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An immune network inspired evolutionary algorithm for the diagnosis of Parkinson’s disease
BioSystems 94 (2008) 34–46
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An immune network inspired evolutionary algorithm for the diagnosis of Parkinson’s disease Stephen L. Smith a,∗ , Jon Timmis a,b a b
Department of Electronics, University of York, Heslington, York YO10 5DD, UK Department of Computer Science, University of York, Heslington, York YO10 5DD, UK
a r t i c l e
i n f o
Article history: Received 13 July 2007 Received in revised form 8 November 2007 Accepted 23 May 2008 Keywords: Evolutionary algorithms Artificial immune systems Immune networks Parkinson’s disease
a b s t r a c t This paper presents a novel evolutionary algorithm inspired by protein/substrate binding exploited in enzyme genetic programming (EGP) and artificial immune networks. The immune network-inspired evolutionary algorithm has been developed in direct response to an application in clinical neurology, the diagnosis of Parkinson’s disease. The inspiration for, and implementation of the algorithm is described and its performance to the application area considered. © 2008 Elsevier Ireland Ltd. All rights reserved.
1. Introduction Proteins are organic compounds which play a central role in living organisms. They are directly involved in a number of key activities in animals including their mechanical structure, motor function, transportation of molecules, control of chemical reactions and the immune system. The mechanisms through which proteins achieve this wide range of functions are both diverse and complex, but have led to a rich source of inspiration for natural computing. This paper describes a novel evolutionary system inspired by protein/substrate binding as exploited in two existing evolutionary paradigms, enzyme genetic programming (EGP) (specifically an implicit context representation of Cartesian genetic programming (CGP)) and the molecular interactions between paratopes and idiotopes on B cell receptors in the immune system. The novel evolutionary system was developed in direct response to an application in the diagnosis of Parkinson’s disease (PD). One symptom of the disease is a slowing of movement, known as bradykinesia. The analysis of data resulting from testing patients for this symptom is particularly challenging to solve by conventional means. In this paper we detail a promising approach to the application of this problem. We have augmented the enzyme genetic programming approach with a simple model inspired by
∗ Corresponding author. E-mail addresses: [email protected] (S.L. Smith), [email protected] (J. Timmis). 0303-2647/$ – see front matter © 2008 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.biosystems.2008.05.024
the interactions of regions on immune B-cell receptors: specifically, between paratopes and idiotopes. This paratope–idiotope interaction has allowed for the development of a novel interaction mechanism for effective identification of patterns in the data set employed, something that to date has proved difficult to obtain. Section 2 provides a description of genetic programming and specifically, enzyme genetic programming, illustrating its basis on protein/substrate binding and the metabolic pathway. An application of the implicit context representation to Cartesian genetic programming is then considered and how it has previously been used in the diagnosis of Parkinson’s disease. Section 3 then provides background material from immunology that has served as inspiration for the development of the immune network aspect of our system. Section 4 then details the implementation of the immune network inspired evolutionary system and in Section 5, how it may be applied to the diagnosis of Parkinson’s disease. Finally, in Section 6, the work presented is summarised and conclusions drawn. 2. Genetic Programming Genetic Programming (GP) (Koza, 1992) is an evolutionary algorithm in which the chromosome representation is based on a parse tree structure as shown in Fig. 1. The nodes are functions which act on the values presented at the inputs and provide the answer to the output. Terminals can either be input variables or constants. A population of individual genetic programs is then subject to an evolutionary strategy employing selection, mutation and recombination (crossover) schemes.
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Fig. 1. Example genetic program individual which evaluates to: OUT = (y/x) + (y × 1).
2.1. Enzyme Genetic Programming Lones and Tyrrell (2001) have developed a form of the conventional parse tree type genetic program called enzyme genetic programming. The biological inspiration for Enzyme GP is the metabolic pathway, and the role of enzymes which express computational characteristics. The representation named implicit context representation employs an enzyme model comprising a shape, activity and specificities (or binding sites) (Lones, 2003), as shown in Fig. 2. Along with inputs and outputs, the enzyme model can be considered a program component from which a genetic program may be constructed. The shape describes how the enzyme is seen by other program components. Similarly, the binding sites determine the shape (and hence type) of program component the enzyme
Fig. 2. Enzyme model illustrating shape, activity and specificities (binding sites) (Lones, 2003).
wishes to bind to. Finally, the activity determines the logical function the enzyme is to perform. A typical EGP will comprise a set number of inputs and outputs and a number of enzyme models or components. Values for each component’s binding sites and logical function are initialized non-deterministically; the component’s shape, however, is derived from a combination of its binding sites’ shapes and logical function as shown in Fig. 3. In this example the
Fig. 3. Calculation of a component’s shape from its binding site shapes and logical function (Lones, 2003).
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conventional GP parse tree is formed through binding of sub-trees whose shapes match the binding site shapes of the AND component. Consequently, the shape of the AND component now represents the functionality of the whole tree below it. Once initialized, components are bound together to form a network. The order in which components are bound is determined by the closeness of match between one component’s binding site and another component’s shape. The best matching components are bound first and the process is repeated until a network has formed in which no further binding is possible. Over time, components may evolve through mutation, which is applied to the component’s binding sites and logical function with a pre-determined probability. When this occurs, a new component shape is derived accordingly and may lead to different binding between components occurring. This in turn may result in a modified network. 2.2. Cartesian Genetic Programming Cartesian genetic programming (Miller and Thomson, 2000; Miller et al., 2000) is a form of Genetic Programming (GP) in which components are arranged in a directed graph, in contrast to conventional GP, which is based on a parse tree structure. CGP exhibits a number of benefits over traditional GP, the best known of which is avoidance of bloat, an uncontrolled expansion of the program during evolution. However, CGP does not exhibit positional independence. The effect or meaning of a component in the evolved or resulting program is determined by its absolute or relative position in the program representation. The manner in which components are referenced in CGP is considered arbitrary as there is no correlation between a component’s absolute coordinates and its behaviour. Therefore, it can be argued that indirect context representation has no effect beyond describing the connectivity of a specific program. This is also the case when considering the behaviour of components in different programs. Components with the same functionality may have different coordinates and those with different functionality the same coordinates. This section reviews the implementation of an implicit context representation of CGP which it is argued overcomes many of the disadvantages described above.
Fig. 4. Implicit context representation. CGP component showing multidimensional shape and binding sites (Cai et al., 2006).
The component’s shape is derived from a combination of the component’s binding sites’ shapes and the component’s function index (using a value of 255 in the relevant dimension) as shown in Fig. 5. Formation of a component’s shape in this way not only describes the logical function of the component itself, but also those components which the binding sites have a desire to bind to. In this way, a shape gives a summary of the functionality of the desired network to be formed from this point onwards.
The processing elements within the CGP are particularly suited to the implicit context representation. However, instead of employing a parse tree arrangement, the existing CGP Cartesian arrangement is maintained. The following sections summarize work undertaken by the author in this implementation—further details can be found in Cai et al. (2006).
2.3.2. Network Formation Binding of components in the CGP network begins with the assignment of an output component that will ultimately provide the resulting value for the problem under consideration. The binding site of the output component is then made active and will bind to the component shape which exhibits the closest match. This is simply determined by summing the difference between each relative pair of dimensions within the vector for one component’s binding site and another component’s shape. The combination of component shape and binding site that exhibits the smallest difference can be considered to be the “best fit”. Once bound, a component’s binding sites will also become active and will bind in the same way to other components located in columns to the left. This continues until all components have been bound, arguably with suboptimal components. A simple example is provided in Fig. 6 (Cai et al., 2006). Once all possible binding has completed, a network description is generated which describes the network in the same manner as for conventional CGP and the fitness of the resulting network is calculated in the normal way. The above process is repeated for each individual in the population and selection criteria for the next generation may be applied as required. Evolution of the selected individual, is however, different to that undertaken in conventional CGP. The concept of mutating both the connections and function of a component is maintained, but in the implicit context representation this is performed by
2.3.1. Network Structure A predetermined number of functional components are generated to form the network. Each component has the same (predetermined) number of binding sites, a function and a shape. The binding sites facilitate binding to other components and hence provide input values to which the selected function is applied. All shapes share a common format and consist of a number of dimensions which represent the different inputs and functions available within the network. For example, a network that has three inputs and a choice of four functions will employ a shape with seven dimensions for each component. Each dimension within the shape contains an integer value between 0 and 255 that represents the strength of that input or function expressed by the component. This is illustrated in Fig. 4.
