel therapies. More
specifically, I recommend he initiate (as soon as possible!) a combination of
several complementary angiogenesis inhibitors (e.g., thalidomide, SU101), an
immune response stimulator (GM-CSF or Poly ICLC) and at least two of three
complementary cytotoxins: IL-4 toxin fusion, HSV-tk plus ganciclovir, and a
replicating virus (G207 or Onyx-015).
II. Rationale
In
the case of glioblastoma multiforme (gbm), death is likely caused not just by
the total tumor burden, but by the extent of penetration into the normal brain
tissue (Burger et al. 1988, Concannon
et al. 1960). There are three key challenges with
gbm. First and foremost, the tumor
cells that are the most invasive (i.e., penetrating the normal brain tissue)
are less apt to be undergoing mitosis (i.e., cell division) (Chicoine and
Silbergeld 1995). Tracqui et al. (1995) use the analogy of a
spreading forest fire. Surgery,
radiation, chemotherapy and other agents that are cell-cycle specific tend to
kill the cells that are towards the interior of the forest fire, not at the
advancing wave front. Not surprisingly, these traditional therapies, while they
may generate promising MRIs, are unable to significantly slow the invasiveness
of the disease, and have not put much of a dent into the grim survival
statistics related to gbm. The second challenge is that gbm is highly
vascularized (Louis and Cavenee 1997); i.e., it has developed its own blood
supply. Third, the tumor cells that remain after radiation are very likely to
contain a number of mutations (e.g., the p53 mutation is very prevalent) that
may confer chemoresistance.
Consequently,
my recommendation is based on three primary concerns: mechanism of action, delivery
and toxicity. Any recommended treatment
must be capable of either employing a killing mechanism that can overcome the
remaining tumor cells' resistant and/or arrested nature, or attacking the
angiogenic process. A successful treatment must also be able to deliver the
appropriate agent to the wavefront of the forest fire; i.e., it must reach the
tumor cells that have penetrated far into the brain tissue. For example, gbm
cells are not restricted to one vertebral artery or internal carotoid, which
makes gbm difficult to treat successfully by intra-arterial therapy (Burger et al. 1988). Finally, because therapy needs to be delivered throughout much of
the brain, a successful treatment must be highly specific to avoid
neurotoxicity.
Chemotherapy,
including novel agents such as CPT-11, typically fails on all three counts.
Hence, it is difficult to recommend
chemotherapy in this specific case: given his indicators (age, no
surgery, highly diffuse disease), he is likely to fall into the significant
(30-40%) proportion of non-responders; if he does respond, chemotherapy will
probably be only a (possibly toxic) Band-Aid, buying him several months.
In
contrast, IL-4 toxin fusion, HSV-tk + ganciclovir, immunology and replicating
viruses all have mechanisms of action that should be both effective against the
remaining tumor cells and independent of one another. All these modes of
therapy are based on solid science, and none of them appear to generate
significant toxicities. My main concern is with the delivery: IL-4 toxin fusion
appears capable of reaching most of the tumor cells in the brain; HSV-tk +
ganciclovir probably will not distribute throughout the entire brain, but its
bystander effect should help. According to my calculations (see 'IV.d.), the replicating
viruses travel slower than the invading gbm, and so they would need to be
administered aggressively and smartly (e.g., on the periphery of the tumor). I
do not foresee any of these drugs conferring resistance on the other, but my
biological expertise is limited on this.
Ideally,
you would want to use an angiogenic inhibitor that directly targets endothelial
cells, such as endostatin. However, it is probably impossible to obtain any at
this time. While resistance, and even cross-resistance, may develop against
thalidomide and SU101, they do attack different targets, and should offer some
help in slowing down the disease. However, I do not think these two inhibitors
in combination are capable of significantly altering the outcome of gbm, but they
would help support the three- or four-pronged attack of the combination in the
last paragraph.
A
crude mathematical analysis (see 'III.a) suggests
that about five or six logs of cell kill are required to get close to a cure.
Because of the uncertainty involved in this estimate and in the efficacies of
these novel therapies, using three or four of them in parallel greatly
increases the probability of achieving a sufficient tumor cell kill to
eradicate the gbm (see the computations in 'III.c).
