The Process of Psychotherapy

We discuss deterministic interventions (Ch. 5) and stochastic influences (Ch. 6) against the background of four major groupings of therapy modalities (behavioral, psychodynamic, humanistic, systemic). A fellowship at the Freiburg Institute for Advanced Studies (FRIAS) sponsored and greatly facilitated much of the writing process.

The Goals of This Book

We will have to deal with stability phenomena when dealing with causal relationships in psychotherapy. In addition, algorithms were developed for approximating the coupling in the two-dimensional alliance system of client and therapist.

Why Use Mathematical Models and Mathematical

Our short answer here is the same as the first objection - we need to deal with quantities that translate semantics into scales based on operationalization conventions. Fourth, there is a tradition of mathematical models in psychology, such as the psychophysics of Gustav Theodor Fechner (1889) or the neo-behaviorist modeling of reinforcement by Clark Hull (1952).

Modeling the Dynamics of a System

A hallmark of many chaotic regimes is that they produce "strange" attractors with fractal properties - the dimension of such attractors is not a natural number. Autoregressive (AR) Models/Markov Models The time series of a variable x can be decomposed in the time domain by calculating the autocorrelation at each lag, ie. the time series is correlated with its copy, lagged by 1, 2, .

Measurement in Psychology

Due to the existence of an absolute zero (no movement corresponds to 0 pixel changes in MEA), the variable even has the properties of a ratio scale. Lower panel: time series of the number of pixel changes along the video and the time intervals of the two situations marked with rectangles.RoIregion of interest.

Fig. 1.3 Body movement measured by pixel changes in video recordings: an example of a ratio scale

Statistics

Since the wave prefers no position, the position of the "particle" is completely uncertain. As long as we maintain that the variables of psychology are macroscopic, the probability of the quantum world can be neglected.

Causation: Deterministic Processes and Goals

It is believed that the friction is so great that the sliding stone lands on the ride, instead of swinging endlessly. We can add a preliminary clarification here: we may occasionally appeal to mechanical interpretations for illustration, but still we harbor no physicalist intentions to reduce biological or psychological processes to mechanics.

Chance and Causation

1996). The Fokker–Planck equation: Methods of solutions and applications (Springer series in synergetics) (2nd ed.). However, we will leave these additional aspects aside and only consider here the main reason for undergoing psychotherapy – the remediation of psychopathological conditions.

Taxonomies of Psychopathology and Their Shortcomings

One problem associated with comorbidity is biological heterogeneity; Completely different biological mechanisms can converge in the same diagnosis. Their startle responses to the aversive stimuli were attenuated, which contrasted with the increase found in all other clients with the same diagnosis of an anxiety disorder.

Alternative Conceptualizations of Psychopathology

The Hierarchical Taxonomy of Psychopathology (HiTOP) is an example of a new classification approach (Kotov et al., 2017). In HiTOP, the hierarchy of psychopathology spans these levels: symptoms, components, syndromes/.

Fig. 2.1 Structure of the Research Domain Criteria (RDoC), exempli ﬁ ed by the domain “ social processes systems

Toward a Dynamical Quanti ﬁ cation of Psychopathological

This is the idealized situation of Fig. 1.5, where the rock (ie, the system) rests at the bottom of the valley. Some attractors, the so-called limit cycles, are characterized by regular oscillatory states - the attractor set in the state space is itself a process with periodic changes.

Fig. 2.4 Time course of psychotic symptoms in a patient with schizophrenia (patient 47 in Tschacher et al., 1997)

The Current Discussion in Psychotherapy Research

Activating the client's problem in the therapeutic setting - Activating the client's resources. Problems are not avoided but actualized in the session Desensitization The client experiences a progressive softening of his/her emotions.

Table 3.1 List of common factors with short de ﬁ nitions (adapted from Tschacher, Junghan, &

Therapist Effects

Therapist effects appear to be larger when clients are more severely disabled at the start of therapy, and the better therapists tend to see their clients for fewer sessions. In short, both resilience and mindfulness allow a therapist to preserve his or her own well-being, even in the face of adversity, that is, with difficult clients and subjects.

A Hierarchical Model of Therapeutic Factors

Common factors and techniques are accordingly placed at different levels in the hierarchical system of all psychotherapeutic variables that make up the therapy process. In the next chapter we continue by proposing a general mathematical model of change processes.

