WO2003008530A2

WO2003008530A2 - A method for determining the therapeutic effectiveness of a substance using a microphysiometer and use of the method

Info

Publication number: WO2003008530A2
Application number: PCT/EP2002/007910
Authority: WO
Inventors: Mirko LÜDDE; Frank Kischkel
Original assignee: Cellcontrol Biomedical Laboratories Ag
Priority date: 2001-07-16
Filing date: 2002-07-16
Publication date: 2003-01-30
Also published as: WO2003008530A3; AU2002328905A1

Abstract

This invention is related to a method for determining the therapeutic effectiveness of a substance using a microphysiometer. It has been found that more accurate results can be achieved by incorporating a statistical model for tumour cells survival under treatment from a chemotherapeutic substance. The statistical model is used in combination with cell metabolic activity measurements obtained using a microphysiometer in order to provide a more accurate and robust method for determining the therapeutic effectiveness of a substance on tumourous cells. The invention also relates to use of the method for improving an objective quantitative measure of chemosensitivity, preferably of tumour cells.

Description

A method for determining the therapeutic effectiveness of a substance using a microphysiometer and use of the method

This invention is directed to a method for determining the therapeutic effectiveness of substance using a microphysiometer and the use of such method for improving an objective quantitative measure of chemosensitivity. The substance may be a pharmaceutical agent or drug used for the treatment of tumours.

The most conventional method for determining the therapeutic effectiveness of a substance or drug is the process of performing clinical trials. Clinical trials may be ideal for providing results which represent an average therapeutic response for an entire group of patients. As a possible application, clinical trials can be carried out to test the effectiveness of chemotherapeutic substances or agents on tumour cells of patients. Such clinical trials then yield the therapeutic responses of the chemotherapeutic agent or substance on the tumour cells of the patients in the group tested. The average of the therapeutic responses obtained is normally calculated and taken as the general therapeutic effectiveness of the substance or agent. However, even with identical tumour pathologies, patients may in practice respond very differently to the same treatment thereby influencing the therapeutic effectiveness of a substance or drug used for that particular patient. Hence, one of the main disadvantages of relying on clinical trials is that these trials do not account for the individual differences in the patient's response to a substance used for treatment.

Therefore, it would be advantageous to provide a method which allows a determination of the therapeutic response of specific tumours to specific substances and, moreover, allows a determination to be made on an individual basis. This would afford the opportunity to choose the most optimal treatment strategy for each individual patient.

Such a method is described by Metzger et al. in an article titled "Towards in-vitro prediction of an in-vivo cytostatic response of human tumour cells with a fast chemosensitivity s.a." (Toxicology, 166: 97-108, 2001). A sensor-chip based diagnostic test is described which permits the functional and continuous real-time measurements of induced tumour cells cytosity following the administration of chemotherapeutic drugs. The diagnostic test also enables a determination of the therapeutic effectiveness of cytostatic treatment of tumour cells on an individual basis and in a relatively fast manner, i.e. in approximately 24 hours.

The sensor-chip based diagnostic test described by Metzger et al. involves measuring the response of the cells to drug exposure in terms of the acidification rate (μV/s) of the surrounding medium using a microphysiometer. Rate data is measured separately and simultaneously on both, cells exposed to drugs and on controlled cells not exposed to drugs. For extracting the necessary information, the rate data is treated by a standard smoothing technique in order to take into account the usual metabolic effects of cells not exposed to drugs, the (normalised and smooth) acidification rate of drug-exposed cells were divided by the (normalised and smooth) acidification rate of cells not exposed. The time average of the resulting data provided the indicator for the overall affect of the drug treatment.

One of the drawbacks of the above method is the final analysis of the data in order to determine the therapeutic effectiveness of the substance. The rate data may be influenced by several factors including the individual profile of the tumour, the mechanism of the drug (i.e. whether it is an anti-metabolite, intercalating drug, inhibitor of a mitosis or alkylating agent) or the magnitude of the measuring instruments accuracy. Hence, an exact determination of the therapeutic effectiveness may inevitably depend on the appropriate evaluation of the rate data considering these factors.

It is therefore an object of the present invention to provide a more accurate and robust method for determining the therapeutic effectiveness of a substance using a microphysiometer.

The object of the present invention is achieved with the features of the independent claims.

Preferred embodiments are described in the dependent claims. The present invention provides a method for determining the therapeutic effectiveness of a substance using measurements obtained by means of a microphysiometer. The microphysiometer is a biological assay that allows to observe the cumulative metabolic activity of small populations of living cells as a function of time. Some common microphysiometers are described in articles by Parce et al. "Detection of cell-affecting agents with a silicon biosensor" (Science, 246:243-247, 1989) and Owicki et al. "Biosensors based on the energy metabolims of living cells: The physical chemistry and cell biology of extracellular acidification" (Biosensors and Bioelectronics, 7-4:255-272, 1992).