Chemotherapy and radiation can easily achieve this amount of killing for some
less deadly forms of solid cancers. Hence, given the solid science behind these
novel therapies, achieving eradication is not out of the realm of possibility.
Moreover, as is the case with HIV, using these novel therapies in sequence is
unlikely to be successful: none of these therapies in isolation is likely to
produce a cure for this patient, and the sequential approach allows the tumor
the time and opportunity to continue its partial growth and oncogenic changes,
which may lead to further drug resistance.
The
remainder of this report is organized as follows. In 'III, we
describe several mathematical models that frame the problem and aid in the
recommendation. We assess the various classes of therapies under consideration
in 'IV, and provide
some concluding remarks in 'V.
III.
Mathematical Models and Analyses
III.a.
Temporal Model. A simple and time-tested (e.g., Skipper et al. 1970) approach to modeling tumors
is to use differential equations for the total number of tumor cells. This
model ignores the spatial aspects of the disease. Let nt be the number of tumor cells at time t. Then the model states that the time
derivative of the total tumor burden, denoted by
(1)
where p
is the proliferation rate of the tumor and kt is the (therapy-dependent) killing rate at time t. This simple model assumes that the
tumor grows exponentially at rate p in
the absence of treatment, and that treatment (such as radiation or
chemotherapy) behaves according to the log cell kill hypothesis (treatment
kills a fixed fraction of tumor cells, not a fixed number of tumor cells; see
the classic works of Skipper et al.
1970, Coldman and Goldie 1983 and Norton and Simon 1977). Also, the tumor cure
probability (TCP) is calculated using the so-called Poisson hypothesis (e.g.,
Travis and Tucker 1987),
(2)
where T
is the length of treatment and f is
the fraction of tumor cells that are clonogenic (capable of repopulating the
tumor). So this model contains four parameters: the proliferation rate, p; the killing rate (for various
treatments), k; the clonogenic
fraction, f; and the initial tumor
cell count, n0.
The doubling time is estimated to be
about two months for gbm (Alvord 1992, Tracqui et al. 1995), and so we set
The
number of tumor cells at the point of initial diagnosis is difficult to
estimate. There were two 1 x 0.2 x 0.2 cm cores, which is 0.08 cm3. Another possible estimate of the volume is a
sphere of 1 cm diameter, which gives a volume of about 0.13 cm3.
Burgess et al. (1997) state that the
average tumor size at presentation is 27 cm3, which is several
hundred times larger than my estimate! This leads me to be highly suspect of my
estimate. To convert the volume to cells, we need an estimate of cell density.
The classic estimate of cell density for solid tumors is 109 cells
per cm3. However, because gbm is so diffuse, it is possible that the
cell density is considerably less. Chicoine and Silbergeld (1995) state that a
3 cm diameter sphere of astrocytoma contains approximately 1011
cells, which corresponds to a cell density of 7.1 x 109 cells per cm3.
Burgess et al. (1997) claims that a 3
cm diameter tumor has only 3.5 x 107 cells, or a cell density of 2.5
x 106 cells per cm3. Thus, there is more than a three
order-of-magnitude difference between these two estimates for cell density!
However, the mathematical model of Burgess et
al. (1997) assumes that tumors become (self-)diagnosed when the diameter of
the portion of the tumor that is visually detectable (defined as having a cell
density above the threshold value of 8 x 106 cells) is 3 cm. Hence,
ignoring the cells outside of this radius and the increased concentration
inside this radius, we see that the total number of cells in their model at the
time of diagnosis must be at least
In
addition to the tumor core of gbm, there is considerable tumor burden in other
parts of the brain. Chicoine and Silbergeld (1995) claim that the
"undetectable" number of tumor cells is typically of the same order
of magnitude as the detectable number. Hence, our estimate for
Chicoine
and Silbergeld (1995) claim that conventional gbm therapy on the bulk disease
(e.g., radiation or surgery or chemotherapy) only achieves a two log cell kill,
at best (i.e., 99% of the cells are killed by treatment); I was unable to find
an independent estimate of the cell killing from the radiation literature
(e.g., Thames and Hendry 1987, Hall 1994). In addition, the tumor has probably
attempted to double in size during the last few months. So the current tumor
burden after radiation might be about 107, and could range from 104
to 1010.