The Goal of This Chapter

The Gaussian

4.1 (a) Area A under the curveh(x) within an intervalΔ. b) Displacement of the curve to the right or to the left (not shown). Changing its width makes the Gaussian curve wider or narrower (not shown). Bwidth at half height, hheight.

Fig. 4.1 (a) Area A under the curve h(x) within an interval Δ . (b) Displacement of the curve to the right or to the left (not shown)

Deterministic Processes: Causation

The same logic applies to the probabilistic description of the change of a state variable of a system. This means that the probability distribution gets smaller and smaller over time, so the width of the distribution gets smaller.

Stochastic Processes: Chance

An individual may, over time, experience a random influence on his current state of affectivity. In equilibrium, the expansion due to stochastic influences is counteracted by the contraction due to the deterministic influence of an attractor, and the result is a Gaussian.

Figure 4.8b illustrates what happens to a ball (or a system state), which was initially located at x 0 (Fig

The Signi ﬁ cance of Fokker-Planck Modeling

This provides a new perspective on the statistical underpinnings of data that are often overlooked in psychological research. Dcontainsk which fixes the shape of the valley (Info-Box4.4) and quantifies the deterministic forces acting on the statex.

How Can We Measure the Fokker-Planck

To do this, we derive the time dependence of the mean, x tð Þ, from the time-dependent Fokker-Planck equation. All in all, we arrive at the following equation for the time-dependent average valuex tð Þ:. continued).

A Prototype of a Deterministic Technique for Behavior

Apart from stochastic influences, deterministic forces always have a certain direction, since they follow the gradient (i.e. slope) of the attractor. Extinction works by reducing the attractiveness of the symptomatic behavior – the parameter decreases (Figure 5.1b).

Fig. 5.1 The attractor of a system (system state symbolized by the red ball), (a) state of the system in its attractor basin prior to intervention, with high anxiety (x large ) and steep gradient (k large )

The Varying Prerequisites of Different Psychotherapy

The purpose of intervention is therefore to allow changes of kandx0 - but this is the client's (the system's) choice, which Fig. This means that the scenario of Fig.5.3 is again appropriate for many interventions in SPT - the majority of systemic deterministic interventions are contextual.

Discussion of Deterministic Interventions

An overview of relevant intervention types for therapy approaches will be provided in Fig. 6.3 and Table 6.1. One might think that the effectiveness of various deterministic interventions is an empirical matter, which can be easily resolved by psychological experiments and randomized controlled trials.

Psychotherapeutic Interventions into the Stochastic

However, the largest source of stochasticity is random input from a system's environment. Q is the parameter that describes the degree to which random events act on the system. We might think of Qas as a result of the system's limit regulation with respect to random events.

Regulating the Social Boundary of a System

Note that such an intervention is "directed" in the sense that we either decrease or increase on purpose, but at the same time it is non-specific and stochastic because we are dealing with the increase or decrease of random inputs, without knowing in which direction these inputs can ultimately drive the system. For example, in connection with the treatment of psychosis, an avoidance of social stimuli became widespread, e.g. in the Soteria approach (Ciompi & Hoffmann, 2004).

Fig. 6.1 Stochastic effects of social boundary regulation: (a) shows the probability distribution of x when the boundary is too permeable

Regulating the Stochasticity of Emotional Processing

We can note again that such restoration of boundaries in SPT has both a stochastic and a deterministic side: stochastic insofar as any uncontrolled stimulation is reduced and deterministic insofar as inappropriate information and thus harmful stress can be specifically reduced. We must again keep in mind that any weakening of emotional and motivational processes can also have deterministic consequences.

Regulating the Stochasticity of Cognitive Processing

Therefore, psychotherapeutic techniques of "paradoxical intention", sometimes also implemented in the context of trance inductions and therapeutic hypnosis, can have the effect of increasing Q. However, as we saw in the previous chapter, paradoxical interventions are also used in family therapy with the direct intention of destabilizing problem behavior only, thus as a specific deterministic technique.

The Functionality of Stochastic Interventions

This is of course part of the common wisdom - for example, convalescents benefit from a bathroom environment that regulates stimulation levels. In Section 9.3, we will elaborate on a type of time series analysis that specifies the stochasticity of a state variable.

Deterministic and Stochastic Interventions Versus

The standard errors of the (deterministic) slopes for each value of x can be illustrated by the function Q(x), shown in several figures throughout the chapter. The specific-nonspecific debate is not the same as our distinction between the deterministic and stochastic components of the Fokker-Planck model of therapeutic intervention.