Fig. 5. Derivation of the component’s shape from the component’s function and binding sites’ shapes (Cai et al., 2006).
2.3. Implicit Context CGP
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Fig. 6. Component binding. (a) Components are arranged, unbound, in the desired Cartesian arrangement. (b) Starting at the Output component, binding sites are bound to the component’s shape with the “best fit”. (c) Binding sites for each component bound are then bound to further components on a “best-fit-first” basis. (d) When no further binding can take place, the network can be evaluated.
mutating the component’s binding sites and function in a nondeterministic manner. Once mutation has been completed, the component’s activity shape needs to be recalculated to represent any changes that have subsequently occurred. A new network can then be formed by rebinding components; again on a “best fit first” basis as previously described. 3. Artificial Immune Systems Artificial immune systems (AIS) have been defined by de Castro and Timmis (2002) as: “adaptive systems inspired by theoretical immunology and observed immune functions, principles and models, which are applied to problem solving.” They are one of many types of algorithms inspired by biological systems, including evolutionary algorithms, swarm intelligence and neural networks. Within AIS, there are many different types of algorithm, and research to date has focussed primarily on the theories of immune networks (de Castro and Von Zuben, 2001; Neal, 2003), clonal selection (Cutello and Nicosia, 2004; Garrett, 2004) and negative selection (Forrest et al., 1994; Stibor et al., 2005). These theories have been abstracted into various algorithms and applied to a wide variety of application areas such as anomaly detection, learning and robotics.
3.1. Vertebrate Immune System The vertebrate immune system is composed of diverse sets of cells and molecules. Traditionally, the immune system is considered to play the role of defence, and protect our bodies from infectious agents such as viruses, bacteria, fungi and other parasites. On the surface of these agents are antigens that allow the identification of the invading agents (pathogens) by the immune cells and molecules, thus provoking an immune response. There are two basic types of immunity, innate and adaptive. Innate immunity is not directed towards specific invaders, but against general pathogens that enter the body. Adaptive or acquired immunity, allows the immune system to launch an attack against any invader that the innate system cannot remove. The adaptive system is directed against specific invaders and is modified by exposure to such invaders. The adaptive immune system mainly consists of lymphocytes, which are white blood cells, more specifically B and T-cells. These cells aid in the process of recognizing and destroying specific substances. Whereas all blood cells are generated in the bone marrow, Tcells migrate and mature in the thymus. To enable recognition of antigen patterns displayed by pathogens, both T-cells and B-cells present receptor molecules on their surfaces as shown in Fig. 7. The B-cell receptor is commonly known as an antibody.
Fig. 7. Lymphocytes and their surface receptor molecules. (a) B-cell receptor (BCR) or antibody. (b)T-cell receptor (TCR) (de Castro and Timmis, 2002).
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Fig. 10. Immune network theory. The recognition of antigen by an antibody leads to network activation, while the recognition of an idiotope by another antibody results in network suppression (de Castro and Timmis, 2002).
Fig. 8. Antibody molecule’s variable region, i.e. the portion of the molecule responsible for recognizing antigens (de Castro and Timmis, 2002).
Antibodies can recognise and bind with antigens in free solution; T-cell receptors can only recognise and bind with antigens presented by molecules of our own body known as major histocompatibility complexes (MHCs). Fig. 8 shows the variable region of antibodies that enable them to recognise antigens and Fig. 9 the binding of an antibody to an antigen. Once successfully identified by binding, a process of clonal selection and affinity maturation is initiated and the pathogen can be eliminated by the immune system. 3.2. Immune Networks In a landmark paper for the time Jerne (1974) proposed that the immune system is capable of achieving immunological memory, and thus subsequent recognition of pathogens at a later stage, by the existence of a mutually reinforcing network of B-cells. This network of B-cells occurs due to the ability of paratopes, located on B-cells, to match against idiotopes on other B-cells. The binding between idiotopes and paratopes has the effect of stimulating the Bcells. This is because the paratopes on B-cells react to the idiotopes on similar B-cells, as it would an antigen. However, to counter the reaction, there is a certain amount of suppression between B-cells, thus giving rise to a regulatory mechanism. This interaction of Bcells contributes to form a memory structure, and was proposed to account for the retainment of memory cells, even in the absence of antigen. This theory was refined and formalised in successive
Fig. 9. Recognition of an antigen by a B-cell receptor (de Castro and Timmis, 2002).
works by Farmer et al. (1986) and Perelson (1989). It is worth noting, however, that the immune network theory is not widely accepted within the immunological community, being very little experimental evidence to support it. However, from a computational point of view, and a view of bio-inspiration, the immune network is very attractive and indeed has served as inspiration for many immuneinspired algorithms (de Castro and Timmis, 2002; Neal, 2003; de Castro and Von Zuben, 2001) whilst this theory is interesting, there is little experimental evidence to suggest that it is true. According to the immune network theory, the antibody molecules contained in the surface of the immune cells present markers, named idiotopes, which can be recognised by antibodies on other immune cells. These idiotopes are displayed in and/or around the same portions of the receptors that recognise nonself antigens. Fig. 10 provides a simple illustration of the immune network theory. To explain the network theory, assume that an antibody, Ab1, on a B-cell recognises a nonself antigen, Ag. This same receptor, Ab1, is also recognised through its idiotope i2, by another antibody, Ab2 via its paratope. Ab1 is capable of recognising both Ag and Ab2. The recognition of idiotopes on an antibody by other antibody, leads to ever increasing sets of connected antibodies. However, the binding of an antibody by its idiotope may negatively affect its binding with its antigen Ab1, but the degree to which it does this is determined by its affinity for the antibody. Therefore, the recognition of antigen by an antibody could be said to lead to “network activation”, while the recognition of an antibody by another antibody could be said to result in “network suppression”. 4. Immune Network Inspired Evolutionary Algorithm It is important to stress that the B-cell and T-cell receptors are proteins which are able to bind to antigens in a similar way to which enzymes bind to substrates. The motivation for this work is to employ a similar model to that used with success in Cartesian genetic programming with artificial immune systems and specifically, immune networks. The proposed model utilises similar network components used to represent enzymes, but with modifications, can now represent B-cell receptors and idiotopes as shown in Fig. 11. The function employed will be one which reflects the biological relationship between the receptors and idiotopes. Fig. 12 illustrates how this model of the B-cell is free to bind with antigens or other B-cells and behave in a similar way to in the human body and a number of B-cells would populate the system with initially random B-cell receptors and idiotopes. Over time each B-cell will encounter pathogens (or training data items) and other B-cells, effectively training in the environment, so that ultimately, the ability to differentiate between classes is achieved. Further, such
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Fig. 11. Model of B-cell featuring receptors and idiotopes.
a distributed model will enable B-cells to occupy different physical areas of space allowing the network to respond immediately in a local sense and over time a global view of the presence of pathogens. 5. Application of Evolutionary Algorithms to the Diagnosis of Parkinson’s Disease
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1 in every 500 people in the UK has PD. The risk of developing PD increases with age and due to the ageing population it is expected that the number of cases of PD will triple in the next 50 years. There are three cardinal motor features of PD: tremor, rigidity and bradykinesia. The symptoms usually start on one side of the body (hemiparkinsonism) but later spread to the other side. About 80% of patients suffer from idiopathic Parkinson disease for which no cause is known. However, the diagnosis of idiopathic PD is based on clinical features which can have poor sensitivity with about 25% of patients diagnosed with the disease actually having other conditions (Playfer, 1997). Considerable research has been conducted to improve the diagnosis of the condition, but most studies to date are reliant on laboratory-based experimentation. The authors are concerned with developing a non-invasive computer-based test that can be conducted in the clinical environment and the doctor’s surgery, using commonly available computing peripherals. Work to date by the authors on such a computer-based assessment using figure-copying tasks has generated promising results. However, it is clear the identification and quantification of the symptoms of Parkinson’s disease is a nontrivial problem that is highly dependent on many factors relating to the patient’s physical as well as medical condition.