The
clonogenic fraction, f, is almost
impossible to measure, but is often taken to be in the range of 0.001 to 0.01.
To get a reasonable (i.e., e-1=36.8%)
chance of a cure, it would be desirable to have the final tumor burden equal to
f -1, which is about 102
to 103 cells. So we need somewhere between one and eight logs of
cell kill by subsequent therapy. Here, we can see our parameter uncertainties
compounding to the point where we are getting unrealistic results: clearly,
more than one log cell kill is needed to eradicate gbm. Let us suppose that we
need five or six logs of cell kill to achieve a cure.
III.b. Spatio-temporal Model. A more detailed, but still relatively
simple, model is to add a killing term to equation (1) of Burgess et al. (1997):
(3)
In this partial differential equation, n(r,t) is the concentration of tumor
cells at location r at time t, and D is the diffusion coefficient (estimated to be 0.0013 cm2
per day for gbm), which captures the invasiveness of the gbm cells. The tumor
spread is assumed to be spherically symmetric in this model, and r measures the distance from the center
(i.e., the origin of the gbm). This type of model has been used by Jim Murray
and his colleagues to investigate the effects of chemotherapy (Tracqui et al. 1995) and surgery (Woodward et al. 1996) on survival. They fit their
model to clinical date by assuming that a tumor is (self-)diagnosed when the
diameter of the portion of the tumor that is visually detectable (defined as
having a cell density above the threshold value of 8 x 106 cells)
reaches 3 cm and that a patient dies when this diameter reaches 6 cm. They
report that the actual median tumor volume at death is between 58 and 84 cm3.
They also estimate that the tumor wave front travels at a rate of 0.1 cm per
week.
While
I think the simple temporal model in equation (1) can be used to estimate TCP,
equation (3) is much more appropriate for survival time and for assessing the
effects of regrowth after therapy. For example, equation (3) has been used to
show why surgery does not add very much time to survival: the wave front of the
"forest fire" is not greatly affected by cutting out its core. This
is why the tumor burden at death is only two or three times as large as the
tumor burden at presentation. In contrast, equation (1), which ignores the
spatial aspects, predicts that it would take the tumor about 13 months to grow
back to its pre-treatment size (radiation reduces the tumor to 1/100th of its
size, and so it takes 6.65 tumor doublings -- or about 13 months if the tumor
doubles every two months -- to grow back, because 26.65 = 100). The
traditional way (e.g., for breast cancer) to estimate time until death with the
temporal model is to assume a lethal tumor burden of 1012 cells. But
this temporal model would overestimate the survival time because it fails to
capture the fact that the most invasive tumor cells are unaffected by
radiation. Hence, the spatial model emphasizes the fact that an effective
therapy must attack the invading wave front as soon as possible.
There
is also a separate literature that models the spatial dynamics of a
macromolecule infused into the brain (Morrison et al. 1994). I am
currently working with an oncologist to combine the pharmacodynamic model of
Morrison et al. with the Burgess et al. model. This effort will use Morrison et
al.'s model to compute c(r,t),
which is the concentration of the macromolecule (such as IL-4 fusion toxin) at
location r at time t, and then multiply the last term in
equation (3) by c(r,t). The analysis of such a model allows one to
explicitly compute the tumor cure probability in terms of the primitive
parameters (diffusion, clearance and killing rate of the toxic agent, the
amount of drug infused, the growth and diffusion rates of the tumor, and the
location and size of the tumor).
However, the mathematical and empirical work will require at least
several more months of analysis.
III.c.