Table 6.1 Overview of intervention types in psychotherapy, summing up the discussion of Chaps

Different Types of Psychopathological Problems

The current state of the client is represented by the red ball (BDI-II of about 40, severe symptomatology). V(x), psychopathological potential and potential minima are stable states, i.e. attractors. Both options are deterministic interventions, yet they have impacts at a different level of the client system.

Fig. 7.3 Attractor landscape of client with depression (same data as Fig. 7.1 but with random inputs added)

Stages of Psychotherapeutic Change: Stochastic,

Synergetics suggests that such secondary change can be achieved by addressing the control parameters (tolerances) of the client system. Stochastic interventions destroy pre-existing attractors by non-specific increase in diffusion, deterministic interventions affect the state of the system within an otherwise unchanged attractor landscape, while contextual interventions change the shape of basic attractors and thus secondarily also the state of the system.

Modeling Interventions of Psychotherapeutic Change

Infobox 7.1: Modeling the effect of an instantaneous deterministic input Let's look at deterministic interventions in the framework of the Fokker-Planck equation. However, the modified probability distribution of Figure 7.7b is only a temporary transformation of the probability distribution.

Fig. 7.7 Result of a momentary deterministic intervention into the state at x 0 . The probability distribution of behavior x (e.g., depression) becomes “ indented ” as a result

A “ Minimal Model ” of Therapeutic Intervention,

Equation (8.6) says that the client's condition depends on the client's long-term personality state and the impact of the therapeutic intervention. This means that the therapist strongly influences the mean value of the client's states (through his or her squared personality trait), but not the variance (Fig.8.1).

Fig. 8.1 Distribution of client ’ s states, following the therapeutic interaction with the therapist8.1A“Minimal Model”of Therapeutic Intervention, Assuming the Slaving Principle 99

The “ Minimal Model ” of Therapeutic Interventions

Leading and following are empirical findings common in the literature on interpersonal synchrony (e.g., Karvonen, Kykyri, Kaartinen, Penttonen, & Seikkula, 2016; Kupper, Ramseyer, 8.2 The “Minimal Model” of Therapeutic Interventions with. In other words , amust, negative, i.e., the client tends to resist the therapist's actions. bis positive, i.e., the therapist has an influence on the client's states.

Fig. 8.2 Oscillations of therapist ’ s and client ’ s state variables as a solution of the minimal model.

Empirical Studies on Synchrony and Social Coupling

We will consider the central metric of the minimal model, the phase shift as elaborated in Sect. We write the cross-correlation function (time lagL) of the client and therapist time series as.

Fig. 8.3 Cross-correlation function (CCF) of client and therapist movement behavior in psycho- psycho-therapy (adapted from Ramseyer & Tschacher, 2016)

Formulation of the Two-Dimensional Fokker-Planck

Moreover, we argued above that the therapist variable xdit is only weakly or not at all affected by xcl. We initially assumed that the therapist is well 'shielded' against fluctuations, so that we can set Qth ¼0.

Modeling Psychotherapy Process

The independent variables, i.e. the predictors in such regression modeling, are often process measures of psychotherapy courses, such as the various interventions described in Chapter 1. Can we estimate our preferred mathematical ansatz, the Fokker-Planck equation, from empirical time series data?

Estimating the Deterministic Term of the One-Dimensional

In the following, we therefore want to investigate how we can derive a system's attractor landscape from a time series of measurements of a state variable. In the example in Fig.9.2, we can choose the value x¼x1 and then search for realizations of the same value at later times in the time series.

Fig. 9.3 Slopes in the time series example shown in Fig. 9.2

Estimating the Stochastic Term of the One-Dimensional

This curve is exactly the function K(x) that describes the deterministic part of the Fokker-Planck equation. This will additionally provide an estimate of the stochastic term of the Fokker-Planck equation.

Estimating the Coupling of the Two-Dimensional

All correlations are converted to Fisher Z correlations and the Z mean of the two-dimensional time series is calculated. The CI of the entire time series is defined by the average of all segments, i.e. the CI.

Fig. 9.7 The result of SUSY is the effect size ES sy that expresses the degree to which the empirical cross-correlation function (Fig

Examples of Fokker-Planck Parameter Estimation

Example 1: Body Motion of Two People
Example 2: Respiration Time Series
Example 3: Simulated Autoregressive (Markov) Process
Example 4: Electrocardiograms (Two-Dimensional)
Example 5: Simulated Bimodal Autoregressive (Markov)
Example 6: Respiration (Two-Dimensional)

From K(x), we can directly reconstruct the attractor landscape V(x) of the dynamics that produced the time series (Figure 9.12, right). We recalculated the average slopes of the time series and approximated the function K(x) with splines.