5.1. Parkinson’s Disease
5.2. Previous EA Approaches for the Diagnosis of Parkinson’s Disease
Parkinson’s Disease is a common, chronic, progressive neurodegenerative brain disease, afflicting about 1 person in 1000, and about 1 person in 100 over the age of 60. The disease sets in insidiously, and in most patients progresses relentlessly, on average within 10 years, to a state of total physical incapacitation. PD is one of the most common late-life neurodegenerative disorders, which typically develops between 50 and 70 years of age. It is estimated that there are a total of four million people with PD worldwide and
Bradykinesia is the core disabling feature of Parkinson disease. It consists of difficulty, slowness (bradykinesia proper) or virtual inability (akinesia) in initiating and executing movements or modifying ongoing motor activity. Poverty of spontaneous movement (hypokinesia), loss of normal associated movements, masked facial expression and sudden freezing in the middle of a motor performance are all part of the disturbance. The aim of previous work by the authors has been to devise a computer-based system that is
Fig. 12. Artificial immune network showing B-cells binding with pathogens and other B-cells.
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Fig. 13. (a) Figure copying task using a conventional digitizing tablet. (b) Task shape to be copied.
capable of measuring these symptoms to aid diagnosis and inform administration of medication. The work described in this section is a review of that undertaken by the authors in computer-based assessment (Smith et al., 2007) and comprises two parts: data acquisition and data processing. Data acquisition stage is the digitization of the patient’s drawing in attempting a conventional figure-copying task, termed here, the task domain. Once the patient’s response has been acquired in digital form, data processing is applied to extract and quantify the symptoms of interest, in this case tremor and bradykinesia. The patient’s response to the task presented is a drawing activity that is digitized in real-time as a set of x–y co-ordinate pairs giving information about pen position. The figure required to be copied by the patient is placed on the digitizing tablet in printed form and covered with a sheet of tracing paper on which the patient traces a copy as shown in Fig. 13 (a). The geometric shape presented for the patient to copy in this study is a modified Archimedes spiral, replacing the smooth spiral with pentagon-like edges as shown in Fig. 13(b). The justification for making this modification is that by introducing a sequential aspect, the change from drawing one edge to another will provide a focus at which symptoms of bradykinesia may be observed. Although the term bradykinesia is defined as the slowness of a performed movement, it is commonly used synonymously with akinesia and hypokinesia, an expression of freezing and smaller
movements, respectively. To quantify these symptoms a measure of movement time and particularly, the movement velocity of the patient’s pen, is required. As the patient’s drawing activity is digitized in real-time and at regular intervals, it is possible to determine the velocity of the pen at any instant. This can be achieved by calculating the distance between two coordinate positions and dividing this by the difference of the relative timestamps. The representation of the velocity of the pen for the duration of the patient’s response to the task attempted, termed the velocity profile, an example is given in Fig. 14. As might be expected, the velocity profile can reflect the nature of the task, e.g. in this case an acceleration and deceleration can often be associated with each side of the spiral pentagon. The main thrust of data analysis to date has focused on the patient’s pen velocity at the end of one edge of the spiral-pentagon and the beginning of the next. It is here that evidence of a slowing and of hesitation, commonly recognized as bradykinesia, is sought that will differentiate a Parkinson’s patient from a normal control. Subjective examination of velocity profiles obtained from the 12 Parkinson’s patients and 10 controls was made with a view to identifying features that could be used as evidence of bradykinesia. One candidate for such a feature is a two-part artefact, which is illustrated in Fig. 15. The initial acceleration of the pen is described by the section of the velocity profile labelled “A”. After a period of remission, a second period of acceleration greater than that of “A” is observed (labelled “B”). A total of 10 occurrences of the twopart velocity feature were detected in the responses of five separate patients. The feature was only located in one of the age-matched control drawing responses. The feature described above is one example of the type of analysis that can be applied to digitized pen movements over a variety of tasks, each of which can be designed to emphasize and quantify the particular symptom of interest. However, it is clear that identification of these features is a difficult and time consuming task and that automating this process using an evolutionary algorithm would be potentially beneficial. The application of an evolutionary algorithm to the problem of locating features within a patient’s velocity profiles is summarised in Fig. 16: (a) first the patient’s response is acquired in real-time from a digitising tablet, (b) the velocity profile is constructed from the stream of x–y co-ordinates, (c) the velocity profile is smoothed to remove noise and other unwanted artefacts, (d) the gradients of the lines within the velocity profile are sampled and represented as an encoded stream of numbers, and (e) this data is presented to the inputs of an implicit context representation Cartesian genetic program. The fitness function for the genetic program is based on the desire to identify some artefact in the patient responses, but not in age-matched controls. The presence of the artefact is determined by a value returned by the output component of each individual network as being greater than 3; a value less or equal to 3 indicating the non-presence of the artefact. (The number 3 is the middle of the range of values possible at the output component.) The fitness score comprises two parts: each dependent on whether a patient or age-matched control is being tested. For a Parkinson’s patient response, the fitness score is the number of artefacts detected; conversely, in an age-matched controls response, the inverse is the case. To achieve the aim of identifying a symptom of Parkinson’s disease it is only necessary to detect one such artefact in a patient response. However, it is equally essential that no such artefacts are found in the age-matched controls. For this reason the fitness function used to evolve the network is weighted heavily in favour of non-detection of artefacts in the age-matched control responses.
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Fig. 14. Example velocity profile of patient’s response before and after smoothing.
This is achieved by using an exponential function to bias the fitness scores accordingly. Responses from eight patients with idiopathic PD were assessed as well as eight controls who did not have PD or other neurolog-
ical disorders, including stroke. Participants were enrolled from a PD specialist clinic and Day Hospital, after giving an informed consent approved by Liverpool Research Ethics Committee. The patient and age-matched control responses were arbitrarily split in to a training set and a testing set of approximately equal sizes. The chromosome representing the network with the highest fitness was saved and used in the testing phase. Specifically, the evolved network was used to discriminate between patient responses and control responses which were not included in the evolution stage.Parameters for the evolution of the network are shown in Table 1. The results are shown in Fig. 17. For each response the number of occurrences of the artefact identified by the evolved network is shown. Ideally, no artefacts should be present in the age-matched control responses and at least one occurrence of the artefact should be present in every patient response. As can be seen, artefacts have been located in every response, but importantly, more have been located in most patient responses than in the age-matched controls. 5.3. Application of Immune Network Inspired Evolutionary Algorithm to the Diagnosis of Parkinson’s Disease The identification of artefacts within Parkinson’s patient’s response to figure copying tasks is effectively a shape matching exercise, locating a region of interest within the velocity profile that may be associated with symptoms of the disease. The velocity
Table 1 Parameters for evolution of implicit context representation CGP network
Fig. 15. Example of two-part velocity feature investigated as evidence of bradykinesia.
Parameter
Setting
Number of binding sites per component Number of functions Number of inputs Number of columns Number of rows Mutation rate (%) Number of generations Number of individuals
2 5 10 3 10 3 1500 5
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Fig. 16. The application of an evolutionary algorithm to the problem of locating features within a patient’s velocity profiles: (a) the patient’s response is acquired in real-time from a digitising tablet, (b) the velocity profile is constructed from the stream of x-y co-ordinates, (c) the velocity profile is smoothed to remove noise and other unwanted artefacts, (d) the gradients of the lines within the velocity profile are sampled and represented as an encoded stream of numbers, and (e) the data is presented to the inputs of an implicit context representation Cartesian genetic program.