A Simple Probabilistic Analysis. A key question we
would like to answer is: how many drugs in the combination do we need to
achieve a tumor cure? Unfortunately, there is not sufficient data to answer
this question in a reliable manner. However, I will analyze a simple
hypothetical example in order to introduce the thought process required to
address this question, and to gain some intuition. In our hypothetical example,
suppose we had up to four agents (e.g., an angiogenesis inhibitor, IL-4 toxin
fusion, a cytotoxic virus and an immunotherapy) that we could simultaneously
employ, and that -- independently of each other -- they each achieved a one log
cell kill (i.e., 90% of cells killed) with probability 0.25, two logs of cell
kill (i.e., 99% of cells killed) with probability 0.5, and three logs of cell
kill (i.e., 99.9% of cells killed) with probability 0.25. Hence, we are
assuming there are no cytotoxic (antagonistic or synergistic) interactions
among the drugs; while naive, this assumption is not unreasonable given the
independent mechanisms of the agents. We are also assuming for simplicity that
each drug is equally efficacious (although the same thought process holds if we
relax this assumption). Recall that conventional gbm therapy achieves about a
two log cell kill, and so each of our drugs is assumed to be as powerful as a
conventional therapy on average, but their efficacies are uncertain.
In
'III.a, we
concluded that roughly five or six logs of cell kill were required (after
radiation) to achieve a reasonable shot at a tumor cure. In Table 1, we display
the probability of achieving x logs
of cell kill (for x=5, 6, 7, 8) by
simultaneously using y agents in
combination (for y=2, 3, 4) for our
hypothetical example.
For
this hypothetical example, the table shows that a three-drug combination
suffices to reliably (89.1%) achieve a five-log reduction and a four-drug
combination is required to reliably (85.5%) achieve a seven-log reduction. In
contrast, a two-drug combination has very little chance of achieving a
reduction greater than or equal to six logs, and a three-drug combination has
very little chance of achieving a reduction greater than or equal to eight
logs. If our efficacies for novel therapies (i.e., between one and three logs)
are of the right order-of-magnitude (note that HSV-tk achieved a three-log
reduction in mice in Rubsam et al.
1999, which seems unusually high in gbm research), then Table 1 argues for the
testing of three- and four-drug combinations for curative purposes.
Table 1:
Cell Kill Rates for Use of Multiple Agents
in Combination: A
Hypothetical Example, Post Radiation
[Probability of achieving 'x' logs of cell kill (x=5,6,7,8)
using a 'y'-drug combination (y=2,3,4)
|
Number of Agents in Combination |
5 logs |
6 logs |
7 logs |
8 logs |
|
2 |
31.2% |
6.2% |
0.0% |
0.0% |
|
3 |
89.1% |
65.6% |
34.4% |
10.9% |
|
4 |
99.6% |
96.5% |
85.5% |
63.7% |
IV. Alternative Therapies
IV.a. Chemotherapy. I will not survey
the FDA-approved chemotherapeutics. They offer several months of median
survival for gbm patients. But the distribution is skewed, with nearly all of
the benefits going to a minority of patients. Chances are small that this
patient would be among the beneficiaries. Of the newer chemotherapeutics,
temozolomide and irinotecan (CPT-11) appear to be the most promising. As
reviewed by Williams (1998), temozolomide achieved a total response rate in 58%
of 103 patients, although the duration was for only 4.6 months. Similarly, 7 of
17 patients responded in a phase I study (Brock et al. 1998); comparable phase II results are reported in Spagnolli
et al. (1999). Moreover, in vitro studies display
cross-resistance between temozolomide and CCNU (Sankar et al. 1999) and suggest that temozolomide is less effective
against p53 mutant tumor cells (Tentori 1998).
In
a phase II study (Friedman et al.
1999), CPT-11, which appears to have complementary resistance profiles to other
chemotherapeutics, achieved slightly better results (9/60 had a partial response
and 33/60 were stable for at least 12 weeks, for patients with recurrent or
progressive malignant glioma); typical chemotoxicities (nausea, etc.) were
reported. An attempt at an every-three-week regimen led to less impressive
results (median time to progression for recurrent gbm was seven weeks)
(Cloughesy et al. 1999).
IV.b. Angiogenesis Inhibitors.
Angiogenesis is a very complex process, and has many promoters and inhibitors.