The metabolic activity is measured in terms of the rate of change per time of the extracellular electrochemical potential in units of μV/s. The potential is dependent on the H⁺-ion concentration, which in turn is dependent e.g. on the. cell's output of carbonic and lactic acids and the impact of its proton pumps. So the potential observed by the microphysiometer is intimately coupled to the ongoing metabolic processes in the cells. By manipulating the extracellular conditions it is possible to immediately record the cell's metabolic responses.

It has become standard to use the microphysiometer in a wide area of fields in microbiology, immunology, pharmacology and toxicology. More recently, it has been suggested to apply this instrument for determining chemosensitivity of human cancer cells on an individual per-patient basis, as is the case with the sensor chip based diagnostic test described by Metzger et al. This eventually aims at providing a means for the in-vitro prediction of the patient's response to chemotherapy.

The present invention has the advantage that it is possible to define an objective quantitative measure of chemosensitivity on the basis of the microphysiometer technique. The present invention has the further advantage that application of statistical decay models allows to accurately describe the measurements and provides a natural parameter for estimating the chemosensitivity of the cell population under investigation. This contributes to a more accurate and robust method for determining the therapeutic effectiveness of a substance using a microphysiometer. In principle, the impact of a chemotherapeutic substance on the cell population as monitored by the microphysiometer might be of a quite complicated nature. There are several possible mechanisms of interaction of the chemotherapeutic substance with the cell metabolism. Every instance of a tumour entity has its characteristic profile of DNA, RNA and proteins. Cell proliferation and cell apoptosis might lead to complicated patterns of metabolic activity.

In one embodiment of the invention, the cell population is obtained from biopsy of a tumour or from a cell clone. In either case, a sample is prepared by a procedure known in the art. Several portions of the resulting cell suspensions then become treated with a chemotherapeutic substance, while some untreated portions serve as a reference.

Preferably, the cell population's size is approximately 10⁵ cells. The cells are preferably separated from each other such that only few small heaps of up to approximately 6 cells remain unseparated. Preferably, the cells are kept in agarose in order to provide a stable extracellular environment. The cells are preferably not grown. Thereby, little or no nutrients are present and no growth factors are supplied. Preferably, the observation takes approximately 16 hours. The preparation can take approximately 3 hours. The concentration of the therapeutic substance is the pharmacological peak plasma concentration in vivo.

It has been observed from analysis that if the population is sufficiently large, a statistical description appear feasible and the complexity of the problem can be controlled.

Further, under the mentioned conditions, cell growth can only occur at a modest rate, and proliferation is depressed. As a result, the treated population and the reference population both show a substantial decrease of activity during the time range of observation. Single Cell Activity and Population Activity

When the cells are contained in a microphysiometer chamber, all the individual cell activities A_k, k e {1 N}, where N is the number of cells, contribute to the overall activity that is measured. The nonlinear interactions between the individual cell activities are neglected. Then, in the simplest approximation, the measured activity in

N a microphysiometer chamber is the sum of the activities of all cells, A = T A_k . t — ^■ 1

Approximating the single Cell Activity

When a cell is still living, its activity is greater than zero. When a cell is dead, its activity A,- should be close to zero. It might not be precisely zero, due to residue activity of the cell organelles.

So for a given cell k e {1 Λ/} let its indicator function be

if cell k lives at times ≤ t,

I_k ⁽?)

if cell k is dead at times ≥ t. 0 )

As a gross approximation, the cell's activity can be modelled as linearly related to the cell's indicator function, A_k = B_k + C_k ^• l_k, C_k > 0. Furthermore, individual differences between the cells are neglected and all the coefficients. are considered to be equal.

Therefore, the activity measured at time t by the microphysiometer is a linear

N function of the sample mean T I_k(t)IN of the cell's indicator functions. If the

constants Sand Care suitably chosen, one obtains

A(t) = B + C- (t)IN. (2)

Since Λ is a constant, the activity in the model must be a non-increasing function.

This approximation may be questionable from a biological point of view. Proliferation and apoptosis of a single cell most certainly show a more complicated pattern of metabolic activity than assumed. However, the main effect is a statistical population effect. It can be shown that the model used by the present invention does at least describe the most dominant contribution to the overall metabolic activity measured and thus is appropriate for use in determining the therapeutic effectiveness on the cell. '

It is assumed that there is a suitable probability measure p on a probability space X. An element xe X models the value of all the unknown and uncontrolled, hence regarded random, variables determining the particular experiment being carried out on a given cell population. The probability measure yields the probability distribution for these variables. Further, it is assured that there are variables T_k : X →- R_≥0 such that T_k (x) is the random lifetime of the /c-th cell in the experiment x.