Fig. 17. The results for implicit context representation CGP for Parkinson’s patients and controls.
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Fig. 18. Modified B-cell model with one input and three outputs.
profile is searched a section at a time using a windowing operation, the elements of which are passed to the inputs of the genetic program, that then processes the values according to a network of functions. It can be hypothesised that the region of interest in the velocity profile may be located directly using a suitable shape-matching algorithm. However, it is also acknowledged that an absolute shape match is unlikely to be suitable for locating similar regions of interest in other areas of the profile or indeed other Parkinson’s patients’ profiles, due to the natural variation in motor actions. An adaptive form of shape matching is required that will detect areas of interest that are considered not normal. An analogy is the simple immune concept of self or nonself which can be applied to normal or abnormal sections of the velocity profile. The artificial immune network was developed, based on the immune network theory as described in Section 4 for use in identifying regions of interest within the velocity profiles described above. A modified version of the B-cell model, featuring once receptor and three idiotopes is shown in Fig. 18. The single receptor simplifies the search for a single region of interest within the velocity profile and three idiotopes replicate the original data bound to and variations of it to enable further similar B-cell receptors to bind
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to the same region of interest reinforcing its significance. Unlike the components in implicit context representation CGP, the B-cell performs no function other than to replicate the shape bound to and present two close approximations, based on the first and second standard deviations. It is now a simple matter for a B-cell model to be randomly initiated and bound to the section of the velocity profile that represent the smallest error in match as depicted in Fig. 19. A pool of randomly initiated B-cells can now be applied to a velocity profile and will bind to the closest matching shape within the data or idiotopes of other B-cells as shown in Fig. 20. An evolutionary algorithm can now be constructed using the B-cell model comprising a training and test phase. The aim of this exercise is to evolve B-cells that will bind strongly to areas of interest in Parkinson’s disease patients’ velocity profiles but weakly (or preferably not at all) to velocity profiles generated by controls with no know neurological disorder. The same training set of velocity profiles from known Parkinson’s patients and controls exhibiting no known disorder was used as for the implicit context representation CGP described in Section 5.2. For each velocity profile in the Parkinson’s set of responses, a separately allocated pool or population of randomly initialised B-cell elements is applied as shown in Fig. 21. Each B-cell from the pool is bound to a section of the velocity profile (or the idiotope of a previously bound B-cell) if its closeness of match is within a predetermined threshold, otherwise the B-cell is reinitialised and reapplied. Once all B-cells are bound to the velocity profile, the fitness of each B-cell in the pool is calculated in the following way: • The B-cell is applied to each Parkinson’s patient and control velocity profile in the training set and the best match in each case is calculated. • The average difference value is calculated for the Parkinson’s patient and control velocity profiles and the difference used as an overall fitness score. This fitness measure is designed to encourage strong binding with Parkinson patients velocity profiles but weak binding with
Fig. 19. B-cell model binds to patient’s response data at the point of closest match and presents the bound shape and variations to its outputs.
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Fig. 20. An individual comprises a pool of B-cells which identify patterns of interest within the patient’s response data.
Fig. 21. B-cells from each individual are associated with a separate Parkinson’s patient responses in the training set.
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Fig. 22. The results for immune network inspired evolutionary algorithm for Parkinson’s patients and controls.
control velocity profiles. The B-cells for each pool are then ranked according to their fitness and the following action taken: • The fittest B-cell is preserved for the next generation. • A fraction (typically 50%) of the fittest B-cells undergo mutation according to a predefined probability. • The remaining B-cells are replaced by clones of the fittest B-cell and then mutated. All B-cells are then reapplied to the assigned velocity profile as the next generation of the evolution process. The process is repeated for a predefined number of generations. The test phase is comparatively straightforward. The fittest Bcell from each training set pool is applied to each velocity profile in the test set. The resulting fitness scores for each velocity profile are averaged and those with an average score above a predefined threshold, indicating a strong binding with B-cells, are classified as exhibiting Parkinsonian traits whilst those below the threshold are classified as not exhibiting Parkinsonian traits. Parameters for the evolution of the B-cells are shown in Table 2. The results of applying the fittest B-cells from the evolution stage are shown in Fig. 22. In the majority of cases the B-cell binding is stronger for Parkinson’s patients than it is for controls. It is also arguable that the separation between the two is clearer than it is
Table 2 Parameters for evolution of implicit context representation CGP network Parameter
Setting
Number of idiotopes per B-cell Number of receptors per B-cell Number of B-cells per individual Number of elements in idiotopes and receptors Max value of elements Mutation rate (%) Number of generations Number of individuals
3 1 8 4 64 3 300 12
for the implicit context representation CGP performance shown in Fig. 17. 6. Conclusion This paper has described how protein/substrate bonding in metabolic pathways and immune systems has inspired two evolutionary algorithms. The first is an extension to genetic programming termed, enzyme genetic programming, which the authors have subsequently applied to Cartesian genetic programming (CGP) and named implicit context representation CGP. The second algorithm is inspired by the immune system and, specifically, immune networks. A previous application of implicit context representation CGP to this same problem demonstrated some success, but highlighted the importance of identifying discriminating artefacts the patient’s data based on its shape which can be considered a model of protein/substrate binding. The novelty of the immune network inspired algorithm is the manner in which artificial Bcells use the model of protein/substrate binding to interact directly with the data representing the Parkinson’s patient’s response to a conventional figure copying task. The B-cells can also bind to idiotopes of other B-cells that have already bound to the data, realising the immune network theory and reinforcing the importance of certain sections of patient data. B-cells that are successful in locating artefacts in patient data that discriminate them as being Parkinsonian symptoms are preserved and evolved in a training phase that subsequently can be used to classify other patients of unspecified as either exhibiting Parkinson’s symptoms or not. The results for the immune network inspired algorithm are comparable, if not better than the implicit context CGP implementation and demonstrate that evolution of the B-cells to discriminate between Parkinson’s patients and controls has been achieved. There is potential benefit in the new technique for location patterns of interest in a primitive way which both represents that problem at a low level and can be potentially more efficient in its execution.
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References Cai, X., Smith, S.L., Tyrrell, A.M., 2006. Positional independence and recombination in cartesian genetic programming. In: Proceedings of Nineth European Conference on Genetic Programming (EuroGP 2006), vol. 3905 of LNCS. Springer, pp. 351–360. Cutello, V., Nicosia, G., 2004. The clonal selection principle for in silico and in vitro computing. In: de Castro, L.N., von Zuben, F.J. (Eds.), Recent Developments in Biologically Inspired Computing. Idea Group Publishing, Hershey, PA, USA, pp. 104–145. de Castro, L.N., Timmis, J., 2002. Artificial Immune Systems: A New Computational Intelligence Approach. Springer. de Castro, L.N., Von Zuben, F.J., 2001. aiNet: an artificial immune network for data analysis. In: Data Mining: A Heuristic Approach. Idea Group Publishing, Hershey, PA, USA, pp. 231–259 (chapter 12). Farmer, J.D.N., Packard, H., Perelson, A.S., 1986. The immune system, adaptation, and machine learning. Physica D 22, 187–204. Forrest, S., Perelson, A.S., Allen, L., Cherukuri, R., 1994. Self–nonself discrimination in a computer. In: Proceedings of IEEE Symposium on Research in Security and Privacy. IEEE Computer Society Press. Garrett, S.M., 2004. Parameter-free clonal selection. In: Proceedings of Congress on Evolutionary Computation 2004 (CEC2004), vol. 1, pp. 1052– 1058. Jerne, N.K., 1974. Towards a network theory of the immune system. Ann. Immunol. (Inst. Pasteur) 125C, 373–389.