One might think of this process as a complex network consisting of different
environmental (e.g., tumor oxygen level), oncogenic (existence of mutations)
and angiogenic factors that can be up- and down-regulated. Tumor endothelial
cells are the key target in anti-angiogenesis therapy. A landmark study (Boehm et al., 1997) has shown that endothelial
cells, unlike tumor cells, do not develop acquired drug resistance. Hence,
ideally one would want to use an angiogenic inhibitor that directly attacks
tumor endothelial cells, such as the much-touted endostatin. However, at this
point in time, it is probably impossible to obtain this (or a similar) agent.
Unfortunately, the agents that inhibit the various upstream targets (e.g.,
VEGF, bFGF) in the angiogenic process are susceptible to resistance (because of
the multiple pathways through the network), and may lose their potency over
time; e.g., Yoshiji et al. (1997) has
shown that vascular endothelial growth factor (VEGF) is essential for initial
but not continued growth of breast cancer. However, combinations of
angiogenesis inhibitors aimed at different targets work better than any
inhibitor alone (e.g., Brem et al.
1993).
Thalidomide,
which blocks basic fibroblast growth factor (bFGF)-induced angiogenesis (bFGF
is over-expressed in gbm), is the only FDA-approved angiogenesis inhibitor. The
studies by Fine (cited in Williams 1998) (50% response rate, including 4/32
regressions) and Glass et al. (1999)
(carboplatin plus thalidomide achieve a median response of 24 weeks and median
survival of 40 weeks for patients with recurrent gbm) suggest that it can be
helpful, but only as a small part of a larger regimen. It also can cause
fatigue and hematologic toxicity.
Marimastat
is a matrix metalloproteinase inhibitor. It can cause (reversible) severe joint
and muscle pain if given in doses greater than 50 mg bid in Steward (1999), but
was well tolerated at these doses in Wojtowicz-Prage et al. (1998). It achieved a 58% response rate for doses greater
than 50 mg bid for other cancer types (colorectal, ovarian and prostate).
SU101
inhibits platelet-derived growth factor, which is over-expressed in gbm. Malkin
(ASCO abstract, 1998) reported prolonged stability in 13/57 and regression in 5/57. Adamson et al. (1999) reported no toxicity in 19
of 20 pediatric patients.
SU5416
(Fong et al. 1999) blocks a VEGF
receptor and inhibits tumor growth in mice. Rosen et al. (1999) reported results from the first phase I trial on
humans: it had mild-to-moderate toxicities and appeared effective, but was not
tested specifically on gbm patients.
Based
on this information, I would recommend the use of Thalidomide and SU101 as the
anti-angiogenic portion of a treatment
regimen. Of course, if direct endothelial cell inhibitors such as endostatin or
angiostatin become available, these would be preferable. Moreover, the second
generation inhibitors (e.g., SU5416) are likely to be more efficacious than the
first-generation ones, but also more difficult to procure. I cannot recommend
the use of marimastat at this point, due to its side effects and the lack of data
on gbm.
Finally,
Mauceri et al. (1998) have shown that
VEGF levels increase for two weeks after radiation in mice. It is likely that
other pro-angiogenic factors are also increased in response to the insult from
radiotherapy. Hence, it may be beneficial to start angiogenesis inhibitors as
soon as possible after radiotherapy.
IV.c. IL-4 Fusion Toxin. IL-4 toxin,
IL-4(38-37)-PE38KDEL binds specifically to IL-4R and is highly cytotoxic to
glioblastoma cells. It has exhibited impressive results in human glioblastoma
xenografts and animals, including some complete regressions and no sign of
toxicity (Puri et al. 1996, Husain et al. 1998). According to its
developer, Dr. Puri, it should not cause any toxicity problems for this
particular patient, although patients at risk for brain stem swelling would not
be able to use it. As far as I know, the IL-4 receptor is independent of
radioresistance and life cycle effects. My main concern is the delivery.
Apparently, it is delivered via convection caused by the natural pressure
within the skull, and it follows the tumor migration path. For some types of
binding drugs, there is a binding site
barrier (e.g., van Osdol et al.
1991): if the binding is too strong, the drug does not penetrate far enough
into the tissue. Overall, this looks to be one of the most promising approaches
available.
IV.d. Replicating Viruses.