The survival function S_k of a cell k is the function of time giving the probability S_k(t) that the cell still lives at the time t. A cell's survival function S_k and its indicator function l_k are related by

S_k(t) = E(l_k(t)), (3)

where by "E" denotes the expectation value (statistical average) in the measure p. S_k is not a random variable, as it is an averaged quantity.

The value l_k(t) of an indicator function at the time t is a random variable. It implicitly depends on the experiment x via the lifetime variable. Explicitly,

w - r 0, o ^ifth^,er^≤w^Ti^tse'. <+>

Computing the expectation value,

≡Orf)) = 0φ(l_k(t) = 0) + 1φ(l_k(t) = 1) (5)

Pit ≤ T_k) (6)

S_k(t). (7)

Here, the first equation ^'(3) is by definition of the expectation value, the second (4) is by definition of the indicator function and the last equation (7) is by definition of the survival function S^

As a further approximation, the cell's lifetime variables T_v ..., T_N are assumed to be statistically independent and identically distributed. Biologically this means that a cell's death does not depend on any other cell's death and that all the cells statistically behave in an identical way. In reality this might not be fulfilled completely, in particular when the cells are not completely separated from each other. However, under this assumption a good estimator for the expectation of any cell's indicator function, say cell number 1, is given by the sample mean of the indicator functions of all cells,

Putting together equations (2), (3) and (8), the model can be simplified as

A(t) ≤ B+C-S(t).- (9)

Here S is a suitable survival function and β, C are constants.

Equation (9) expresses, under the stated assumptions, the change per time of the extracellular potential by a survival probability distribution of the single cells.

It is possible to perform educated guesses about the probability of a single cell's death as a function of time and to describe it by suitable families of survival functions. Equation (9) then indicates that this family actually provides a model for the measured cumulative metabolic activity of the whole cell population.

The applicability of the equation (9) combined with the selected family of survival function can eventually be checked by experiment. If this model turns out to be feasible for a certain type of measurement, a suitable parameter of the survival function as a quantitative measure of the chemosensitivity of the cells under investigation can be used. According to the invention, a model is used to represent the survival function S. Preferred models are, for example, the Weibull and the Verhulst model.

The hazard rate h (with respect to the probability measure p) gives the conditional probability h(t) that a cell will die in the next infinitesimal time interval, given that it has survived up to time t. The decay time of a survival function S is defined as σ

where T is the lifetime variable associated to S. This is actually equal to the standard deviation of the underlying probability distribution. Often the half time σ_m :=log(2)-σ is used.

Weibull Model

A family of survival functions is obtained by using a monomial hazard rate h(t) :=α-b- t^b~x , α, b > 0. This leads to the W. Weibull survival function

S_w (t) := exp(-α -t^b). (12)

The decay time is

σ_w = α- -(T(X + 2/b) -r(L+υb)), (13)

where ris the Euler gamma function.

The Weibull model allows a monotonically changing value of the hazard rate over time. For example, choosing b = 2 yields a model in which the hazard rate increases linearly with time. So it is capable of describing processes in which cumulative effects are involved. For b = 1 the exponential distribution is retained.

However, computing the Weibull decay time according to equation (13) leads to a poor differentiation between the treated and the untreated populations. This did not actually reflect the different shapes of the treated -and the untreated curves. Therefore, the Weibull scale parameter σ_w := ^{_1 i}was chosen instead, which means the dimensionless factor containing the Euler gamma function from equation (13) is neglected.

Verhulst Model

The P.F. Verhulst survival function, also called logistic function, is given by

1

S_v (t) := (14) l + exp(α -/t -b))

with a>0. Its hazard rate is proportional to the death probability, h(t) = a-(1 -S(t)).The decay time is

The Verhulst function assumes the birth of the cell to be at -∞, that is "far away in the past". In contrast, the Weibull function assumes cell birth at a finite time.

Using the following, preferred embodiments of the description are described in further detail:

Fig.1 Cell activity by time. Vincristine treatment.

Fig. 2 Cell activity by time. Untreated reference.