Koza, J., 1992. Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press. Lones, M. A., 2003. Enzyme genetic programming: modelling biological evolvability in genetic programming. PhD Thesis. University of York, UK. Lones, M.A., Tyrrell, A.M., 2001. Enzyme genetic programming. In: Kim, J.-H., Zhang, B.-T., Fogel, G., Kuscu, I. (Eds.), Proceedings of the 2001 Congress on Evolutionary Computation, vol. 2. IEEE Press, pp. 1183–1190. Miller, J., Thomson, P., 2000. Cartesian genetic programming. In: Poli, R., Banzhaf, W., Langdon, W.B., Miller, J.F., Nordin, P., Fogarty, T.C. (Eds.), Third European Conference on Genetic Programming, vol. 1802 of Lecture Notes in Computer Science. Springer, pp. 121–132. Miller, J., Job, D., Vassilev, V., 2000. Principles in the evolutionary design of digital circuits–part I. Genet. Progr. Evol. Mach. 1, 7–36. Neal, M., 2003. Meta-stable memory in an artificial immune network. In: Proceedings of the Second International Conference on Artificial Immune Systems (ICARIS), vol. 2728 of LNCS. Springer, pp. 168–180. Perelson, A.S., 1989. Immune network theory. Immunol. Rev. 110, 5–36. Playfer, J.R., 1997. Parkinson’s disease. Postgrad. Med. J. 73 (859), 257–264. Smith, S.L., Gaughan, P., Halliday, D.H., Ju, Q., Aly, N.A., Playfer, J.R., 2007. Diagnosis of Parkinson’s disease using evolutionary algorithms. Genet. Progr. Evol. Mach. 8 (4), 433–447. Stibor, T., Timmis, J., Eckert, C., 2005. A comparative study of real-valued negative selection to statistical anomaly detection techniques. In: Proceedings of the Fourth International Conference on Artificial Immune Systems (ICARIS), vol. 3627 of LNCS. Springer, pp. 262–275.
Contents lists available at ScienceDirect
BioSystems journal homepage: www.elsevier.com/locate/biosystems
An immune network inspired evolutionary algorithm for the diagnosis of Parkinson’s disease Stephen L. Smith a,∗ , Jon Timmis a,b a b
Department of Electronics, University of York, Heslington, York YO10 5DD, UK Department of Computer Science, University of York, Heslington, York YO10 5DD, UK
a r t i c l e
i n f o
Article history: Received 13 July 2007 Received in revised form 8 November 2007 Accepted 23 May 2008 Keywords: Evolutionary algorithms Artificial immune systems Immune networks Parkinson’s disease
a b s t r a c t This paper presents a novel evolutionary algorithm inspired by protein/substrate binding exploited in enzyme genetic programming (EGP) and artificial immune networks. The immune network-inspired evolutionary algorithm has been developed in direct response to an application in clinical neurology, the diagnosis of Parkinson’s disease. The inspiration for, and implementation of the algorithm is described and its performance to the application area considered. © 2008 Elsevier Ireland Ltd. All rights reserved.
1. Introduction Proteins are organic compounds which play a central role in living organisms. They are directly involved in a number of key activities in animals including their mechanical structure, motor function, transportation of molecules, control of chemical reactions and the immune system. The mechanisms through which proteins achieve this wide range of functions are both diverse and complex, but have led to a rich source of inspiration for natural computing. This paper describes a novel evolutionary system inspired by protein/substrate binding as exploited in two existing evolutionary paradigms, enzyme genetic programming (EGP) (specifically an implicit context representation of Cartesian genetic programming (CGP)) and the molecular interactions between paratopes and idiotopes on B cell receptors in the immune system. The novel evolutionary system was developed in direct response to an application in the diagnosis of Parkinson’s disease (PD). One symptom of the disease is a slowing of movement, known as bradykinesia. The analysis of data resulting from testing patients for this symptom is particularly challenging to solve by conventional means. In this paper we detail a promising approach to the application of this problem. We have augmented the enzyme genetic programming approach with a simple model inspired by
∗ Corresponding author. E-mail addresses: [email protected] (S.L. Smith), [email protected] (J. Timmis). 0303-2647/$ – see front matter © 2008 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.biosystems.2008.05.024
the interactions of regions on immune B-cell receptors: specifically, between paratopes and idiotopes. This paratope–idiotope interaction has allowed for the development of a novel interaction mechanism for effective identification of patterns in the data set employed, something that to date has proved difficult to obtain. Section 2 provides a description of genetic programming and specifically, enzyme genetic programming, illustrating its basis on protein/substrate binding and the metabolic pathway. An application of the implicit context representation to Cartesian genetic programming is then considered and how it has previously been used in the diagnosis of Parkinson’s disease. Section 3 then provides background material from immunology that has served as inspiration for the development of the immune network aspect of our system. Section 4 then details the implementation of the immune network inspired evolutionary system and in Section 5, how it may be applied to the diagnosis of Parkinson’s disease. Finally, in Section 6, the work presented is summarised and conclusions drawn. 2. Genetic Programming Genetic Programming (GP) (Koza, 1992) is an evolutionary algorithm in which the chromosome representation is based on a parse tree structure as shown in Fig. 1. The nodes are functions which act on the values presented at the inputs and provide the answer to the output. Terminals can either be input variables or constants. A population of individual genetic programs is then subject to an evolutionary strategy employing selection, mutation and recombination (crossover) schemes.
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Fig. 1. Example genetic program individual which evaluates to: OUT = (y/x) + (y × 1).
2.1. Enzyme Genetic Programming Lones and Tyrrell (2001) have developed a form of the conventional parse tree type genetic program called enzyme genetic programming. The biological inspiration for Enzyme GP is the metabolic pathway, and the role of enzymes which express computational characteristics. The representation named implicit context representation employs an enzyme model comprising a shape, activity and specificities (or binding sites) (Lones, 2003), as shown in Fig. 2. Along with inputs and outputs, the enzyme model can be considered a program component from which a genetic program may be constructed. The shape describes how the enzyme is seen by other program components. Similarly, the binding sites determine the shape (and hence type) of program component the enzyme
Fig. 2. Enzyme model illustrating shape, activity and specificities (binding sites) (Lones, 2003).
wishes to bind to. Finally, the activity determines the logical function the enzyme is to perform. A typical EGP will comprise a set number of inputs and outputs and a number of enzyme models or components. Values for each component’s binding sites and logical function are initialized non-deterministically; the component’s shape, however, is derived from a combination of its binding sites’ shapes and logical function as shown in Fig. 3. In this example the
Fig. 3. Calculation of a component’s shape from its binding site shapes and logical function (Lones, 2003).
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conventional GP parse tree is formed through binding of sub-trees whose shapes match the binding site shapes of the AND component. Consequently, the shape of the AND component now represents the functionality of the whole tree below it. Once initialized, components are bound together to form a network. The order in which components are bound is determined by the closeness of match between one component’s binding site and another component’s shape. The best matching components are bound first and the process is repeated until a network has formed in which no further binding is possible. Over time, components may evolve through mutation, which is applied to the component’s binding sites and logical function with a pre-determined probability. When this occurs, a new component shape is derived accordingly and may lead to different binding between components occurring. This in turn may result in a modified network. 2.2. Cartesian Genetic Programming Cartesian genetic programming (Miller and Thomson, 2000; Miller et al., 2000) is a form of Genetic Programming (GP) in which components are arranged in a directed graph, in contrast to conventional GP, which is based on a parse tree structure. CGP exhibits a number of benefits over traditional GP, the best known of which is avoidance of bloat, an uncontrolled expansion of the program during evolution. However, CGP does not exhibit positional independence. The effect or meaning of a component in the evolved or resulting program is determined by its absolute or relative position in the program representation. The manner in which components are referenced in CGP is considered arbitrary as there is no correlation between a component’s absolute coordinates and its behaviour. Therefore, it can be argued that indirect context representation has no effect beyond describing the connectivity of a specific program. This is also the case when considering the behaviour of components in different programs. Components with the same functionality may have different coordinates and those with different functionality the same coordinates. This section reviews the implementation of an implicit context representation of CGP which it is argued overcomes many of the disadvantages described above.