One of the main reasons that conventional gene therapy has not lived up to its
potential is delivery: it has been
difficult to deliver sufficient quantities of the vehicle (e.g., monoclonal
antibody, adenovirus) into a tightly compressed solid tumor. One way around
this is to use a replicating virus: such a virus does to cancer cells what HIV
does to white blood cells: it attaches to the cell surface, infects the cell,
replicates exponentially inside the cell, and
kills the cell (i.e., causes lysis). When lysis occurs, all of the new
virus particles (hundreds or even thousands) are released from the cell and are
free to undergo new rounds of infection and lysis. These viruses are designed
to be highly selective to tumor cells, so that they do not run amok in the
normal tissue.
In
conjunction with Onyx pharmaceuticals (they have developed ONYX-015 (Heise et al. 1997), which is the lead drug in
this field and is supposed to be starting Phase III trials soon), I have performed a mathematical analysis
(paper is in preparation) of replicating viruses. Each injection of this virus
into a solid tumor generates a traveling wave of infection in the tumor (not unlike
the traveling wave of the brain tumor into the normal tissue). These viruses
have shown impressive and non-toxic results in head and neck tumors, and are
beginning to be tested on brain tumors. The two main options are G207, (Martuza
1999, who pioneered this field), which is used in trial #00554, and Onyx-015,
which I believe is the drug being used in Trial #00397 (www.virtualtrials.com).
Neurovir, makers of G207, announced their phase I results for G207. Five of 21
very advanced patients were stable for 3-9 months. This is not that impressive,
but 18 out of 21 patients received only a single injection, and phase II
clinical trial patients will receive five injections into the tumor at the time
of surgery.
I
still have some concerns about delivery with replicating viruses. My analysis
of replicating viruses suggests that the wave of infection travels at a speed
of about three cell radii divided by the infected cell lifetime, which is
roughly 30:m/48 hours=0.01
cm/week; the herpes virus G207 may travel at about twice this speed. This is
still 5-10 times slower than the tumor wave front velocity reported in 'III.b. Hence,
the replicating virus needs to be injected liberally and peripherally to be
effective (I know that Onyx delivers its virus around the periphery of the
tumor, but I do not know about G207). Moreover, the wave needs a sufficient
tumor cell density in order to propogate, and so the wave could die out at the
very edges of the tumor invasion. Consequently, a replicating virus is not
likely to be able to cure a gbm by itself.
IV.e. Nonreplicating Viruses. There are
several interesting nonreplicating viruses. CRM107 had reasonably impressive
results (median survival of 46 weeks, 2/18 patients alive after 140 weeks)
despite using a nonreplicating virus that had mediocre specifity (Laske et al. 1997). Hence, I suspect that
G207, which is a replicating virus, could be considerably more efficacious (see
Martuza's letter that accompanies Laske et
al.'s 1997 paper).
The
herpes simplex virus thymidine kinase (HSV-tk) plus ganciclovir works
impressively on rats: e.g., it kills tumor endothelial cells (Tanaka et al. 1999) and achieves a greater than
three log cell kill (Rubsam et al.
1999). Its mechanism (see the first paragraph of LeMay et al. 1998) causes a "bystander effect" that allows the
effective killing of invasive gbm cells. However, hematopoietic toxicity is a
serious side effect (Davey 1990), but the blood-brain tumor barrier
permeabilizer, RMP-7, may lessen this effect (LeMay et al. 1998), and at least this toxicity is different than the
neurotoxicities caused by most other gbm therapies. In summary, this is a very
promising approach, and several trials are ongoing. But low gene transfer and
insufficient delivery of ganciclovir will probably prevent this approach from
providing a cure in humans (Di Meco et
al. 1997).
Then
there is the provocative Newcastle disease virus vaccine (MTH-68/H). Csatary et al. (1999) present a case study of a
14-year old boy with a 95% tumor shrinkage of a gbm, and mention two other
children with two-year responses. These are the only reports for gbm. In a
phase II double-blind placebo trial (Csatary et al. 1993), it achieved significant regressions in only 3 of 20
tumors (none of them brain tumors). Yet it performed very well (17 out of 18
complete regressions) on neuroblastoma xenografts on mice (Lorence et al. 1994). Unfortunately, the
researchers do not seem to know the mechanism of action. In summary, it is
difficult to know what to make of this. I think G207 or ONYX-015 or HSV-tk +
ganciclovir would be preferable, but the Newcastle virus may be more accessible
(if you are willing to fly to Europe and get it).