Fig. 3 Weibull approximation and residual (with rescaled y-axis) for a selected vincristine channel. Fig. 4 Weibull approximation and residual (with rescaled y-axis) for a selected reference channel. Fig. 5 Decay parameters by medium and model. Nine treated and nine untreated samples. Experimental Results

The model according to the present invention was checked on an adapted KB cell line (i.e. a human cervix carcinoma type cell line). The sensitivity of these cells against a set of 8 cytostatics was determined. It was shown on. the basis of a proliferation assay and by determining 50% - inhibitory concentrations (IC₅₀) that the cells have the highest sensitivity, i.e. the lowest IC₅₀ for vicristine (a chemotherapeutic substance).

Setup

24 samples, each consisting of approximately 0.1- 10⁶ cells were prepared. The adapted KB (ATCC-CCL-17) cell line was provided by Prof. C. Granzow of the German Cancer Research Centre. The preparation was basically similar to that described in Metzger et al. with the following exceptions.

1. A balanced salt solution was used as medium. Glucose 10 mM, NaCI 138 mM, KCI 5 mM, CaCI₂ 1.3 mM, MgCI₂ 0.5 mM, NaH₂P0₄ 0.23 mM, Na₂HPO₄ 0.77 mM at a pH of 7.3.

2. The experiment was performed under darkened conditions using red light.

The microphysiometers used were standard Cytosensor™ instruments. Independent experiments showed that the accuracy and stability of the measured signals were in the range of 1 to 4 MV/s. The 24 samples occupied 3 cytosensors of each 8 measurement chambers.

During the measurement, 12 samples were treated with vicristine, at a concentration of 0.433-10"⁶ M = 0.4- 10"³ g/l. The other 12 samples served as reference. 5 chambers dropped out during initial calibration, probably due to inaccurate pipetting or due to air bubbles. Among the 19 remaining chambers, one was later seen to clearly have produced an artificial signal, thus it was dropped from the following considerations. In the end there were 9 signals from vicristine treated populations and another 9 signals from the reference populations. Empirical Data

Fig. 1 shows the original together with the smoothed signal from one of the vincristine channels. The accuracy of the measurement can be estimated from the residual, the difference of the original minus the smoothed signal. A signal from a reference channel is shown in Fig. 2. A numerical summary of the data from these channels is provided in Table 1.

Comparison of the figures shows that the signal from the vicristine channel shows a steeper decrease, particularly in the first 30000 s, than the reference signal.

Application of the Models

The numerical computations presented in the sequel were carried out using the R statistics system 1.3.1 such as described in Ihaka et al., R: A language for a data analysis and graphics. Journal of Computational and Graphical Statistics, 5(3): 299- 314, 1996.

Vincristine Reference

Minimum 16.59 22.28

Quartile l 35.17 52.47

Median 91.56 113.58

Quartile 3 199.25 178.83

Maximum 297.00 228.54

Mean 120.73 117.15

Std. Dev 92.71 66.72

Num. records 379 379

Table 1 : Summary of cell activity [μV/s] in two selected channels.

In order to suppress the noise and to stabilise the subsequent non-linear optimasation, the measured data first was smoothed by the OWESS algorithm with a relative smoother span of 1/5. The data was then approximated by the decay models (in different contexts regarded as growth models) ssasymp , ss eibuli and ssfpl respectively, using the R system's non-linear least squares algorithm NLS as disclosed by Venables et al. in Modern Applied Statistics with S-PLUS. Springer, 2000. 3^rd edition, 2^nd printing.

Quality to fit

Figs 1 and 2 show the approximated activities and the residuals for the two selected channels. The Verhulst approximations do no reveal much visible difference to the Weibull model. A quantitative measure of the overall quality of the approximations can be given in terms of the residual sum of squared errors (RSS) and of the Akaike information criterion (AIC).

The RSS is the sum of squared differences of the approximation minus the signal. The Akaike information criterion is a tradeoff between the quality of fit and the number of parameters needed to achieve the fit. RSS and particularly AIC should not be considered for a single approximation, but rather for comparing different approximations of the same data. Smaller values mean that the approximation is better.

As the RSS can be considerably increased by Gaussian high frequency noise, which however does no harm to an observed low frequency signal, the RSS and AIC for the approximations to the smoothed curves are computed, as opposed to the original signals.

The data from Table 2 infers the quality of models. So cytostatic treatment seems to enforce a non-Euler shaped distribution on the cell's lifetimes.