Fig. 4. Implicit context representation. CGP component showing multidimensional shape and binding sites (Cai et al., 2006).
The component’s shape is derived from a combination of the component’s binding sites’ shapes and the component’s function index (using a value of 255 in the relevant dimension) as shown in Fig. 5. Formation of a component’s shape in this way not only describes the logical function of the component itself, but also those components which the binding sites have a desire to bind to. In this way, a shape gives a summary of the functionality of the desired network to be formed from this point onwards.
The processing elements within the CGP are particularly suited to the implicit context representation. However, instead of employing a parse tree arrangement, the existing CGP Cartesian arrangement is maintained. The following sections summarize work undertaken by the author in this implementation—further details can be found in Cai et al. (2006).
2.3.2. Network Formation Binding of components in the CGP network begins with the assignment of an output component that will ultimately provide the resulting value for the problem under consideration. The binding site of the output component is then made active and will bind to the component shape which exhibits the closest match. This is simply determined by summing the difference between each relative pair of dimensions within the vector for one component’s binding site and another component’s shape. The combination of component shape and binding site that exhibits the smallest difference can be considered to be the “best fit”. Once bound, a component’s binding sites will also become active and will bind in the same way to other components located in columns to the left. This continues until all components have been bound, arguably with suboptimal components. A simple example is provided in Fig. 6 (Cai et al., 2006). Once all possible binding has completed, a network description is generated which describes the network in the same manner as for conventional CGP and the fitness of the resulting network is calculated in the normal way. The above process is repeated for each individual in the population and selection criteria for the next generation may be applied as required. Evolution of the selected individual, is however, different to that undertaken in conventional CGP. The concept of mutating both the connections and function of a component is maintained, but in the implicit context representation this is performed by
2.3.1. Network Structure A predetermined number of functional components are generated to form the network. Each component has the same (predetermined) number of binding sites, a function and a shape. The binding sites facilitate binding to other components and hence provide input values to which the selected function is applied. All shapes share a common format and consist of a number of dimensions which represent the different inputs and functions available within the network. For example, a network that has three inputs and a choice of four functions will employ a shape with seven dimensions for each component. Each dimension within the shape contains an integer value between 0 and 255 that represents the strength of that input or function expressed by the component. This is illustrated in Fig. 4.
Fig. 5. Derivation of the component’s shape from the component’s function and binding sites’ shapes (Cai et al., 2006).
2.3. Implicit Context CGP
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Fig. 6. Component binding. (a) Components are arranged, unbound, in the desired Cartesian arrangement. (b) Starting at the Output component, binding sites are bound to the component’s shape with the “best fit”. (c) Binding sites for each component bound are then bound to further components on a “best-fit-first” basis. (d) When no further binding can take place, the network can be evaluated.
mutating the component’s binding sites and function in a nondeterministic manner. Once mutation has been completed, the component’s activity shape needs to be recalculated to represent any changes that have subsequently occurred. A new network can then be formed by rebinding components; again on a “best fit first” basis as previously described. 3. Artificial Immune Systems Artificial immune systems (AIS) have been defined by de Castro and Timmis (2002) as: “adaptive systems inspired by theoretical immunology and observed immune functions, principles and models, which are applied to problem solving.” They are one of many types of algorithms inspired by biological systems, including evolutionary algorithms, swarm intelligence and neural networks. Within AIS, there are many different types of algorithm, and research to date has focussed primarily on the theories of immune networks (de Castro and Von Zuben, 2001; Neal, 2003), clonal selection (Cutello and Nicosia, 2004; Garrett, 2004) and negative selection (Forrest et al., 1994; Stibor et al., 2005). These theories have been abstracted into various algorithms and applied to a wide variety of application areas such as anomaly detection, learning and robotics.
3.1. Vertebrate Immune System The vertebrate immune system is composed of diverse sets of cells and molecules. Traditionally, the immune system is considered to play the role of defence, and protect our bodies from infectious agents such as viruses, bacteria, fungi and other parasites. On the surface of these agents are antigens that allow the identification of the invading agents (pathogens) by the immune cells and molecules, thus provoking an immune response. There are two basic types of immunity, innate and adaptive. Innate immunity is not directed towards specific invaders, but against general pathogens that enter the body. Adaptive or acquired immunity, allows the immune system to launch an attack against any invader that the innate system cannot remove. The adaptive system is directed against specific invaders and is modified by exposure to such invaders. The adaptive immune system mainly consists of lymphocytes, which are white blood cells, more specifically B and T-cells. These cells aid in the process of recognizing and destroying specific substances. Whereas all blood cells are generated in the bone marrow, Tcells migrate and mature in the thymus. To enable recognition of antigen patterns displayed by pathogens, both T-cells and B-cells present receptor molecules on their surfaces as shown in Fig. 7. The B-cell receptor is commonly known as an antibody.
Fig. 7. Lymphocytes and their surface receptor molecules. (a) B-cell receptor (BCR) or antibody. (b)T-cell receptor (TCR) (de Castro and Timmis, 2002).
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Fig. 10. Immune network theory. The recognition of antigen by an antibody leads to network activation, while the recognition of an idiotope by another antibody results in network suppression (de Castro and Timmis, 2002).
Fig. 8. Antibody molecule’s variable region, i.e. the portion of the molecule responsible for recognizing antigens (de Castro and Timmis, 2002).
Antibodies can recognise and bind with antigens in free solution; T-cell receptors can only recognise and bind with antigens presented by molecules of our own body known as major histocompatibility complexes (MHCs). Fig. 8 shows the variable region of antibodies that enable them to recognise antigens and Fig. 9 the binding of an antibody to an antigen. Once successfully identified by binding, a process of clonal selection and affinity maturation is initiated and the pathogen can be eliminated by the immune system. 3.2. Immune Networks In a landmark paper for the time Jerne (1974) proposed that the immune system is capable of achieving immunological memory, and thus subsequent recognition of pathogens at a later stage, by the existence of a mutually reinforcing network of B-cells. This network of B-cells occurs due to the ability of paratopes, located on B-cells, to match against idiotopes on other B-cells. The binding between idiotopes and paratopes has the effect of stimulating the Bcells. This is because the paratopes on B-cells react to the idiotopes on similar B-cells, as it would an antigen. However, to counter the reaction, there is a certain amount of suppression between B-cells, thus giving rise to a regulatory mechanism. This interaction of Bcells contributes to form a memory structure, and was proposed to account for the retainment of memory cells, even in the absence of antigen. This theory was refined and formalised in successive
Fig. 9. Recognition of an antigen by a B-cell receptor (de Castro and Timmis, 2002).
works by Farmer et al. (1986) and Perelson (1989). It is worth noting, however, that the immune network theory is not widely accepted within the immunological community, being very little experimental evidence to support it. However, from a computational point of view, and a view of bio-inspiration, the immune network is very attractive and indeed has served as inspiration for many immuneinspired algorithms (de Castro and Timmis, 2002; Neal, 2003; de Castro and Von Zuben, 2001) whilst this theory is interesting, there is little experimental evidence to suggest that it is true. According to the immune network theory, the antibody molecules contained in the surface of the immune cells present markers, named idiotopes, which can be recognised by antibodies on other immune cells. These idiotopes are displayed in and/or around the same portions of the receptors that recognise nonself antigens. Fig. 10 provides a simple illustration of the immune network theory. To explain the network theory, assume that an antibody, Ab1, on a B-cell recognises a nonself antigen, Ag. This same receptor, Ab1, is also recognised through its idiotope i2, by another antibody, Ab2 via its paratope. Ab1 is capable of recognising both Ag and Ab2. The recognition of idiotopes on an antibody by other antibody, leads to ever increasing sets of connected antibodies. However, the binding of an antibody by its idiotope may negatively affect its binding with its antigen Ab1, but the degree to which it does this is determined by its affinity for the antibody. Therefore, the recognition of antigen by an antibody could be said to lead to “network activation”, while the recognition of an antibody by another antibody could be said to result in “network suppression”. 4. Immune Network Inspired Evolutionary Algorithm It is important to stress that the B-cell and T-cell receptors are proteins which are able to bind to antigens in a similar way to which enzymes bind to substrates. The motivation for this work is to employ a similar model to that used with success in Cartesian genetic programming with artificial immune systems and specifically, immune networks. The proposed model utilises similar network components used to represent enzymes, but with modifications, can now represent B-cell receptors and idiotopes as shown in Fig. 11. The function employed will be one which reflects the biological relationship between the receptors and idiotopes. Fig. 12 illustrates how this model of the B-cell is free to bind with antigens or other B-cells and behave in a similar way to in the human body and a number of B-cells would populate the system with initially random B-cell receptors and idiotopes. Over time each B-cell will encounter pathogens (or training data items) and other B-cells, effectively training in the environment, so that ultimately, the ability to differentiate between classes is achieved. Further, such
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Fig. 11. Model of B-cell featuring receptors and idiotopes.