IV.f. Immunology. Intracavitary
interleukin-2 and lymphokine-activated killer cells (IL-2/LAK) showed some
response in humans, but generated significant neurotoxicity (Hayes et al. 1995). The two patients in their
60s in this study did not fare well. Liau et
al. (1999) show that dendritic cell immunotherapy (Trial #00487 on
www.virtualtrials.com) works on rats. However, this requires another biopsy
because close to 3 gm of tumor are needed to derive the necessary antigens.
Results on the first humans (reported in Biotechnology Newswatch, 2/1/1999)
have shown an increase in the immune response, but only minimal tumor
shrinkage. Researchers are also planning a GM-CSF trial that is not patient
specific. GM-CSF has impressive results (40% alive after 300 days vs. controls dying
by day 59) in rats (Wallenfriedman et al.
1999). It takes a while to kick in: the tumor volume peaked at day 23 and then
regressed completely. GM-CSF is probably more practical than the
patient-specific approach, and may prove effective. I recommend Poly ICLC,
which achieved 19 month survivals and no toxicity in humans, as reported by
Williams (1998), or GM-CSF.
IV.g. Antineoplastons. The FDA-approved
drug, Tamoxifen, is the most popular compound in this therapeutic area. Very
high doses (160-320 mg/day) of this protein kinase C inhibitor are needed for
gbm patients, which can cause blood clots. A stage II clinical trial (Couldwell
et al. 1996) shows that tamoxifen
achieves tumor regression in about 20% of recurrent gbm cases. Chang et al. (1998) report neurotoxicity when
tamoxifen is administered with interferon "-2a. Hypericin
(Zhang et al. 1997) is another
protein kinase C inhibitor, and Burzynski's (1990) A10 + As2-1 combination has
low toxicity and may work better, but only early results are available.
Overall, the risk of toxicity combined
with their modest benefit do not make this class of drugs very attractive as
part of a potentially curative arsenal.
IV.h. Boron Neutron Capture Theory.
According to Diaz et al. (1998), low
doses of this approach gives comparable results to conventional radiation.
Higher doses are likely to be more efficacious, but may have some toxicity. I
cannot recommend this option at this point in time.
V.
Concluding Remarks.
The recommendation in this report assumes that the "utility
function" of the patient and his family is to maximize the probability of
tumor cure. In many decision problems under uncertainty (e.g., investing in the
stock market), there is a tradeoff of risk and return: you can either play it
safe (e.g., invest in bonds) and receive a moderate reward with a high
probability, or you can attempt to get a big reward by exposing yourself to the
risk of a devastating outcome (e.g., bankruptcy in the stock market example).
For
this particular disease (gbm) at this particular point in time (summer 1999), I
honestly do not see much of a tradeoff. The chances of the patient surviving
for another year using only FDA-approved drugs appears to be slim; the chances
of long-term survival are essentially nil. (In contrast, the decision for HIV
patients is more difficult, due to the existence of some long-term
nonprogressors.) On the other hand, there is an unusually large differential in
potential efficacies between the FDA-approved drugs and novel, largely untested
drugs. It is conceivable that an aggressive combination of these drugs could
either cure the tumor, or at least buy the patient several years, at which
point more effective treatments may be available. Because these novel therapies
have a high uncertainty of success, the more approaches that are tried in
parallel, the more likely is success (at least for the first 3 or 4 modes of
therapy; after that, decreasing returns are possible, as shown in Table 1). Of
course, the likelihood of serious toxicity also goes up as the number of modes
of therapy is increased. Nonetheless, the biggest downside risk appears to be
fatal toxicities due to an untested drug combination, which would result in
death perhaps a handful of months earlier than if the patient followed the
"business as usual" route.
If
this was me or my loved one, and we had the financial resources, and the
patient had the will and the physical strength to undergo an enormously
demanding (put perhaps not highly toxic) regimen, I would not only (in David
Ho's words) "hit early, hit hard",
but would "hit everywhere with everything".
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