Decay Times

The parameters computed from the approximations are shown in Figure 5. These boxplots show the parameters computed from the respective model against the two subsets, each containing 9 samples, that were treated differently. The plots show the full range of obtained values, where the 0-th up to the 4-th quartiles are indicated by horizontal lines. The triangular notches show confidence intervals for the median on a confidence level of Vθ.95. So non-overlapping notches of boxes mean that the medians from both subsets are different on a significance level of 0.05. Variable Medium Model Minimum Median Maximum

RSS Reference Weibull 136.93 561.49 1848.64

Verhulst 74.07 354.36 1473.29

. Vincristine Weibull 125.24 204.20 351.73

Verhulst 101.10 171.33 373.33

AIC Reference Weibull 689.23 1226.52 1684.99

Verhulst 458.19 1055.61 1598.52

Vincristine Weibull 659.36 843.16 1043.96

Verhulst 577.75 776.66 1066.36

Table 2: Quality of approximations. 9 treated and 9 untreated samples.

The numerical tabulation of the values is in Table 3.

Weibull Verhulst

Ref Vine Ref Vine

Minimum 29716.64 24803.97 17485.81 13928.60

Quartile 1 31022.59 25335.29 18973.45 14958.00

Median 31199.25 25914.14 19717.20 15489.79

Quartile 3 32502.17 26495.33 21088.80 15988.83

Maximum 34577.40 27044.55 22693.33 17405.03

Mean 31788.54 26010.18 19920.80 15473.28

Std. Dev 1489.68 758.18 1706.66 980.90

Cff. Var 0.05 0.03 0.09 0.06

Table 3: Decay parameters [s] by medium and model. 9 treated and 9 untreated samples.

From the boxplots it is seen that the hypothesis that the decay parameter is smaller for vincristine treatment is confirmed by all the models. For completeness a Mann- Whitney-Wicoxon test is applied. Table 4 shows the output of the algorithm wilcox.test. The alternative hypothesis that the vincristine decay parameter is smaller than the reference decay parameter can be accepted with highly significant p-value for all models.

Besides the models discussed so far, others might be applicable as well. The Weibull and Verhulst models have been described because the residual signal for the Weibull and Verhulst model has approximately the same magnitude as the accuracy of the cytosensor. Weibull Verhulst

Difference -5702.84 -4584.02

99.9%-conf. interval ]-∞, -3835.37] ]-∞, -1865.38]

Table 4: Mann-Whitney-Wilcoxoh test. Alternative hypothesis: difference of decay parameters [s] is smaller than zero. P-value 2.06e-05. 9 treated and 9 untreated samples.

Independent experiments with other cytostatics and human tumour samples indicate that the model of the invention also applies. In addition, the data presented can be regarded as quite representative for virtually all measurements performed according to other techniques, for example to the technique of Metzger et al. described in "Towards in-vitro prediction of an in-vivo cytostatic response of human tumour cells with a fast chemosensitivity assay." (Toxicology, 166: 97-108, 2001)

In summary, with regard to an adapted KB cell line, that was prepared according to a known procedure described in Metzger et al., was treated by vincristine and was observed with a microphysiometer. The leading order effect in the described microphysiometer measurements was found to be a statistical one depending on the cell's survival function only.

Further, the remaining residual data for the Weibull and Verhulst models is in the same order of magnitude as the instrument's inaccuracy. So the residual is likely to be due to technical limitations or environmental influences, and these models are complete within the experimentally prescribed accuracy.

Also, the decay parameter of the treated population minus that of the reference population, computed from Weibull or Verhulst model, is a highly significant indicator for the chemosensitivity of the cell population.

Claims

1. A method for determining the therapeutic effectiveness of a substance using a microphysiometer comprising the steps of

obtaining a first metabolic activity data on a first in-vitro population of biological cells using a microphysiometer to measure the metabolic activity;

exposing a second in-vitro population of biological cells to a substance, said second in-vitro population of biological cells having the same derivation as said first in-vitro population of biological cells;

obtaining a second metabolic activity data from said second in-vitro population of biological cells;

comparing said metabolic data of said first population of biological cells with that of said second population of biological cells, the differences indicating the therapeutic effectiveness of the substance on the population of biological cells;

wherein a statistical model is applied to said first and said second metabolic activity data to derive survival distributions for said first population of biological cells and said second population of biological cells, and said difference between the survival distributions of said first and said second population of biological cells indicating the therapeutic effectiveness of said substance.

2. The method of claim 1 , wherein said statistical model is a Verhulst logistic model.

3. The method of claim 1 , wherein said statistical model is a Weibull logistic model.

4. The method of claim 1 , wherein said first population of biological cells and said second population of biological cells is obtained from biopsy of a tumour.

5. The method of claim 1 , wherein said first population of biological cells and said second population of biological cells is obtained from a cell clone.

6. Use of the method according to any of claims 1 to 5 for improving an objective quantitative measure of chemosensitivity preferably of tumour cells.