a distributed model will enable B-cells to occupy different physical areas of space allowing the network to respond immediately in a local sense and over time a global view of the presence of pathogens. 5. Application of Evolutionary Algorithms to the Diagnosis of Parkinson’s Disease
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1 in every 500 people in the UK has PD. The risk of developing PD increases with age and due to the ageing population it is expected that the number of cases of PD will triple in the next 50 years. There are three cardinal motor features of PD: tremor, rigidity and bradykinesia. The symptoms usually start on one side of the body (hemiparkinsonism) but later spread to the other side. About 80% of patients suffer from idiopathic Parkinson disease for which no cause is known. However, the diagnosis of idiopathic PD is based on clinical features which can have poor sensitivity with about 25% of patients diagnosed with the disease actually having other conditions (Playfer, 1997). Considerable research has been conducted to improve the diagnosis of the condition, but most studies to date are reliant on laboratory-based experimentation. The authors are concerned with developing a non-invasive computer-based test that can be conducted in the clinical environment and the doctor’s surgery, using commonly available computing peripherals. Work to date by the authors on such a computer-based assessment using figure-copying tasks has generated promising results. However, it is clear the identification and quantification of the symptoms of Parkinson’s disease is a nontrivial problem that is highly dependent on many factors relating to the patient’s physical as well as medical condition.
5.1. Parkinson’s Disease
5.2. Previous EA Approaches for the Diagnosis of Parkinson’s Disease
Parkinson’s Disease is a common, chronic, progressive neurodegenerative brain disease, afflicting about 1 person in 1000, and about 1 person in 100 over the age of 60. The disease sets in insidiously, and in most patients progresses relentlessly, on average within 10 years, to a state of total physical incapacitation. PD is one of the most common late-life neurodegenerative disorders, which typically develops between 50 and 70 years of age. It is estimated that there are a total of four million people with PD worldwide and
Bradykinesia is the core disabling feature of Parkinson disease. It consists of difficulty, slowness (bradykinesia proper) or virtual inability (akinesia) in initiating and executing movements or modifying ongoing motor activity. Poverty of spontaneous movement (hypokinesia), loss of normal associated movements, masked facial expression and sudden freezing in the middle of a motor performance are all part of the disturbance. The aim of previous work by the authors has been to devise a computer-based system that is
Fig. 12. Artificial immune network showing B-cells binding with pathogens and other B-cells.
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Fig. 13. (a) Figure copying task using a conventional digitizing tablet. (b) Task shape to be copied.
capable of measuring these symptoms to aid diagnosis and inform administration of medication. The work described in this section is a review of that undertaken by the authors in computer-based assessment (Smith et al., 2007) and comprises two parts: data acquisition and data processing. Data acquisition stage is the digitization of the patient’s drawing in attempting a conventional figure-copying task, termed here, the task domain. Once the patient’s response has been acquired in digital form, data processing is applied to extract and quantify the symptoms of interest, in this case tremor and bradykinesia. The patient’s response to the task presented is a drawing activity that is digitized in real-time as a set of x–y co-ordinate pairs giving information about pen position. The figure required to be copied by the patient is placed on the digitizing tablet in printed form and covered with a sheet of tracing paper on which the patient traces a copy as shown in Fig. 13 (a). The geometric shape presented for the patient to copy in this study is a modified Archimedes spiral, replacing the smooth spiral with pentagon-like edges as shown in Fig. 13(b). The justification for making this modification is that by introducing a sequential aspect, the change from drawing one edge to another will provide a focus at which symptoms of bradykinesia may be observed. Although the term bradykinesia is defined as the slowness of a performed movement, it is commonly used synonymously with akinesia and hypokinesia, an expression of freezing and smaller
movements, respectively. To quantify these symptoms a measure of movement time and particularly, the movement velocity of the patient’s pen, is required. As the patient’s drawing activity is digitized in real-time and at regular intervals, it is possible to determine the velocity of the pen at any instant. This can be achieved by calculating the distance between two coordinate positions and dividing this by the difference of the relative timestamps. The representation of the velocity of the pen for the duration of the patient’s response to the task attempted, termed the velocity profile, an example is given in Fig. 14. As might be expected, the velocity profile can reflect the nature of the task, e.g. in this case an acceleration and deceleration can often be associated with each side of the spiral pentagon. The main thrust of data analysis to date has focused on the patient’s pen velocity at the end of one edge of the spiral-pentagon and the beginning of the next. It is here that evidence of a slowing and of hesitation, commonly recognized as bradykinesia, is sought that will differentiate a Parkinson’s patient from a normal control. Subjective examination of velocity profiles obtained from the 12 Parkinson’s patients and 10 controls was made with a view to identifying features that could be used as evidence of bradykinesia. One candidate for such a feature is a two-part artefact, which is illustrated in Fig. 15. The initial acceleration of the pen is described by the section of the velocity profile labelled “A”. After a period of remission, a second period of acceleration greater than that of “A” is observed (labelled “B”). A total of 10 occurrences of the twopart velocity feature were detected in the responses of five separate patients. The feature was only located in one of the age-matched control drawing responses. The feature described above is one example of the type of analysis that can be applied to digitized pen movements over a variety of tasks, each of which can be designed to emphasize and quantify the particular symptom of interest. However, it is clear that identification of these features is a difficult and time consuming task and that automating this process using an evolutionary algorithm would be potentially beneficial. The application of an evolutionary algorithm to the problem of locating features within a patient’s velocity profiles is summarised in Fig. 16: (a) first the patient’s response is acquired in real-time from a digitising tablet, (b) the velocity profile is constructed from the stream of x–y co-ordinates, (c) the velocity profile is smoothed to remove noise and other unwanted artefacts, (d) the gradients of the lines within the velocity profile are sampled and represented as an encoded stream of numbers, and (e) this data is presented to the inputs of an implicit context representation Cartesian genetic program. The fitness function for the genetic program is based on the desire to identify some artefact in the patient responses, but not in age-matched controls. The presence of the artefact is determined by a value returned by the output component of each individual network as being greater than 3; a value less or equal to 3 indicating the non-presence of the artefact. (The number 3 is the middle of the range of values possible at the output component.) The fitness score comprises two parts: each dependent on whether a patient or age-matched control is being tested. For a Parkinson’s patient response, the fitness score is the number of artefacts detected; conversely, in an age-matched controls response, the inverse is the case. To achieve the aim of identifying a symptom of Parkinson’s disease it is only necessary to detect one such artefact in a patient response. However, it is equally essential that no such artefacts are found in the age-matched controls. For this reason the fitness function used to evolve the network is weighted heavily in favour of non-detection of artefacts in the age-matched control responses.
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Fig. 14. Example velocity profile of patient’s response before and after smoothing.