Fig. 9.12 Respiration data: Left, K(x) yields the mean slopes of the time series shown in Fig

Fokker-Planck Terms of Two-Dimensional Time Series

Example 1*: Two Simultaneously Monitored Movement

Real and surrogate cross-correlations show a clear difference in that there is significant synchrony at a phase shift of +3 s and at 3 s. Figure 9.28 shows the potential functions of both the true cross-correlations and the surrogate cross-correlations.

Figure 9.28 illustrates that there is a clear deterministic signature in the cross- cross-correlations Z real , likely indicating two attractors, the stronger one at a correlation value of approximately 0.21, and a smaller attractor at 0.32

Example 4*: Two Simultaneously Monitored

The normalized value for Zreal was calculated by averaging all standard errors divided by the sampling rate, that is Qnorm¼21.4, and for theZsurr:Qnorm¼1.73. The normalized value for Zreal, calculated by averaging all standard errors divided by the sampling rate, is Qnorm¼10.67 and Qnorm¼4.83 for theZsurr.

Example 6*: Two Simultaneously Monitored Respiration

We estimated the functions K(x) that describe the deterministic part of the Fokker-Planck equation Zreal and Zsurr (Figure 9.30). The potential values of the real data are much lower than those of the surrogate data, proving that the dynamics in Figure 2 are deterministic.

Fig. 9.32 Respiratory coupling: Potential functions, i.e., deterministic signatures of the cross- cross-correlations of 50 min of therapy

Discussion of Time Series Estimation

In the case of cardiac time series (Example 4), the results suggested rejection of the hypothesis of coupled dynamics. We have shown that it is in principle possible to couple the empirical cross-correlations to phase shiftsϑ and oscillation periods ω, and from these calculate the coupling constants for the minimal model.

Focusing on Dynamics

Instead, we want to refine our understanding of the “true dynamics” of a therapist, a client, and their relationship. Unraveling the 'true dynamics' is the main goal of our causation-and-probability approach.

Focusing on Phenomena of Synchronization

As an initial step, a dynamic analysis of the individual case and its corresponding time series must therefore always be carried out. Yet movement synchrony is only one aspect of the embodiment of social interaction and is conceptually not very closely connected to the therapeutic relationship.

Focusing on the Archimedean Function of the Therapist

We think that the immovable pivot that allows change in psychotherapy appears in the personality of the therapist and the levers can be the therapeutic interventions. Therefore, the process of therapeutic change resulting from input (1) actually depends on the personality of the therapist, i.e., the variables of the therapist act as the "pivots" of the therapeutic intervention.

Focusing on Embodiment

The client may be "fast" initially in accordance with the assumption of the enslavement principle, however during treatment and perhaps toward the end of therapy, the client's relaxation time may also be increased in order to optimize the therapist using the location of the client's states. (the mean of the distribution according to Eq. 8.7 in Section 8.1), while the diffusion (variance of Eq. 8.7)) of the client states remains quite narrow due to the boundary arrangement. In other words, when there is some fluctuation, diffusion is small and thus customer appeal is well defined and clearly bounded.

Focusing on Free Energy

Our assertion that state variables should have high temporal resolution also points in this direction of recognizing the embodied aspects of psychotherapy: only motor-behavioral and physiological measures allow sampling rates of 1 Hz or higher. To explore the timescale of consciousness quantitatively, as we propose in this book, we must therefore focus on bodily variables.

Focusing on Affordances

The most optimal pattern is possibly the one that can reduce the affordance(s) acting on the system in the most efficient way. Paths in a steppe, or hiking trails in the mountains, develop in a self-organizing process based on affordability (unless, of course, the paths are externally dictated by paved roads or manufactured trails).

Fig. 10.1 Path evolution in grassy landscape — the erosion of the grass by vehicles shows which trajectories emerged in dealing with the affordances of landscape and terrain

Chances and Limitations

Our general predictions about the outcomes of contextual interventions are testable—the creation of new attractors, the depletion of implicated benefits—but time-series studies addressing contextual interventions are still lacking. Now we can localize regions of stability, i.e. attractors in potential landscapes and in synchronization patterns of individual psychotherapy courses.