This is achieved by using an exponential function to bias the fitness scores accordingly. Responses from eight patients with idiopathic PD were assessed as well as eight controls who did not have PD or other neurolog-
ical disorders, including stroke. Participants were enrolled from a PD specialist clinic and Day Hospital, after giving an informed consent approved by Liverpool Research Ethics Committee. The patient and age-matched control responses were arbitrarily split in to a training set and a testing set of approximately equal sizes. The chromosome representing the network with the highest fitness was saved and used in the testing phase. Specifically, the evolved network was used to discriminate between patient responses and control responses which were not included in the evolution stage.Parameters for the evolution of the network are shown in Table 1. The results are shown in Fig. 17. For each response the number of occurrences of the artefact identified by the evolved network is shown. Ideally, no artefacts should be present in the age-matched control responses and at least one occurrence of the artefact should be present in every patient response. As can be seen, artefacts have been located in every response, but importantly, more have been located in most patient responses than in the age-matched controls. 5.3. Application of Immune Network Inspired Evolutionary Algorithm to the Diagnosis of Parkinson’s Disease The identification of artefacts within Parkinson’s patient’s response to figure copying tasks is effectively a shape matching exercise, locating a region of interest within the velocity profile that may be associated with symptoms of the disease. The velocity
Table 1 Parameters for evolution of implicit context representation CGP network
Fig. 15. Example of two-part velocity feature investigated as evidence of bradykinesia.
Parameter
Setting
Number of binding sites per component Number of functions Number of inputs Number of columns Number of rows Mutation rate (%) Number of generations Number of individuals
2 5 10 3 10 3 1500 5
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Fig. 16. The application of an evolutionary algorithm to the problem of locating features within a patient’s velocity profiles: (a) the patient’s response is acquired in real-time from a digitising tablet, (b) the velocity profile is constructed from the stream of x-y co-ordinates, (c) the velocity profile is smoothed to remove noise and other unwanted artefacts, (d) the gradients of the lines within the velocity profile are sampled and represented as an encoded stream of numbers, and (e) the data is presented to the inputs of an implicit context representation Cartesian genetic program.
Fig. 17. The results for implicit context representation CGP for Parkinson’s patients and controls.
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Fig. 18. Modified B-cell model with one input and three outputs.
profile is searched a section at a time using a windowing operation, the elements of which are passed to the inputs of the genetic program, that then processes the values according to a network of functions. It can be hypothesised that the region of interest in the velocity profile may be located directly using a suitable shape-matching algorithm. However, it is also acknowledged that an absolute shape match is unlikely to be suitable for locating similar regions of interest in other areas of the profile or indeed other Parkinson’s patients’ profiles, due to the natural variation in motor actions. An adaptive form of shape matching is required that will detect areas of interest that are considered not normal. An analogy is the simple immune concept of self or nonself which can be applied to normal or abnormal sections of the velocity profile. The artificial immune network was developed, based on the immune network theory as described in Section 4 for use in identifying regions of interest within the velocity profiles described above. A modified version of the B-cell model, featuring once receptor and three idiotopes is shown in Fig. 18. The single receptor simplifies the search for a single region of interest within the velocity profile and three idiotopes replicate the original data bound to and variations of it to enable further similar B-cell receptors to bind
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to the same region of interest reinforcing its significance. Unlike the components in implicit context representation CGP, the B-cell performs no function other than to replicate the shape bound to and present two close approximations, based on the first and second standard deviations. It is now a simple matter for a B-cell model to be randomly initiated and bound to the section of the velocity profile that represent the smallest error in match as depicted in Fig. 19. A pool of randomly initiated B-cells can now be applied to a velocity profile and will bind to the closest matching shape within the data or idiotopes of other B-cells as shown in Fig. 20. An evolutionary algorithm can now be constructed using the B-cell model comprising a training and test phase. The aim of this exercise is to evolve B-cells that will bind strongly to areas of interest in Parkinson’s disease patients’ velocity profiles but weakly (or preferably not at all) to velocity profiles generated by controls with no know neurological disorder. The same training set of velocity profiles from known Parkinson’s patients and controls exhibiting no known disorder was used as for the implicit context representation CGP described in Section 5.2. For each velocity profile in the Parkinson’s set of responses, a separately allocated pool or population of randomly initialised B-cell elements is applied as shown in Fig. 21. Each B-cell from the pool is bound to a section of the velocity profile (or the idiotope of a previously bound B-cell) if its closeness of match is within a predetermined threshold, otherwise the B-cell is reinitialised and reapplied. Once all B-cells are bound to the velocity profile, the fitness of each B-cell in the pool is calculated in the following way: • The B-cell is applied to each Parkinson’s patient and control velocity profile in the training set and the best match in each case is calculated. • The average difference value is calculated for the Parkinson’s patient and control velocity profiles and the difference used as an overall fitness score. This fitness measure is designed to encourage strong binding with Parkinson patients velocity profiles but weak binding with
Fig. 19. B-cell model binds to patient’s response data at the point of closest match and presents the bound shape and variations to its outputs.
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Fig. 20. An individual comprises a pool of B-cells which identify patterns of interest within the patient’s response data.
Fig. 21. B-cells from each individual are associated with a separate Parkinson’s patient responses in the training set.
S.L. Smith, J. Timmis / BioSystems 94 (2008) 34–46
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Fig. 22. The results for immune network inspired evolutionary algorithm for Parkinson’s patients and controls.
control velocity profiles. The B-cells for each pool are then ranked according to their fitness and the following action taken: • The fittest B-cell is preserved for the next generation. • A fraction (typically 50%) of the fittest B-cells undergo mutation according to a predefined probability. • The remaining B-cells are replaced by clones of the fittest B-cell and then mutated. All B-cells are then reapplied to the assigned velocity profile as the next generation of the evolution process. The process is repeated for a predefined number of generations. The test phase is comparatively straightforward. The fittest Bcell from each training set pool is applied to each velocity profile in the test set. The resulting fitness scores for each velocity profile are averaged and those with an average score above a predefined threshold, indicating a strong binding with B-cells, are classified as exhibiting Parkinsonian traits whilst those below the threshold are classified as not exhibiting Parkinsonian traits. Parameters for the evolution of the B-cells are shown in Table 2. The results of applying the fittest B-cells from the evolution stage are shown in Fig. 22. In the majority of cases the B-cell binding is stronger for Parkinson’s patients than it is for controls. It is also arguable that the separation between the two is clearer than it is
Table 2 Parameters for evolution of implicit context representation CGP network Parameter
Setting
Number of idiotopes per B-cell Number of receptors per B-cell Number of B-cells per individual Number of elements in idiotopes and receptors Max value of elements Mutation rate (%) Number of generations Number of individuals
3 1 8 4 64 3 300 12
for the implicit context representation CGP performance shown in Fig. 17. 6. Conclusion This paper has described how protein/substrate bonding in metabolic pathways and immune systems has inspired two evolutionary algorithms. The first is an extension to genetic programming termed, enzyme genetic programming, which the authors have subsequently applied to Cartesian genetic programming (CGP) and named implicit context representation CGP. The second algorithm is inspired by the immune system and, specifically, immune networks. A previous application of implicit context representation CGP to this same problem demonstrated some success, but highlighted the importance of identifying discriminating artefacts the patient’s data based on its shape which can be considered a model of protein/substrate binding. The novelty of the immune network inspired algorithm is the manner in which artificial Bcells use the model of protein/substrate binding to interact directly with the data representing the Parkinson’s patient’s response to a conventional figure copying task. The B-cells can also bind to idiotopes of other B-cells that have already bound to the data, realising the immune network theory and reinforcing the importance of certain sections of patient data. B-cells that are successful in locating artefacts in patient data that discriminate them as being Parkinsonian symptoms are preserved and evolved in a training phase that subsequently can be used to classify other patients of unspecified as either exhibiting Parkinson’s symptoms or not. The results for the immune network inspired algorithm are comparable, if not better than the implicit context CGP implementation and demonstrate that evolution of the B-cells to discriminate between Parkinson’s patients and controls has been achieved. There is potential benefit in the new technique for location patterns of interest in a primitive way which both represents that problem at a low level and can be potentially more efficient in its execution.
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